/Quantum Computing In Finance – Where We Stand And Where We Could Go (via Qpute.com)

Quantum Computing In Finance – Where We Stand And Where We Could Go (via Qpute.com)

Quantum computers
(QCs) operate totally differently than classical computers. Due to the quantum
effects known as superposition and entanglement, quantum bits (called qubits) can
take on non-binary states represented by complex numbers. This facilitates
computational solutions to mathematical problems that cannot be solved by
classical computers because they require sequentially computing an astronomical
number of combinations or permutations. 

This ability of QCs
mean that they particularly excel at optimization problems, where the optimal
combination is only found after trying out an enormous number of possible
combinations. Several important problems in finance are in essence optimization
problems which meet this description. The portfolio-optimization problem in
finance is one good example of such a problem. Asset pricing, credit-scoring,
and Monte Carlo-type risk analysis are other examples. For example, it is
estimated that running a risk assessment of a large portfolio which needs to be
done overnight or can even take days with classical computers, could one day be
done in real-time by a full-scale QC. That explains the keen interest of the
finance industry in quantum solutions.

The calculating
power of a QC grows exponentially with the number of qubits. Quantum-computing
roadmaps cite the number of qubits or competing metrics to indicate the rising
power of these machines, with some setting thresholds for so-called quantum supremacy,
the point at which QCs will surpass classical supercomputers. But there are
still enormous technical challenges to solve before at-scale QCs can be
commercialized, most notably the challenges of stability and error correction.

However, quantum-inspired
software – which is software running on classical computers but based on novel
algorithms that reframe mathematical problems in terms of quantum principles –
is already here. Several quantum-inspired solutions are currently focused on
portfolio-optimization problems, and seem well positioned for their near-future
adoption by the financial asset-management industry.

Even the
limited-size, noisy QCs currently available lend themselves to
portfolio-optimization solutions. Early proofs-of-concept (POCs) of hybrid or
full quantum solutions to asset-portfolio optimizations such as stock selection
have already been demonstrated with encouraging results. Many of the largest
names in finance are already investing in quantum, or at least partnering with
technology providers to explore finance applications. Financial services
companies who wait too long to gain experience in the field run the risk of
getting left behind.

Quantum computing exploits quantum mechanics, the properties
and behavior of fundamental particles at the subatomic level, as predicted by
our best current understanding of quantum physics. The goal of quantum
computing is to build hardware and develop suitable algorithms that process
information in ways that are superior to so-called classical computers, i.e.
the ubiquitous digital computers that the Information Age was built on.

The essential elements of a QC were postulated in the early
1980s, but of late work in this area has accelerated with several large
established companies and start-ups building quantum-computing hardware. An
even larger ecosystem of software platforms and solution providers exist around
the hardware providers. Collaboration models such as alliances and partnerships
are common. Many universities are involved, while governments are also
supporting quantum-computing research.

Typical of a new industry, standards and metrics are still
in flux, and competing architectures, which leverage different mechanisms and
implementations of quantum principles, vie for technical supremacy and
investment dollars. Announcements of new breakthroughs are made almost daily,
which makes it important to distinguish the hype from real progress.

This paper attempts to demystify the technology, by
explaining the basic principles of quantum computing and the competing
technologies vying for quantum supremacy. An overview of the current quantum
computing industry and the main players is provided, as well as a look at the
first applications and the different industries that could benefit. The focus
then turns to the finance industry, with an overview of the most important
computational problems in finance that lends themselves to quantum computing,
with a deeper dive into portfolio optimization. Notable recent case studies and
their participants are reviewed. The paper concludes with an assessment of the
current state of quantum computing and the business impact that can be expected
in the short and medium term.

What we now call classical
(or conventional) digital computers perform all their
calculations in an aggregate of individual bits that are either 0 or 1 in
value, because they are implemented by transistors that are each either
switched completely on or off. This is called binary logic,
which is the essence of any digital computer, and implemented in a longstanding
computer-science paradigm originating with Turing and Von Neumann. Conventional
computers operate by switching billions of little transistors on and off, with
all state changes governed by the computer’s clock cycle. With n transistors,
there are 2n possible states for the computer to be in at any given
time. Importantly, the computer can only be in one of these states at a time. Digital computers are highly complex
with typical computer chips holding 20×1019 bits, yet incredibly
reliable at the semiconductor level with fewer than one error in 1024
operations. (Software and mechanical-related errors are far more common in

Analog computers
precede digital computers. In contrast to digital computers, classical analog
computers perform calculations with electrical parameters (voltage or current)
that take a full range of values along a continuous linear scale. Analog
computers do not necessarily need to be electrical – they can be mechanical
too, such as the first ones built by the ancient Greeks

– but the most sophisticated ones from the 20th century ones were
electrical. Unlike digital computers, analog computers do not need a clock cycle,
and all values change continuously. Before the digital revolution was enabled
through the mass integration of transistors on chips, analog computers were
used in several applications, for example, to calculate flight trajectories or
in early autopilot systems. But since the 1960s analog computers have largely
fallen into disuse due to the dominance of digital computers over the last few

Both classical digital and analog computers are at their
core electrical devices, in the sense that they perform logic operations that
are reflected by the electrical state of devices, typically semiconductor
devices such as transistors (or vacuum tubes for mid-20th century
analog computers), which comes about because of voltage differences and current
flow. Current flow is physically manifested in terms of the flow of electrons in an electrical

Quantum computers
on the other hand, directly exploit the strange and counterintuitive
behavior of sub-atomic particles (electrons, nuclei or photons) as predicted by
quantum theory to implement a new type of mathematics. In a QC, quantum bits
called qubits can be measured as
|0> or |1>, which are the quantum equivalents of the binary 0 and 1 in
classical computers. However, due to a quantum property called superposition, qubits can be non-binary
in a superposition state and interact with one another in that state during
processing. It is this special property that allows QCs to theoretically offer
exponentially more processing power than classical computers in some
applications. Once the processing is complete, the result can only be measured
in the binary states, |0> or |1>, because superpositioning is always
collapsed by the measurement process.

Because of another curious quantum property called entanglement, the behavior of two or
more quantum objects is correlated even if they are physically separated.
According to the laws of quantum mechanics, this pattern is consistent whether
a millimeter or kilometer or an astronomical distance separates them.

While one qubit is situated in a superposition between two basis states, 10
qubits utilizing entanglement, could be in a superposition of 1,024 basis

Unlike the linearity of classical computers, the calculating
power of a QC grows exponentially with the number of qubits. It is this ability
that gives QCs the extraordinary power of processing a huge number of possible
outcomes simultaneously. When in the unobserved state of superposition, n
qubits can contain the same amount of information as 2n classical
bits. So, four qubits are equivalent to 16 classical bits, which might not
sound like a big improvement. But 16 qubits are equivalent to 85,536 classical
bits, and 300 qubits can contain more states than all the atoms estimated to be
in the universe. That is not only an astronomical number; it is beyond
astronomical. This exponential effect is why there is so much hope for the
future of quantum computing. With single- or double-digit numbers of qubits,
the advantage over classical computing is not immediately clear, but the power
of quantum computing scales exponentially beyond that in ways that are truly
hard to imagine. This explains why there is so much anticipation about the
technology exploding once a certain number of qubits have been reached in a
reliable QC.

However, to reliably encode information and expect it to be
returned upon measurement, there are only two acceptable states for a qubit: 0
and 1.
This means a qubit can only store 1 bit of information at a time. Even with
many qubits, the scaling of information storage doesn’t improve beyond what
you’d get classically: ten qubits can store 10 bits of information and one
thousand qubits can store 1,000 bits. Because a qubit can only be measured in one of these two states,
qubits cannot store any more data than conventional computer bits. There is
thus no quantum advantage in data storage. The advantage is in information
processing, and that advantage comes from the special quantum properties of a
qubit –  that it can occupy a
superposition of states when not being measured.

Another point to keep in mind is that due to probabilistic
waveform properties of qubits, QCs do not typically deliver one answer, but
rather a narrow range of possible answers. Multiple runs of the same
calculation can further narrow the range, but at the expense of lessening speed

Classical computers will not be replaced by QCs. A primary
reason for this is that QCs cannot run the “if/then/else” logic functions that
are a cornerstone of the classical Von Neumann computer architecture. Instead
QCs will be used alongside classical computers to solve those problems that
they are particularly good at, such as optimization problems.

The strengths of QCs in simultaneous calculations mean that
they excel at finding optimal solutions to problems with a large number of
variables, where the optimal combination is only found after trying out an
enormous number of possible combinations or permutations. Such problems are
found, for example, in optimizing any portfolio composition, or trying out
millions of possible new molecular combinations for drugs, or in routing many
aircraft between many hubs. In such problems there are typically 2n
possibilities and they all have to be tried out to find an optimal solution. If
there are 100 elements to combine, it becomes a 2100 computation,
which is almost impossible to solve with a classical computer but a 100-qubit
computer could solve it in one operation.

Quite a few hard problems in finance are in essence
optimization problems and therefore meet the description of problems that can
be solved by QCs. The portfolio-optimization problem in finance is one good
example of such a problem. Asset pricing, credit-scoring, and Monte Carlo-type
risk analysis are other examples. That explains the keen interest of the
finance industry in quantum solutions. The finance industry is also well
positioned to be an early adopter, because financial algorithms are much
quicker to deploy than algorithms that drive industrial or other physical

A QC architecture can be seen as a stack with the following
typical layers:

At the bottom is the actual quantum hardware (usually held at near-absolute zero temperatures
to minimize thermal noise, and/or in a vacuum)

The next level up comprises the control systems that regulate the
quantum hardware and enable the calculation

Above those comes the software layer that implements the algorithms (and in future, also
will do the error correction). It includes a quantum-classical interface that
compiles source code into executable programs

The top of the stack comprises the wider variety
of services to utilize the QC, e.g. the operating
and software platforms
that help translate real-life problems into a format suitable for quantum

There are many different ways to physically realize qubits—
from using trapped calcium ions to superconducting structures.

In each case, quantum states are being manipulated to perform calculations.
Quantum computers can entangle qubits by passing them through quantum logic gates. For example, a
“CNOT” (conditional NOT) gate flips—or doesn’t flip—a qubit based on the state
of another qubit. Stringing multiple quantum logic gates together creates a quantum circuit.

The designers of QCs need to master and control both superposition and entanglement:

Without superposition, qubits would
behave like classical bits, and would not be in the multiple states that allow
quantum programmers to run the equivalent of many calculations at once. Without
entanglement, the qubits would sit in superposition without generating
additional insight by interacting. No calculation would take place because the
state of each qubit would remain independent from the others. The key to
creating business value from qubits is to manage superposition and entanglement

The simplest and most typical physical properties that can
serve as a qubit is the electron’s internal angular momentum, spin for short. It has the quantum
property of having only two possible projections on any coordinate axis, +1/2
or -1/2 in units of the Planck constant. For any chosen axis the two basic
quantum states of the electron’s spin can be denoted as ↑ (up) or ↓ (down). But
these are not the only states possible for a quantum bit, because the spin
state of an electron is described by a quantum-mechanical wave function. That
function includes two complex
numbers, called quantum amplitudes, α
and β, each with its own magnitude. The rules of quantum mechanics dictate that

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. Both α and β have real and imaginary
parts. The squared magnitudes α2 and β2 correspond to the
probabilities of the spin of the electron to be in the basic states ↑ or ↓ when
they are measured. Since those are the only two outcomes possible, their squared
magnitudes must equal 1. In contrast to a classical bit, which can only be in
one of its two binary states, a qubit can be in any continuum of possible
states, as defined by the quantum amplitudes α and β. In the popular press this
is often explained by the oversimplified, and somewhat mystical, statement that
a qubit can exist simultaneously in both its ↑ or ↓ states. That is analogous
to saying that a plane flying northwest is simultaneously flying both west and
north, which is not incorrect strictly speaking, but not a particularly helpful
mental model either.

Because a qubit can only be measured in one of these two states, qubits cannot store any more
data than conventional computer bits. There is thus no quantum advantage in
data storage. The advantage is in information processing, and that advantage
comes from the special quantum properties of a qubit meaning it can occupy a
superposition of states when not being measured. During computation, qubits can
interact with one another while in their superposition state. For example, a
set of 6 qubits can occupy any linear combination of all the 26 = 64
different length 6-bit strings. With 64 continuous variables describing this
state, the space of configurations available to a QC during a calculation is much
greater than a classical one. The measurement limitations of storing
information do not apply during the runtime execution of a quantum algorithm:
During processing every qubit in a quantum algorithm can occupy a
superposition. Thus, in a superposition state, every possible bit string (in
this example, 26 = 64 different strings)) can be combined. Each bit
string in the superposition has an independent complex number coefficient with
a magnitude (A) and a phase (θ):

αi      = Aiei

A modern digital computer, with billions of transistors in
its processors, typically has 64 bits, not 6 as in our quantum example above.
This allows it to consider 64 bits at once, which allows for 264
states. While 264 is a large number, equal to approximately 2 x 1019,
quantum computing can offer much more. The space
of continuous states of QCs is much larger than the space of classical bit
states. That is because the possibility of many particles interacting at the
quantum level to form a common wave function, allowing changes in one particle
to affect all others instantaneously and in a well-ordered manner. That is akin
to massive parallel computing, which can beat classical multicore systems.

Quantum computing operations can mostly be handled according
to the standard rules of linear algebra, in particular matrix multiplication. The quantum state is represented by a state vector

written in matrix form, and the gates in the quantum circuit (whereby the calculations are executed) are
represented as matrices too. Multiplying a state vector by a gate matrix yields
another state vector. Recent progress has been made to use quantum algorithms
to crack non-linear equations, by using techniques that disguise non-linear
systems as linear ones.

The possibility of quantum computing was raised by Caltech
physicist, Richard Feynman, in 1981. The person considered by most to be the
founder of quantum computing, David Deutsch, first defined a QC in a seminal
paper in 1985.[iii]

In 1994, a Bell Labs mathematician, Peter Shor, developed a
quantum computing algorithm that can efficiently decompose any integer number
into its prime factors.[iv]
It has since become known as the Shor
and has great significance for quantum computing. Shor’s
algorithm was a purely theoretical exercise at the time, but it anticipated
that a hypothetical QC could one day solve NP-hard problems of the type used as
the basis for modern cryptography. Shor’s algorithm relies on the special
properties of a quantum machine. While the most efficient classical factoring
algorithm, known as the general number field sieve, uses an exponential function of a constant x d1/3
to factor an integer with d digits; Shor’s algorithm can do that by
executing a runtime function that is only a polynomial
, namely a constant x d3. Accordingly, classical
computers are limited to factoring integers with only a few hundred digits,
which is why using integers in the thousands in cryptography keys is considered
to make for practically unbreakable codes. But a QC using the Kitaev version of
Shor’s algorithm only needs 10d qubits, and will have a runtime roughly equal
to d3.[v]

In summary, the Shor algorithm means that a QC can solve an
NP-hard mathematical problem in polynomial time that classical computers can
only solve in exponential time.
Therefore, Shor’s algorithm can demonstrate by how much quantum computing can
improve processing time over classical computing. While a full-scale QC with
the thousands of qubits needed to employ Shor’s algorithm in practice to crack
codes is not yet available, many players are working towards machines of that

Another important early QC algorithm is Grover’s algorithm, a search algorithm which finds a particular
register in an unordered database. This problem can be visualized as a
phonebook with N names arranged in completely random order. In order to find
someone’s phone number with a probability of ½, any classical algorithm
(whether deterministic or probabilistic) will need to look at a minimum of N/2
names. But the quantum algorithm needs only  QUOTE
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This algorithm can also be adapted for optimization problems.

Most quantum calculations are performed in what is called a quantum circuit. The quantum circuit is
a series of quantum gates that
operate on a system of qubits. Each quantum gate has inputs and outputs and
operates akin to the hardware logic gates in classical digital computers. Like
digital logic gates, the quantum gates are connected sequentially to implement
quantum algorithms.

Quantum algorithms
are algorithms that run on QCs, and which are structured to use the unique
properties of quantum mechanics, such as superposition or quantum entanglement,
to solve particular problem statements. Major quantum algorithms include the
quantum evolutionary algorithm (QEA), the quantum particle swarm optimization
algorithm (QPSO), the quantum annealing algorithm (QAA), the quantum neural
network (QNN), the quantum Bayesian network (QBN), the quantum wavelet
transform (QWT), and the quantum clustering algorithm (QC).[vii]
A comprehensive catalog of quantum algorithms can be found online in the Quantum Algorithm Zoo.[viii] 

Quantum software
is the umbrella term used to describe the full collection of QC instructions,
from hardware-related code, to compilers, to circuits, all algorithms and
workflow software.

Quantum annealing
is an alternative model to circuit-based algorithms, as it is not built up out
of gates. Quantum annealing naturally returns low-energy solutions by utilizing
a fundamental law of physics that any system will tend to seek its minimum
state. In the case of optimization problems, quantum annealing uses quantum
physics to find the minimum energy state of the problem, which equates to the
optimal or near-optimal combination of
its constituent elements

An Ising machine
is a non-circuit alternative that works for optimization problems specifically.
In the Ising model, the energy from interactions between the spins of every
pair of electrons in a collection of atoms is summed. Since the amount of energy
depends on whether spins are aligned or not, the total energy of the collection
depends on the direction in which each spin in the system points. The general
Ising optimization problem is determining in which state the spins should be so
that the total energy of the system is minimized. To use the Ising model for
optimization requires mapping parameters of the original optimization problem,
such as an optimal route for the Traveling
into a representative set of spins, and to define how the spins influence one

Hybrid computing
typically entails transferring the problem (say optimization) into a quantum
algorithm, of which the first iteration is run on a QC. This provides a very
fast answer, but only a rough assessment of the valid total solution space. The
refined answer is then found with a powerful classical computer, which only has
to examine a subset of the original solution space.[xi]

The Achilles heel of the QC is the loss of coherence, or decoherence, caused by mechanical
(vibration), thermal (temperature fluctuations), or electromagnetic disturbance
of the subatomic particles used as qubits. Until the technology improves,
various workarounds are needed. Commonly algorithms are designed to reduce the
number of gates in an attempt to finish execution before decoherence and other
sources of errors can corrupt the results.[xii]
This often entails a hybrid computing scheme which moves as much work as
possible from the QC to classical computers.

Current guestimates by experts are that truly useful QCs
would need to be between 1,000 and 100,000 qubits. However, quantum-computing
skeptics such as Mikhail Dyakonov, a noted quantum physicist, point out that
the enormous number of continuous parameters that would describe the state of a
useful QC might also be its Achilles heel. Taking the low end of a 1,000 qubits
machine, would imply a QC with 21,000 parameters describing its
state at any moment. That is roughly 10300, a number greater than
the number of subatomic particles in the universe: “A useful QC needs to
process a set of continuous parameters that is larger than the number of
subatomic particles in the observable universe.”[xiii]
How would error control be done for 10300 continuous parameters?
According to quantum-computing theorists the threshold theorem proves that it can be done. Their argument is
that once the error per qubit per quantum gate is below a certain threshold
value, indefinitely long quantum computation becomes possible, at a cost of
substantially increasing the number of qubits needed. The extra qubits are
needed to handle errors by forming logical qubits using multiple physical qubits.
(This is a bit like error correction in current telecom systems, which use
extra bits to validate data.) But that greatly increases the number of physical
qubits to handle, which as we have seen, are already more than astronomical. At
the very least, this brings into perspective the magnitude of the technological
problems that scientists and engineers will have to overcome.

To put the comparative size of the QC error-correction
problem in practical terms: For a typical 3-Volt CMOS logic circuit used in
classical digital computers, a binary 0 would be any voltage measured between
0V and 1V, while a binary 1 would be any voltage measured between 2V and 3V.
Thus when e.g. 0.5V of noise is added to the signal for binary 0, the
measurement would be 0.5V which would still correctly indicate a binary value
of 0. For this reason, digital computers are very robust to noise. However, for
a typical qubit, the difference in energy between a zero and a one is just 10-24
Joules—one ten-trillionth as much energy as an X-ray photon. Error correction
is one of the biggest hurdles to overcome in quantum computing, the concern
being that it will impose such a huge overhead, in terms of auxiliary
calculations, that it will make it very hard to scale QCs.

After Dyakonov published the skeptic’s viewpoint two years
ago, a vigorous debate followed.[xiv]
A typical response to the skeptic’s case comes from an industry-insider,
Richard Versluis, systems architect at QuTech, a Dutch QC collaboration.
Versluis acknowledges the engineering challenges to control a QC and to make
sure its state is not affected. However, he states that the challenge is to
make sure that the control signals and qubits perform as desired. Major sources
of potential errors are quantum rotations
that are not perfectly accurate, and decoherence
as qubits lose their entanglement and the information they contain. Versluis
goes on to define a five-layered QC architecture that he believes will be up to
the task. From top to bottom, the layers are 1. Application layer, 2. Classical
processing, 3. Digital processing, 4. Analog processing, and 5. Quantum
processing. Together the digital-, analog-, and quantum-processing layers
comprise the quantum processing unit (QPU). But Versluis also has to
acknowledge that quantum error correction could solve the fundamental problem
of decoherence only at the expense of 100 to 10,000 error-correcting physical
qubits per logical (calculating) qubit. Furthermore, each of these millions of
qubits will need to be controlled by continuous analog signals. And the biggest
challenge of all is doing the thousands of measurements per second in a way
that they do not disturb quantum information (which must remain unknown until
the end of the calculation), while catching and correcting errors. The current
paradigm of measuring all qubits with analog signals will not scale up to
larger machines, and a major advance in the technology will be required.[xv] 

Most experts agree that we will have to live with QCs over
the next few years that will have high levels of errors that go uncorrected.
There is even an accepted industry term and acronym for such QCs: NISQ (Noisy Intermediate-Scale Quantum)
devices. The NISQ era is expected to last for the next five years at least, bar
any major breakthroughs that might shorten that timeline.

Once critical technical breakthroughs are made, QC adoption
may happen faster than expected due to the prevalence of cloud computing.
Making QC services easily accessible over the cloud speeds both adoption and
learning. It has the added advantage that it forces hardware makers to focus on
building QCs with a high percentage of uptime, so as to ensure continued
availability over the cloud.

Most QC makers already offer cloud access to their latest
QCs. There are programming environments – software
development kits (SDKs)
that facilitate the building of quantum circuits –
available over the cloud for QC programmers to learn how to write the software
that unleashes the magic of quantum computing, and to experiment with it. As
more functionality is added to the hardware, these SDKs are continually updated.

The implication is that a whole ecosystem is being brought
up to speed on how to make the best use of a quantum capability that does not
quite exist yet. An analogy would be having had flight simulators to train
future pilots while the Wright brothers were still figuring out how to keep
their plane in the air for more than a few hundred feet. The upside of this
approach is that any real advances in making reliable QCs with capabilities
superior to classical computers will be very quickly exploited by real-world
applications. This situation is in contrast to most major technological
breakthroughs we have seen in the past. For example, it took a generation or
two for industrial engineers to learn how to properly use electrical power in
the place of steam power in factories. More recently, it took a generation to
fully exploit the capabilities of digital computing in business and elsewhere.
But in the case of quantum computing, all the knowledge building in
anticipation of a successful QC could be rapidly translated into applications
by a corps of developers who are all trained up and ready to “fly the plane”
once it is finally built. That is the optimistic perspective.

Quantum circuits are already being developed using quantum
programming languages and so-called quantum
development kits (QDKs)
such as Qiskit by IBM and Google Cirq based on Python; and Q# by Microsoft
based on the C# language.  The next step
is to develop libraries and workflows for different application domains.
Examples of the former are IBM’s Aqua and Q# libraries. Examples of the latter
are D-Wave’s Ocean development tool kit for hybrid quantum-classical
applications and to translate quantum optimization problems into quantum
circuits; or Zapata’s Orquestra to compose, run and analyze quantum workflows.
On top of the circuits and libraries come the domain-specific application
platforms. “Orchestrating and integrating classical and quantum workflows to
solve real problems with hybrid quantum-classical algorithms is the name of the
game for the next few years.”

Quantum-inspired software is already in operation, because
these applications run on classical computers and not on quantum machines. A
major example is Fujitsu Quantum-Inspired Digital Annealer Services.[xvii]
Even on a theoretical level, quantum ideas have already been fruitful in
several problem areas, where restructuring problems using quantum principles
have resulted in improved algorithms, proofs, and refuting erroneous old
Quantum-inspired software is closely related to quantum-ready software, which can be run on suitable QCs once they
are available.

The industrialization of QCs has entered a critical period.
Major countries and leading enterprises in the world are investing huge human
and material resources to advance research in quantum computing.

Google perhaps prematurely used the term quantum supremacy in October 2019 when
it announced the results of its “quantum supremacy experiment” in a blog[xix]
and an article in Nature.[xx]
The experiment used Google’s 54-qubit processor, named “Sycamore,” to perform a
contrived benchmark test in 200 seconds that would take the fastest
supercomputer 10,000 years to do. But at some point in the future, true quantum
supremacy may indeed be achieved.

Quantum supremacy
was originally defined by Caltech’s John Preskill[xxi]
as the point at which the capabilities of a QC exceed those of any available
classical computer; the latter is usually understood to be the most advanced
supercomputer built on classical architecture. At one point this was estimated
be when a QC with 50 or more qubits could be demonstrated. But some experts say
it depends more on how many logical operations (gates) can be implemented in a
system of qubits before their coherence decays, at which point errors
proliferate and further computation becomes impossible. How the qubits are
connected also matters.[xxii]

This led IBM-researchers to formulate the concept of quantum volume (QV) in 2017. More QV
means a more powerful computer, but QV cannot be increased by increasing only
the number of qubits. QV is a hardware-agnostic performance measurement for
gate-based QCs that considers a number of elements including the number of
qubits, connectivity of the qubits, gate fidelity, cross talk, and circuit
compiler efficiency. In late 2020, IonQ announced that it has calculated a QV
of 4 million for its 5th generation QC.  Before this announcement, Honeywell’s 7-qubit
ion-trap QC had the industry’s highest published quantum volume of 128, and IBM
had the next highest QV of 64 with its 27-qubit superconducting quantum
In early March 2021, Honeywell claimed to have regained the lead by achieving a
QV of 512 with an updated version of System Model H1 QC.[xxiv]
Alternating announcements like these from the major QC developers are likely to
continue for the time being, as each compete for the title of most powerful QC.

Rather than thinking about quantum supremacy as an absolute
threshold or milestone, it is wiser to think about so-called quantum supremacy
experiments as benchmarking experiments for the new technology, perhaps similar
to the way we came to express automobile engine power in measures of horse
power. There is also an intriguing question lingering over the whole concept of
quantum supremacy, which is: “How could anyone know… that a quantum computer is
genuinely doing something that is impossible for a classical one to do – rather
than that they just haven’t yet found a classical algorithm that is clever enough
to do the job?”[xxv]
It may be that the advent of quantum computing will force and inspire new
developments in classical computing algorithms, something we are already seeing
in the concept of quantum-inspired computing software, which will be discussed
further in a later section.

There is a difference between quantum advantage and quantum supremacy. Quantum supremacy is when
it can be demonstrated that a QC can do something that cannot be done on a
classical computer. Quantum advantage is that a quantum solution can provide a
real-world advantage over using the classical approach. (It does not imply that
a classical computer could not do it at all.)

There is a second meaning one could attach to quantum
supremacy, which is to mean which nation will hold the technological advantage
to this technology of the future. The current list of Top 500 (classical)
provides a good indication of where the hot spots of quantum computing will
likely be, since no country or region will want to cede a hard-gained advantage
in classical computing. Currently, 43 percent of supercomputers are in China,
23 percent in the United States, 7 percent in Japan, and about 19 percent in
Europe (including the United Kingdom but excluding Russia).

In the European Union, the European Commission founded the Quantum Flagship as a ten-year
coordinated research initiative which will have at least €1 billion in funding.
The long-term vision is the creation of a “Quantum Web,” defined as “quantum
computers, simulators and sensors interconnected via quantum networks
distributing information and quantum resources such as coherence and

The equivalent U.S. initiative is known as the National Quantum Initiative (NQI), and
the $1.2 billion of U.S. government funds are going to the National Institute
of Standards and Technology (NIST), National Science Foundation (NSF)
Multidisciplinary Centers for Quantum Research and Education and to the
Department of Energy Research and National Quantum Information Science Research
NIST partners with the University of Colorado Boulder on quantum computing
research through JILA’s Quantum Information Science&Technology (QIST).[xxix]
NIST, the Laboratory for Physical Sciences (LPS), and the University of Maryland
have formed the Joint Quantum Institute (JQI)[xxx]
to conduct fundamental quantum research. The Joint Center for Quantum
Information and Computer Science (QuICS)[xxxi]
was founded in another partnership between NIST and the University of Maryland
to specifically advance advances research QC science and quantum information

The Chinese government is investing upwards of $10bn in
quantum computing, an order of magnitude greater than the respective
investments of $1.2bn by the U.S. government and the E.U. The U.K. and Japanese
governments are each investing in the order of $300m, with Canada and South
Korea investing about $40m each.[xxxii]

China’s multi-billion quantum computing initiative aims to
achieve significant breakthroughs by 2030. President Xi has committed billions
to establish the Chinese National Laboratory for Quantum Information Sciences.

The implication of the difference in funding with China, is
that United States is mostly relying on private investments by its tech giants
to remain competitive. Time will tell if that is a wise strategy. It is not as
if large tech companies in China are not investing in quantum computing too –
Alibaba, Tencent, and Baidu are all known to be heavily investing in the
technology. According to some metrics, China has already gained an early advantage
by accumulating more quantum computing-related patents than the United States.[xxxiii]
In 2019 Google announced that its a QC performed a particular computation in
200 seconds that would take today’s fastest supercomputers 10,000 years. But in
December 2000, Chinese researchers at the University of Science and Technology
in China (USTC) claimed that their prototype QC (based on photons) is 10
billion times faster than Google’s.[xxxiv]

The Chinese desire to lead the world on quantum computing is
not purely motivated by a desire for industrial competitiveness and economic
power. Threat assessments[xxxv]
point to Chinese quantum research and experiments in defense applications such

Using entanglement for secure long-distance
military communications, e.g. between satellites and earth stations

Quantum radar that could nullify current U.S.
advantages in stealth technology against conventional radars

Quantum submarine detection to ranges of over
five kilometers that would limit the operations of U.S. nuclear submarines

Quantum computers are very hard to build. They require
intricate manipulations of subatomic particles, and operating in a vacuum
environment or at cryogenic temperatures.

The state of quantum computing resembles the early days of
the aircraft and automobile industries, when there was a similar proliferation
of diverse architectures and exotic designs. Eventually, as quantum technology
matures, a convergence can be expected similar to what we have seen in those
industries. In fact, the arrival of such a technological convergence would be a
good measure of a growing maturity of quantum computing technology.

There are a number of technical criteria[xxxvi]
for making a good QC:

Qubit must stay coherent for long enough to allow the computing to be completed in
the state of superposition. That requires isolation because decoherence occurs
when qubits interact with the outside world

Qubits must be highly connected. This occurs through entanglement and is needed for
operations to act on multiple qubits

are needed. As pointed out above, classical digital computers
rely on the digital nature of signals for noise resistance. However, since
qubits need to precisely represent numbers that are not just zero and one
during the computation state, digital noise reduction is not possible and the
noise problem is more analogous to that in an old-fashioned analog computer.
Since noise cannot be easily prevented and must therefore be mitigated, the
focus of current research is on noise-correction techniques

Gate operations must be fast. In practice, this is a trade-off between maintaining
coherence and high-fidelity

 It should be obvious
that QCs will only be useful when they can be scaled large enough to solve
valuable problems

Currently, the two quantum technologies showing the greatest
promise and attracting the most interest and investment dollars are superconducting qubits and trapped ions. These and other more
nascent or theoretical technologies are presented in Table 1, along with the
main proponents in each technology.



Table SEQ Table * ARABIC1. Qubit Technologies and Main


Main Proponents

Superconducting qubits (called transmons by some) are realized by using
a microwave signal to put a resistance-free current in a superposition state.
This technology has fast gate times and the advantage of more proven technologies
– superconducting circuits are based on well-known complementary metal-oxide
semiconductor technology (CMOS) used in digital computers. But
superconducting qubits have fast decoherence times and require more error
correction. Superconduction requires cooling to a temperature very close to
absolute zero. The technology is considered to be highly scalable.








Quantum Circuits

Oxford Quantum Circuits

Ion Trap QCs work by trapping ions
electric fields and holding them in place. The outermost electron orbiting
the nucleus is put in different states and used as a qubit. Ion Trap qubits
have longer coherence times and can operate with minor cooling, but do
require a high vacuum. Thought the first quantum logic gate was demonstrated
in 1995 using trapped atomic ions, at a system level this technology is less
mature and require progress in multiple domains including vacuum, laser, and
optical systems, radio frequency and microwave technology, and coherent
electronic controllers



Alpine Quantum Technologies


Photonic qubits are photons (light particles) that operate on silicon chip pathways.
Such qubits do no require extreme cooling, and silicon chip fabrication
techniques are well-established, making this technology highly scalable.



Neutral atoms are similar to Ion Traps but do not use ionized charges to keep the qubits
in place, but laser “tweezers” instead. The technology would share the
advantage of longer coherence times with Ion Traps but also the same
challenges to scaling up. The technology is considered unproven and highly

Atom Computing



Silicon qubits entails making ions by adding an electron to silicon. The electron’s
state is then controlled using microwaves. If proven this approach could
support longer coherence times than the superconducting approach. It has the
advantage of working with silicon and building on decades of semiconductor
industry experience. The technology is still nascent.


Silicon Quantum Computing

Topological qubits would operate
on different principles by utilizing exotic new quasiparticles such as
Majorana Fermions and Anyons. The hope is for long coherence times and higher
fidelity based on the theory. However, the existence of these particles has
not been experimentally confirmed, so this technology is not even nascent,
but purely theoretical.


Note: There is not yet a universally-accepted measure to
compare the computing power of the different technologies. That is because
obvious measures such as calculation cycles (qubit lifetime / gate operation
time) is skewed by the current infidelities of gate operations, and the varying
overheads imposed by error-correction schemes. For all gate-based technologies,
clock speeds will also be limited for the foreseeable future due to the need
for fault tolerance.[xxxvii]

The QC hardware covered above is of course only one layer of
the quantum-computing stack. Immediately above the hardware is the systems
layer, and on top of the systems layer are the software and applications
layers. At the very top is the systems layer, which is most commonly
cloud-enabled these days.[xxxviii]

Only a relatively small proportion of firms in the quantum
computing ecosystem actually build working QCs, since that requires major resources
and highly-specialized skills in quantum physics and hardware engineering. Many
of the companies that self-identify as quantum-computing companies are actually
on the software and services side.  It is
more common for providers of QC hardware to move upwards in the ecosystem by
adding software and services, than it is for software and services players to
attempt to move downward by developing their own quantum computing hardware.

Hardware makers typically enable access to their QCs over
the internet and through the cloud, often through subscription plans, sometimes
for free. The cloud-based offering is typically a hybrid quantum-classical computing system, which breaks up the
problem to be solved into parts that can be solved by conventional computers
and parts that are best solved by the QC. This situation resembles the early
days of classical computing when only a few computers were available, these
computers filled whole rooms, and they had to be shared among many users.

Below are short profiles of some of the major players in
quantum computing, divided between mainly hardware providers versus software
platform and solution providers.

Hardware and Systems

The major competitors in the QC hardware space each make
their own QCs with competing architectures and specifications. The most
significant of these general systems are made by the large companies IBM,
Google, and Honeywell, and the start-ups Rigetti, and IonQ. D-Wave, another
startup, makes and sells hybrid QCs that are specialized for quantum annealing
and particularly well-suited to solving optimization problems, such as those of
interest to the finance industry.

Regardless of how this major setback is resolved by
Microsoft, it draws attention to the extremely high technical risks in trying
to build computers upon technologies that are not only unproven, but for which
the fundamental physics are not even well-established yet.

D-Wave is Canadian startup and a foremost proponent of quantum annealing,
which includes optimization for finance applications. It is a pioneer in
selling QCs to other organizations.
These QCs are packaged as complete systems within physical enclosures measuring
10′ x 7′ x 10′ (L x W x H) that each houses the complete cryogenic
refrigeration, shielding, and I/O systems to support a single thumbnail-sized
QPU (quantum processing unit). Its latest model, the D-Wave Advantage QC, has
5,000 qubits up from the 2,000 qubits of the previous model. The company claims
that It can solve problems with up to 10,000 variables.
D-Wave also lets customer access its quantum hardware through its “hybrid solver,”
which breaks up the computing task into components, some of which is solved by
its QC, and the rest that is solved by traditional computers over a cloud-based
interface. In October 2020, The Globe and
reported that D-Wave was forced to undertake a costly refinancing
round that devalued the shares of several long-term investors. D-Wave has
struggled to generate revenue with only a handful over buyers for its machines.[xli]

Google (Alphabet Inc.) showed their strategic commitment to quantum computing
with their fall 2019 announcement that their QC had achieved so-called quantum
supremacy, surpassing classical supercomputers at a particular task. Their current
QC, “Sycamore,” has a 54-qubit processor with fast, high-fidelity quantum logic
gates. Already a leader on AI, Google is at the forefront of exploring
AI-related applications of quantum technology. Google researchers have
published a great number of articles on quantum computing.

Honeywell Quantum
In October 2020, Honeywell announced its next generation QC, System Model H1,
using Honeywell’s differentiated quantum charge-coupled device1 (QCCD) trapped-ion
This QC initially has 10 connected physical qubits for a quantum volume of 128
(claimed to be the highest in the industry). System Model H1 may be directly
accessed via a cloud application programming interface (API), as well as through
Microsoft Azure Quantum, and through certain channel partners including Zapata
Computing and Cambridge Quantum Computing.[xlv]
Honeywell has a unique mid-circuit measurement capability and reset function.[xlvi]

IBM Quantum.[xlvii]
IBM is one of few remaining manufacturers of classical mainframe computers.
IBM Q systems is based around the transmon qubit. IBM prefers the term quantum advantage over quantum
supremacy, and they specific the power of their QCs as quantum volume (QV) not
qubits. (Quantum advantage is where a problem can be solved faster on a QC than
on a classical supercomputer so it makes sense to use over classical
computers.) QV takes into account the number of qubits, connectivity, and gate
and measurement errors. The latest QV to be announced by IBM was 32. While they
have made a 53-qubit system, IBM also operates 16- and 20-qubit systems.[xlviii]
IBM is intent on building a cloud-enabled ecosystems of quantum partners, and
are actively promoting coding skills for quantum computing through annual
coding challenges.[xlix]
This is consistent with IBM’s longstanding strategy of supporting open-source
software tools. JPMorgan Chase and Barclays were charter members of the IBM
quantum computing network.[l]

Intel. Intel is a
component maker for QCs, not a system builder. It is determined to continue its longstanding leadership
in the silicon processor market with quantum computing chips. Intel Labs have
developed “Horse Ridge,” a first-of-its-kind cryogenic control chip (meaning it
operates close to the qubits inside the cryogenic freezer but at a slightly
higher temperature), which will enable the control of multiple qubits. Horse
Ridge brings the qubit controls into the quantum refrigerator — as close as
possible to the qubits themselves and reduces the complexity of quantum control
engineering from hundreds of cables running into and out of a refrigerator to a
single, unified package operating near the quantum device.[li]
Intel’s research partner is QuTech at TU-Delft. It recently announced the
ability to control multiple qubits with Horse Ridge.[lii]

IonQ is a startup, which introduced the first commercial trapped-ion QC. The
company has a five-year roadmap and plans to deploy rack-mounted modular QCs
small enough to be networked together in a datacenter by 2023. That will result
in a quantum advantage in building for machine learning, the company expects.
IonQ then plans to achieve broad quantum advantage by 2025. In late 2020, IonQ
announced a new 32-qubit QC available in private beta, and two next-gen
computers also in the works. IonQ has made progress towards error correction,
having incorporated a new error correction code that only uses 13 qubits, and is
also working on a capability to do mid-circuit measurement in future.[liv]
IonQ counts AWS, Samsung, Lockheed Martin, HPE, Hyundai Motor, and others as
investors. The Wall Street Journal
recently reported that IonQ planned to go public via a merger with a special-purpose
acquisition company in a deal worth about $2 billion.[lv]

This major IT company with a strong history in classical mainframes and
supercomputers is developing quantum annealing machines with grants from the
Japanese government. In 2020 it began a joint QC-development project with
D-Wave. Recently it entered a partnership with a ParityQC, an Austrian QC startup,
to develop quantum annealing solutions. NEC will be combining this technology
with its own superconducting parametron quantum devices, with the aim of
building quantum annealers by 2023. Major applications targeted by NEC are
financial portfolio optimization and manufacturing logistics and planning.

This Silicon-Valley startup is developing a large-scale linear optical QC
(LOQC), with a target of 1 million qubits. The company believes that photonic
technology is the only route to the large number of qubits needed to fully
scale up an error-corrected QC. PsiQuantum’s QC is based on photonic technology
that incorporates extensive error correction and can be manufactured in a
standard semiconductor wafer fab. Prominent investors are Microsoft and

Rigetti Computing.[lviii]
This Berkeley, California- based startup presents itself as an integrated
systems company. It builds QCs and the superconducting quantum processors that
power them. Through their Quantum Cloud Services (QCS) platform, their QCs can
be integrated into public, private, or hybrid clouds.

Silicon Quantum
Computing (SQC).[lix]
SQC is an Australian startup
launched in 2017 as a spinoff from the University of New South Wales (UNSW)
Sydney to silicon-based QC. It received funding from both the federal and
provincial governments as well as the Commonwealth Bank of Australia (CBA) and
Telstra. SQC is building a QC based on donor
spin qubit technology
, which is a phosphorus donor embedded in a silicon
structure originally conceived at UNSW. Potential advantages of donor qubits
are high fidelities (more than 99%) with long coherence times measured in
seconds for the electron spin states.[lx]
CBA invested over $14 million in the startup.[lxi]

Xanadu is a Canadian quantum startup funded by Series-A financing and
government grants from the U.S. DARPA and Canada’s SDTC agency. Xanadu is
betting that photonics offers the most viable approach towards universal
fault-tolerant quantum computing. It claims to develop photonic chips that will
result in near-term QCs. X-series chips are made from silicon and silicon
nitride. It is the first company to offer cloud access to photonic computers.
Currently, cloud customers may access its 8- or 12-qubit photonic QCs, but a
24-qubit processor is in the pipeline already. The aim is to double the number
of qubits available every six months.[lxiii]
Early clients include Creative Destruction Lab, Bank of Nova Scotia, Bank of
Montreal, and the U.S. Oak Ridge National Laboratory.[lxiv]

Addendum on QC

In December 2020, Bloomberg
reported that Amazon was laying the
groundwork to build its own QC and had started to hire a hardware team.[lxv]

Cisco seems to be
getting ready to enter the QC field. The company is making strategic hires and
looking to collaborate with quantum researchers at universities.[lxvi]

Microsoft planned
its own QC, based on the Majorana fermion (a class of elementary particle),
which would make for ideal qubits because they would be longer lived and less
prone to noise. By placing its hope on the Majorana fermion, Microsoft hoped to
leapfrog rivals IBM and Google, whose QCs are based on more established
technology. However, this endeavor was thrown into turmoil in early 2021, when
a 2018 paper in Nature confirming the
existence of the Majorana by Dutch researchers was retracted and corrected.[lxvii]
(The new article[lxviii]
containing the retraction was posted in January 2021.) Microsoft is expected to
regroup around better-known technologies such as superconducting qubits or
trapped-ion systems. This is, however, a major setback for Microsoft, who was
trying to beat the competition by betting on a more esoteric computer model.
But now quantum computing experts suggest that a computer using Majorana
particles may be as much as 30 years on the future.[lxix]

However, QCs based on ion-trap providers, superconducting
qubits, photonics, neutral atoms, silicon-based and annealing are left in the

Software Platforms and Solutions

The two main competing platforms in North America for
general cloud-based quantum computing solutions are those from Microsoft and
Amazon, with the platform from the Canadian-Spanish startup, Multiverse, being
particularly relevant to the financial services sector due to its focus on
financial applications. Superconducting, trapped ion, and quantum annealing
(not gate-based) are offered through the Amazon Braket and Microsoft Azure
cloud platforms. For now, photonic QCs are provided only on Xanadu’s cloud.

This Vancouver-based startup provides hardware-agnostic QC platforms. It
has applications for material science, optimization and market sentiment
measurement. RBS was a major early investor in 2015 and has contributed to a
new round in 2020.[lxxi]
Allianz is another a major investor.[lxxii]

Alibaba Cloud. Alibaba
Cloud, the cloud computing arm of Alibaba Group and Chinese Academy of Sciences
(CAS) have partnered to launch a quantum-computing cloud service. The CAS QC is
accessible through Alibaba’s cloud service. The first quantum laboratory in
China was established in 2015 as a joint venture between Alibaba and CAS.[lxxiii]
Alibaba Cloud Quantum Development Platform (ACQDP) is their simulator-driven
development tool for quantum algorithms and QCs. Damo, Alibaba’s Quantum Lab,
also conducts hardware research into quantum processors, quantum memory, and
quantum computing systems.[lxxiv]

Amazon Braket.[lxxv]
Amazon Braket is a fully-managed cloud-based (over AWS) quantum computing
service that offers access to quantum computing hardware from D-Wave, IonQ, and
Rigetti. Amazon focuses on three main application areas: molecular simulation,
optimization, and quantum machine learning. Collaboration with other
organizations are facilitated through the Amazon Quantum Solutions Lab. Amazon
Braket provides access to several QCs from other companies, including hardware
based on superconducting qubits from Rigetti, ion-trap QCs from IonQ, and
quantum annealing technology based on superconducting qubits from D-Wave.

Baidu established the Institute for Quantum Computing early in 2018, and
focused on building a bridge between AI and quantum computing. Paddle Quantum
is a quantum machine-learning toolkit to facilitate the rapid building and
training of neural network models. It is based on Baidu’s deep-learning
platform PaddlePaddle.[lxxvii]

Cambridge Quantum
Computing (CQC).[lxxviii]
CQC builds architecture-agnostics QC solutions focusing in chemistry, machine
learning, cybersecurity and finance. It recently announced version 0.7 of its
t|ket> software platform, that removes all license restrictions for use of
the tket’s Python module (known as pytket) making that software free to use.

This startup operates at the intersection between machine learning and
quantum computing. It solves NP hard and other complex optimization problems.
Through partnerships with Toshiba and D-Wave it offers optimization and
simulation solutions that range from quantum-inspired to hybrid to pure
quantum. It caters to the financial industry with a “Financial Services
Operation Layer” that sits on top of the quantum cloud.

Chicago Quantum.[lxxx]
The company is very active in researching the application of quantum algorithms
to optimize financial portfolios. It has developed a quantum algorithm, loosely
based on the Sharpe ratio,
that picks attractive stock portfolios based on one year of historical pricing
data. The algorithm is run on the D-Wave quantum annealer and on Chicago
Quantum’s own classical computers. The company occasionally publishes stocks picks
selected with its algorithms. It recently published an efficient portfolio of
128 stocks selected from 3,514 stocks, as well as smaller portfolios and stocks
with positive momentum and low risk.

Microsoft Quantum.[lxxxii]
Microsoft’s Azure Quantum, is a
full set of public-cloud ecosystem quantum solutions, which has recently been
opened for public review. It is intended for learning and solution building by
developers, researchers, systems integrators, and customers. The ecosystem
gives customers access to diverse quantum software and hardware solutions, a
network of leading quantum researchers and developers, a robust resource
library, and flexible self-service or tailored development programs.[lxxxiii]
Microsoft’s open-source quantum development kit (QDK), a software development
kit that allows development of new algorithms with Q#, a quantum-focused
high-level programming language. QDK has a GitHub repository with open-source
Q# libraries and sample programs.[lxxxiv]
Microsoft’s main partners are Honeywell, IonQ, QCI, Toshiba, an 1Qbit.

This quantum computing startup with offices in San Sebastian, Spain and
Toronto, Canada focusses on quantum-computing software solutions for the
financial industry. They claim that their software runs on all quantum hardware
technologies. In addition, Multiverse offers quantum-inspired solutions such as
tensor networks, digital annealing, qi optimization, and artificial

QC Ware.[lxxxvii]
This enterprise-software startup has a large team of quantum algorithm
experts. It aims to provide solutions that can run on near-term quantum
hardware. It partners with hardware providers D-Wave, IBM, IonQ, and Rigetti.

Quantum Computing Inc
QCI is a startup developing
platform-agnostic software for quantum computing. Its platform, named “Mukai,”
enables users to use quantum-inspired
methods on classical computers and
quantum-ready methods on QCs. The Mukai platform supports developing
applications to address complex optimization problems that are NP-hard, often
involving multi-dimensional solution spaces with thousands if not hundreds of
thousands of variables. Its Quantum Asset Allocator (QAA) enables fund managers
to use quantum-inspired techniques to solve the NP-hard problems standing in
the way of optimal portfolio allocation. QCI claims that QAA can quickly
calculate optimal or near-optimal interactive solutions for complex financial
asset allocation problems on classical computers.[lxxxix]

Toshiba. Toshiba
is a leader in quantum-inspired computing, using a deeper understanding of quantum
mechanics to run optimizers on classical hardware. Toshiba’s claims that its
Simulated Bifurcation Machine (SBM), which is derived from research on quantum
bifurcation machines, is a ready-to-use Ising[xc]
machine which can solve large-scale combinatorial
optimization problems
at high speed. In September 2020, Toshiba announced
that it was joining Microsoft’s Azure Quantum ecosystem. As a consequence, the
SBM is accessible over the Azure Quantum cloud service, allowing it to harness
the GPU resources in the Azure cloud.[xci]
The SBM is also available over Amazon’s AWS platform.[xcii]
Toshiba is aiming to be a large player in the nascent global quantum encryption
market, and is planning to launch a quantum cryptography service by 2025.
Conventional cryptography, which relies on the impracticality of factoring very
large numbers, is at a real risk of getting cracked when sufficiently large
QCs, which will far outperform classical supercomputers in such calculations,
become available.[xciii]

Zapata Computing.[xciv]
Zapata’s quantum-computing-powered workflow solution, Orquestra,[xcv]
that automates the workflow management of supply chain optimization, materials
discovery, and asset- allocation optimization. The software solution is
designed to be hardware-agnostic, so that it will work with any major QC.
Bosch, a large German Tier-1 automotive supplier, is an investor in Zapata.

Academic and Other Research Centers

The U.S. National Institute of Standards and Technology
(NIST) has been at the center of quantum computing research since the early
1990s. Partnerships between NIST and public universities have created research
institutes such JILA[xcvi]
(with the University of Colorado Boulder) and the Joint Quantum Institute (JQI)[xcvii],
formed as partnership between NIST, the University of Maryland, and the
Laboratory for Physical Sciences. There is a long and growing list of
universities that have quantum computing research groups.[xcviii]
According to a recent list compiled by the Quantum
the top 12 university-based QC-research organizations are:

1.       The Institute for Quantum Computing[c]
at the University of Waterloo

2.       Oxford Quantum[ci]
at the University of Oxford

3.       The Harvard Quantum Initiative[cii]

4.       The Center for Theoretical Physics[ciii]
at MIT

5.       The Centre for Quantum Technologies[civ]
at the National University of Singapore and Nanyang Technological University

6.       The
Berkeley Center for Quantum Information
at the University of California Berkeley

7.       The Joint Quantum Institute (JQI) [cvi]
at the University of Maryland

8.       The Division of Quantum Physics and Quantum Information[cvii]
at the University of Science and Technology of China (USTC)

9.       The Chicago Quantum Exchange (CQE)[cviii]
at the University of Chicago

10.   The Quantum Science Group[cix]
at the University of Sydney, Australia

11.   The Quantum Applications and Research
Laboratory (QAR-Lab)
at LMU Munich

12.   Quantum Information & Computation[cxi]
at the University of Innsbruck

Major Alliances

Google operates its own complete QC stack, but in most other
cases QC companies partner to complement one another’s capabilities.

Some major quantum computing partnerships and alliances are:

Microsoft Quantum Network – Microsoft (software
and Azure cloud services) partnering with Honeywell Quantum Solutions
(hardware) and IonQ (hardware), as well as Toshiba (software –
quantum-inspired), 1Qbit (software), and QCI (i.e. Quantum Computing Inc. –

IBM Quantum Network – IBM hardware (20 QCs, of
which 10 are available free) partnering with 140 participating organizations
that include Samsung, JPMorgan,
Barclays, and Daimler

Honeywell – Honeywell has invested in both
Zapata and CQC

D-Wave with Multiverse, and NEC

1Qbit with Azure Quantum (Microsoft)

NEASQC (NExt ApplicationS of Quantum Computing),[cxii]
a European consortium for NISQ quantum computing. HSBC recently joined as the
first financial services organization.[cxiii]

In advance of a full-scale QC being available, there may be
QC applications for and QC influence on the financial sector in the near term.
There are a few paths for these. The most prominent one is the combination of
small-scale quantum computing with classical computing in so-called hybrid
quantum computing. Another is the potential implementation of quantum-inspired computing algorithms on classical computer hardware. Quantum-inspired
computing is based on the idea that a problem that is hard to solve on a
classical computer may become easier to solve it is reframed in a way that is
inspired by quantum physics. But the execution is still classical.

A good practical definition to distinguish between classical
and quantum computing is:

If a solution leverages the quantum
mechanical principles of superposition and entanglement it can be called a
quantum solution, or at least a hybrid classical/quantum solution.  If the solution does not utilize these
phenomena, we will call it a classical solution even though it may not look
like a normal classical computing solution.[cxiv]

Quantum-inspired computing could
either be implemented with standard
computer hardware
, or with special-purpose
computer hardware
(that is still classical in origin). Typically,
quantum-inspired software is also quantum-ready
in the sense that it can be easily ported to run on a true QC once hardware
becomes available. When run on a true QC, the software will be much more powerful.

quantum-inspired algorithms are designed to run on classical computers, and
they have already had success with use cases such as improved cancer detection
in radiology scans. Microsoft claims that its quantum-inspired algorithms are
“particularly useful for optimization problems — which involve sifting through
a vast number of possibilities to find an optimal or efficient solution — that
are so complex and require so much computing power that current technologies
struggle to solve them.”
[cxv] Microsoft also claims orders of magnitude of
performance acceleration in Azure from recasting hard computational problems
into quantum-inspired solutions. They have been collaborating with Willis
Towers Watson (a global advisory, broking and solutions firm) to explore how
such algorithms may help in the areas of risk management, financial services,
and investing.

Quantum Computing
Inc. (QCI) is another example of a standard-computer-hardware implementation –
they provide a software platform, called Mukai,
[cxvii] that enables users to leverage the latest
breakthroughs in quantum computing by running quantum-inspired software on
classical computer hardware. In fact, one of the applications is a quantum asset allocator (QAA) that uses
quantum-inspired techniques to solve NP-hard problems standing in the way of
optimal portfolio allocation. The company claims that QAA can solve NP-hard
problems including cardinality constraints and minimum buy-in constraints.
Mukai software is also quantum-ready and can thus be used on true QCs as these
become available.

Toshiba’s SBM is
also an example of a standard-computer-hardware implementation, as it runs on
general-purpose classical computers, claiming to large-scale combinatorial
optimization problems at high speed, 100 times faster than simulated annealing

Fujitsu’s Digital
Annealer is an example of a special-purpose-computer-hardware implementation.  Its hardware was “purposefully designed for
more efficiently solving larger and more complex combinatorial optimization
(CO) problems.”

A BCG analysis[cxx] from 2018 identified future use cases of
quantum computing across five major sectors:

High-tech use cases include AI and machine
learning, cybersecurity, search, and bidding strategies for online ads

Industrial goods use cases include logistics
scheduling, product distribution, autonomous driving, traffic distribution,
semiconductor chip layout optimization, aerospace fault analysis, and materials
science applications

Chemistry and pharma use cases include faster
drug discovery, genomics, catalyst and enzyme design, and improved diagnostics
capability (e.g. MRI)

Finance use cases include trading strategies,
portfolio optimization, asset pricing and risk analysis (Finance use cases will
be covered in more detail in the next section)

Energy use cases include energy distribution,
network design, and oil-well optimization

A McKinsey analysis[cxxi]
of 100 use cases by industry had the following distribution, which is a proxy
for the impact of quantum computing and for which industries will be most

Finance, in first place with 28 use cases

Global energy and materials, in second place
with 16 use cases

Advanced industries (incl. aerospace and
automotive) in third place with 11 use cases

In early 2021, Forbes
reported that the leading quantum computing proofs of concept (POCs) were in
AI/machine language, financial services, molecular simulation, material
science, oil/gas, security, manufacturing, transportation/logistics, IT, and
healthcare (pharmaceuticals). Many of the AI-related applications also apply to
financial services, with applications in “trading strategies / treasury &
asset management, option pricing, new financial models, portfolio optimization,
predicting risk and uncertainty, customer product targeting from behaviors in
real-time.” If financial services companies are currently too risk averse to
grow their customer base because of limitations in computation ability, quantum
computing could enable the industry to reach two billion unbanked people by
reducing the $40 billion lost annually from fraud/poor data analysis and
reducing 80 percent false positives. The conclusion is that the “largest near
and far-term benefits” of quantum computing will be in financial services,
which explains why industry heavyweights such as JP Morgan, BBVA, and Goldman Sachs
are actively exploring quantum computing.[cxxii]


There are two ways to think about the influence
of quantum computing on finance. The first, and most obvious, is that the
special abilities of quantum computing will enable solving certain types of
problems that even the most powerful classical computers cannot do in the time
Where companies currently run large-scale analytics computations
for risk management, forecasting, planning, and optimization, quantum computing
could change future operations and even strategy. If an operation is not just
run faster, but a million times faster, executives should ask themselves what
fundamental changes in business operations become possible.[cxxiii]

However, there is also a second, and perhaps
more important way the quantum computing can influence finance and economics
over time. And that is to change the way problems are shaped, structured, and
modeled. We often forget that economics in its infancy as a social science was
heavily influenced by the prevailing physics of its time, which was
thermodynamics. The paradigms of partial and general equilibrium in economics
were borrowed from thermodynamics, the science that made the steam power of the
first industrial revolution possible. And so, classical and neo-classical
economics theories were based on the paradigm that everything will always want
to go back to an equilibrium, and any departures from that equilibrium are only
temporary. Much of the ongoing dissatisfaction with neo-classical economics
theory comes from the fact that the real world does not seem to behave that

David Orrell has coined the term Quantum Economics in an eponymous book,
where he expounds on his idea that quantum theory holds great promise as a new
and better way of modeling, for example, stock price movements. As Orrell

Perhaps the most useful
contribution of quantum finance will be to change the way we think about the
financial system. Instead of seeing stock prices as particles that are randomly
jostled from their stable resting place by interactions with many independent
investors, we begin to see them as fundamentally indeterminate quantities. In
quantum physics, particles can never be perfectly still because that would
violate the uncertainty principle.[cxxiv]

This is an ambitious long-term vision for changing the very
foundations of current economic models. However, this paper is primarily
concerned with the near-term utility of quantum computing for the finance
industry. Therefore, the discussion that follows will be focused on QC’s
promise to solve particular problems in finance, in areas where the performance
of QCs can already, or will shortly, exceed those of classical computers.

In a recent report on quantum computing in the financial industry,[cxxv]
BCG estimated that quantum computing could add $70 billion in operating income
for financial services companies after the technology has sufficiently matured.
While the technology is still in its infancy, a rapid rise in
financial-services applications is plausible. Quantum computing has the
potential to be a game changer for the competitiveness of banks and other
financial institutions. The three capabilities it is projected to revolutionize

Current optimizations have to use unrealistic assumptions to simplify scenarios
so that they are solvable problems for classical computers. But QCs promise to
solve problems in which the full complexity of the real world is captured.

and pricing.
Monte Carlo simulations can take days or weeks to run, but QCs
promise to run them in real time.

Machine learning is currently limited by the inability of
classical computers to handle complex and computationally intensive algorithms.
Quantum computing will overcome this constraint and promise to make large
complex systems understandable to machines in a short period of time.

IBM Quantum confirms that the types of financial-industry
problems that quantum computing can solve may be divided into these three
capability categories. For example, portfolio optimization and diversification
fall into the optimization category, option pricing and portfolio risks in the
simulation and pricing category, credit scoring and fraud detection in the
machine-learning category. IBM has already developed quantum algorithms in
these areas.[cxxvi]

According to McKinsey, the rationale for using QCs is based
on the need for financial institutions to crunch large and unstructured
datasets. It sees powerful use cases in capital markets, corporate finance, portfolio
management, and encryption-related activities. Quantum computing can offer real
competitive advantage in an increasingly commoditized world. McKinsey sees four
capital markets industry archetypes: sellers, buyers, matchmakers (including
trading platforms and brokers), and rule setters. Buyers and rule setters
require more complex models. For example, quant-driven hedge funds aim to
profit through analytical complexity could be a natural constituency for
ultra-powerful processing. Large banks, which take on multiple roles in financial
markets, are also significant early experimenters. Areas where artificial
intelligence techniques such as machine learning have already improved
traditional classification and forecasting are ripe for quick wins.[cxxvii]

The specific finance applications of quantum computing tools
may also be grouped by finance vertical, according to Multiverse (a quantum-algorithm provider for the financial
industry): [cxxviii]

Capital markets

Portfolio optimization

Optimal trajectory detection for investment/divestment

Training of traders on best trajectories

Trend/Anomaly detection for trading and

Market crash predictions

Credit and risk

Credit scoring on automated lending

Loan portfolio supervision and alert

ALCO/ALM matching optimization

Capital allocation optimization

Customer buying propensity

Insurance feature selection (automated)

Insurance individual pricing

Fraud detection

Credit-card fraud

Instant money transfer fraud


Tax fraud detection

As previously mentioned, a recent analysis of 100 hundred
use cases for potential near-term value creation was done by McKinsey. There
were 28 use cases in Finance – the most of any industry analyzed – and the
value at stake in both the medium and long term was high. Finance is clearly
what McKinsey calls a “first-wave industry” for quantum computing, and the
authors of the report made a call to action to executives in the first-wave

We believe that industries such as
finance, travel, logistics, global energy and materials, and advanced
industries will start reaping significant value from the hybrid
classical/quantum approach in the early 2020s. Business leaders in these
first-wave sectors need to develop a quantum strategy quickly or they will be
left behind by innovative companies such as Barclays, BASF, BMW, Dow,
ExxonMobil, and others that already have taken strategic steps into quantum

This conclusion is shared by a recent Fitch Solutions
analysis of cloud computing technology megatrends to 2050. The report finds
that quantum computing has the greatest disruption potential; that quantum
computing is closer to reality than it has ever been, with expectations it
might happen within the next ten years; and that the winners will be the
companies and governments investing in the technology.[cxxx]

In a recent report on the impact of emerging technologies in
financial services – the result of a collaboration between the World Economic
Forum (WEF) and Deloitte – the potential of quantum computing to “solve a narrow,
but critical range of problems significantly more efficiently than classical
is also recognized. Portfolio optimization, credit scoring, risk analysis, and
cryptography are the major areas of impact seen by the WEF.

In only the past couple of years, several major companies in
the financial industry have announced quantum computing experiments. For
example, BBVA has been exploring portfolio optimization, CaixaBank risk
management, and JPMorgan asset pricing. Many financial institutions are also
actively partnering with quantum players or networks, or even directly
investing in startups. The list of financial firms involved in quantum
computing is getting longer. It includes global FIs such as Allianz, Barclays,
Citigroup, Goldman Sachs, HSBC, JPMorgan, and Mizuho, but also major regional
or national players such as ABN Amro Bank, Anthem, Bank of Canada, BBVA, BMO,
BNP Paribas, CaixaBank, Commonwealth Bank of Australia, NatWest Group, Nomura,
RBS, Scotiabank, Standard Chartered, UBS, and Wells Fargo.

Financial services companies that may find quantum computing
too exotic could enter the field by investing in quantum-inspired computing. In
a survey and study commissioned by Fujitsu,[cxxxii]
70 percent of survey respondents made aware of the abilities of the Fujitsu
Digital Annealer to solve combinatorial optimization problems without the need
for a QC stated that it would accelerate their journey to a quantum future.

Quantitative investors are hoping that quantum computing
will solve many of the current computational problems in portfolio
optimization, arbitrage strategy, and trading cost minimization. Classical
computers encounter problems with the complex computing load imposed by adding
more realistic assumptions and constraints to models:

Adding noncontinuous, nonconvex
functions such as interest rate yield curves, trading lots, buy-in thresholds,
and transaction costs to investment models makes the optimization surface so complex
that classical optimizers often crash, simply take too long to compute, or,
worse yet, mistake a local optimum for the global optimum. To get around this problem,
analysts often simplify or exclude such constraints, sacrificing the fidelity
of the calculation for reliability and speed. Such tradeoffs, many experts
believe, would be unnecessary with quantum combinatorial optimization.[cxxxiii]

Researchers have developed a number of techniques that aim
to use various quantum approaches to solve portfolio problems. The main
approaches put forward are:

Algorithms based on quantum annealing

Gate-based quantum algorithms

Quantum-inspired models based on tensor networks

Whichever approach is used, there is a need to translate the
real-world problem into a polynomial
unconstrained binary optimization (PUBO)
expression. This is not a trivial
problem in itself. In a recent preprint article, researchers from Zapata
propose quantum enhanced optimizers (QEOs), a type of black-box solver which is
independent of the details of the objective function, which can scale to large
problems when combinatorial problems are intractable due to real-world

The quantum computing technology that is getting the most
current and near-term attention in the finance industry is quantum annealing,
due to annealing’s natural strengths in modeling and solving optimization
problems. D-Wave Systems is a leader in the field. They focus on NP-hard
optimization problems, and have been pursuing a highly empirical approach to these
problems. In the case of an NP problem, it is possible to verify the solution
in polynomial time. In the case of NP-hard problems, it is possible to find a
solution but without knowing whether is optimal or not. (The distinction
between P and NP problems is a theoretical one. D-Wave’s Catherine McKeough
points out that in the 30 years since P vs NP was posed, no one has proposed an
experiment to settle it, likely because such an experiment cannot be designed.[cxxxv])
For an optimization problem, the lowest point is the ground state, but there
are also local minimums with higher state neighbors. Problem containing several
of the latter are choppy which makes it hard to find the optimal solution.

Adiabatic quantum computing (AQC) is an alternative to the
gate model, but AQC is polynomially equivalent to the gate model. Bot
approaches are universal (Turing equivalent). Quantum annealing algorithms can
be run either on classical computers or on AQC platforms. The quantum version
provides probabilistic results, which means that a solution has to be run a
hundred or a thousand times to provide an answer distribution. Compared to the
polynomial solutions running on a classical computer, the annealing solution
running on D-Wave’s QC converges much faster, and there is no gain in running
it for a long time.[cxxxvi]

Sam Mugel, the CTO of Multiverse, a quantum software company
that runs its algorithms on D-Wave hardware, sets out a few practical criteria
for selecting a good problem that can be better solved on current QCs than on
classical computers. First, the input questions should be quite small, so that
only a low number of qubits are needed. Second, there should be many possible
solutions or states to explore. Third, it should be a high value problem. And
fourth, it is a good choice when the current best classical solution is a
brute-force solution. This is typically the case when the problem is known to
be NP-hard with no classical method of finding the optimal solution. By
combining classical and QCs in so-called hybrid solvers, big gains can be made.
A powerful classical computer with ample resources can manage the problem and
data management, shooting off to the QC a small, extremely difficult problem
that quantum computing is best at solving. Annealing-based systems are ready
for use today.[cxxxvii]

A number of recent case studies, experiments, and proofs of
concept (POCs) conducted between financial institutions and QC companies have
been made public. These cases reveal not only what is being done and by whom,
but sometimes also the rationale of the financial institutions involved:

Barclays created
an internal QC working group in 2017, with modelers running programs on IBM’s
quantum cloud.[cxxxviii]
In one example, they worked with IBM on a POC for a quantum algorithm that can
be used in securities transaction settlement.[cxxxix]
Transaction settlement (which trades to settle when) is computationally complex
and difficult to optimize because of a combination of various legal constraints
and optionality in collateralizing assets and utilizing credit facilities.
While it takes a long time for a classical computer to solve, the researchers
published a joint paper[cxl]
describing how a QC with a small number of qubits could execute the most
complex parts of the algorithm.

BBVA is following
six lines of research, working hand in hand with Spain’s Senior Council for
Scientific Research (CSIC), Accenture, Fujitsu, Zapata Computing, and
Multiverse. While the project is still in an exploratory phase, the early
results suggest that the technology can solve certain complex problems — such
as investment-portfolio optimization — “quickly, accurately, and
efficiently.”  According to Carlos
Kuchkovky, BBVA global head of research and patents: “Although this technology
is still in an early stage of development, its potential to impact the sector
is already a reality. Our research is helping us identify the areas where
quantum computing could represent a greater competitive advantage, once the
tools have sufficiently matured. We believe this will be, for certain concrete
tasks, in the next two to five years,” explains.”[cxli]

BMO Financial Group
and Scotiabank collaborated with
Xanadu to benchmark a quantum Monte Carlo algorithm for a variety of trading
products. According to Xanadu, the algorithm shows the potential disruptive
potential of quantum computing for derivatives pricing over the coming years,
leading to near real-time pricing and significantly lower power overhead.[cxlii]

Commonwealth Bank of
Australia (CBA)
and Rigetti Computing conducted a joint experiment applying
the quantum approximate optimization algorithm (QAOA) to portfolio rebalancing.
CBA and Rigetti used a simulated gate-model QC.[cxliii]
The experiment was a success, identifying portfolios within 5 percent of the
optimal adjusted returns and with optimal risk for a small portfolio, and
demonstrating the potential tractability of this application on more advanced
quantum hardware.[cxliv]

teamed up with Fujitsu for a quantum-inspired POC that optimized the selection
process for a securitized loan portfolio. 
Using the Fujitsu Digital Annealer, Commerzbank was able to handle
multiple loan selection factors simultaneously (e.g. regulatory requirements,
absolute volume limits, percentage limits for specific asset characteristics
etc.) in order to achieve greater risk diversification in the portfolio.[cxlv]

GloFund leveraged
cloud-based quantum computing to rebalance portfolios in optimal ways with
significantly more speed. GloFund claims that quantum computing allows it to take
into account more constraints (e.g. regulatory requirements, volume limits,
percentage limits etc.) and examine a larger set of inputs (e.g. different
security classes) when rebalancing their portfolios. Historically, this
computationally-intensive calculation took several hours or days to complete.
That forced them to sacrifice accuracy of the calculation (e.g. simulated
annealing, threshold accepting etc.) to make faster, more efficient portfolio
decisions. However, by running quantum algorithms, GloFund is able to fully
solve the combinatorial optimization of the portfolio and conduct advanced
market simulations. Portfolio managers at GloFund are able to process
significantly more portfolio combinations simultaneously to find rapid and more
accurate results.[cxlvi]

Goldman Sachs is
working with QC Ware to explore the acceleration of Monte Carlo algorithms with
quantum computing.[cxlvii]

JPMorgan Chase
and IBM tested a methodology to price options and portfolios of options on a
gate-based QC using amplitude estimation, an algorithm which provides a
quadratic speedup compared to classical Monte Carlo methods. A simple
error-mitigation scheme significantly reduced errors from noisy two-qubit

JPMorgan Chase also
tried out Honeywell’s trapped-ion QC to produce what is called a quantum
oracle, a black-box operation used as an input to another algorithm.[cxlix]
The oracle’s purpose was to ease the computation of Fibonacci
numbers, which has application in investing and information security.

NatWest Bank is
using Fujitsu’s quantum-inspired Digital Annealer to optimize its composition
of the bank’s £120bn HQLAs
(high-quality liquid assets) portfolio, including bonds, cash, and government
securities. It has completed a highly complex calculation that needs to be undertaken
regularly by the bank, at 300 times the speed of a traditional computer, with
an even higher degree of accuracy. Natwest also believes this process reduces
the risk of human error, and that it can complete a comprehensive risk
assessment for its portfolio much faster, as well as, gaining access to a far
wider range of results and permutations, therefore helping to ensure an
optimized spread and reduced risk.

Nomura Asset
Management (NAM)
is exploring quantum-computing applications with Tohoku
University, focusing on portfolio optimization and stock-return prediction.[clii]

RBS is using
quantum-inspired computing to help portfolio managers optimize the composition
of the bank’s $150bn high quality liquid assets portfolio. The bank is
investigating which other portfolios could be calculated by the same
RBS has also evaluated algorithms from 1Qbit (in which it is an investor) to
determine amounts to set aside for bad loans. John Stewart, RBS’s head of
innovation, believes that RBS is “18 to 24 months” ahead of its rivals in using
quantum computing. He justifies RBS’s investment as an insurance policy against
getting caught off-guard: “Maybe a million-dollar investment in order to
understand something that could jeopardise your multi-billion-dollar business
is a great trade-off at this stage.”[cliv]

Standard Chartered
has worked with Nasa and the Universities Space Research Association to
investigate the benefits that quantum computers can bring to optimizing
investment portfolios.[clv]

In January 2021, Multiverse confirmed that its clients BMO and Scotiabank were studying trading problems, Goldman Sachs was working on option pricing, Bankia was interested in minimum holding periods, and VW in making financial market
Earlier it was disclosed by D-Wave that for Bankia, Multiverse and D-Wave partnered to solve the NP-hard
problem of dynamic portfolio optimization – determining the optimal trading
trajectory for an investment portfolio of assets over a period of time, taking
into account transaction costs and other possible constraints.[clvii]

A closer glimpse into the nature of Multiverse’s work (sans
client names) can be found in posted papers in which it shares progress made in
running four years of market data through its tensor network algorithms in
order to determine optimal
portfolios. The algorithms ran very fast on D-Wave hardware, suggesting that it
was ready for “commercially-valuable applications.” The portfolio-optimization
results were also very encouraging: The algorithm found a set of holdings that
would give a 60 percent return at 15 percent volatility.
(The details can be found in a preprint paper by Mugel et al.[clix])
Multiverse has also demonstrated the optimization of an investment portfolio
spanning 4 years and 7 assets using D-Wave and Tensor Networks, and have
demonstrated a 50 percent return on investment at 14 percent volatility.
According to D-Wave, time-series clustering and post-processing algorithms were
key to this successful demonstration.

Similar work has been done by Multiverse competitor, Chicago
Quantum, who has published a number of results over the last year from its
efforts to prove that quantum techniques can select an efficient portfolio, run
using the D-Wave annealer. Their latest demonstrations involved running the
full list of U.S. common stocks from all major U.S. equity exchanges through
their algorithm to prove that it could have picked a portfolio with superior
returns over a certain past period.[clx]
Two papers lay out the results from portfolio optimization exercises with
respectively 40[clxi]
and 60[clxii]
U.S. stocks, contrasting QC with classical results.

Accenture has also used D-Wave’s hybrid solver for its
banking clients to pilot quantum applications currency arbitrage, credit
scoring, and trading optimization.[clxiii]


Some significant quantum-computing milestones have been
reached over the last two years:

Google made news when it declared so-called quantum supremacy
in 2019, solving a contrived mathematical problem not realistically possible
with classical computers on its 54 qubit Sycamore QC in 200 seconds vs. 10,000
years estimated for a supercomputer. In 2020 there were several significant

 IBM, Google
and others demonstrated chemical molecular-bonding simulations with practical
application potential such as novel material design, understanding chemical
processes such as nitrogen fixation which potentially improves food production

IBM also published its ambitious 1 million qubit
roadmap out to 2030, with envisaged quantum advantage from a 1,121-qubit system
by 2023) 2020 Honeywell Quantum Solutions—10x Quantum Volume annually (2025: QV
of 650,000) (model H0 QV 128; model H1 with 32 atomic ions released in Oct

USTC (China) demonstrated that its QC could do
Gaussian boson sampling (detected 76 photons approx. 200 seconds) that would
take a supercomputer 2.5 billion years

IonQ launched its new computer with 32 QB and QV
4 million, equaling 22 Algorithmic Qubits

Many ongoing experiments and POCs (see previous
section) also continued

BCG expects the first gains of quantum computing to accrue
to firms in industries with complex simulation and optimization requirements.
The financial industry has several such challenges in portfolio optimization,
arbitrage strategy, and trading costs. A “slow build” is forecast until about
2024, but value is then expected to increase rapidly as the technologies
matures and becomes more commercially viable. A distinct early-mover advantage
is predicted:

Since quantum computing is a
step-change technology with substantial barriers to adoption, early movers will
seize a large share of the total value, as laggards struggle with integration,
talent, and IP…Quantum computing is a candidate for a precipitous
breakthrough that may come at any time. Companies that have invested to
integrate quantum computing into the workflow are far more likely to be in a
position to capitalize—and the leads they open will be difficult for others to
close. This will confer substantial advantage in industries in which
classically intractable computational problems lead to bottlenecks and missed
revenue opportunities.[clxv]

Quantum Computing was placed at the peak of the Gartner Hype Cycle for Compute
Infrastructure 2020.[clxvi]

But Gartner also points out that while quantum computing may be overhyped, it
could offer companies real competitive advantage, and that there are real risks
in ignoring it. One major risk of being a late mover is jeopardizing intellectual
property (IP) and patent portfolios, as early movers move quickly to patent
innovations, for example, a rival bank patenting an innovation in Monte Carlo
Another major risk is being locked out of the QC talent pool as first movers rapidly
absorb scarce QC talent.

But maybe the biggest risk of being a late mover is the loss
of competitive advantage in trading activities: Whichever financial institution
makes a huge breakthrough in quantum computing will choose not to announce it,
but to rather reap the rewards in obscurity for as long as possible, akin to
the start of high-frequency trading.[clxviii]

The first
official Quantum Computing Roadmap was
published by ARDA’s Los Alamos National Laboratory in 2002.[clxix]  The roadmap was originally intended to be
updated annually. However, it was last refreshed in 2004, which makes it very
dated. Still the 268-page document has a lot of depth on the different quantum
computing technologies, and it provides some historical context. For example,
it was originally predicted that a 50-qubit QC would be attained by 2012. Subsequent
roadmaps have recent come from major private organizations pursuing the
technology, such as IBM, Honeywell, and IonQ, as well as from some consultants.

IBM Roadmap

In September 2020, IBM released an ambitious quantum
hardware roadmap, which showed a pathway to a QC (codenamed “Condor”) with over
1,000 qubits by the end of 2023, and eventually on to a million qubits and
In 2021, IBM will release its 127-qubit IBM Quantum processor codenamed
“Eagle”. The Condor milestone will include error correction and enough scale to
explore what IBM calls quantum advantage, where its QC can solve problem more
efficiently than the world’s best supercomputers.

Then, in February 2021, IBM followed up by releasing a
roadmap for building an open quantum-software ecosystem.[clxxi]
IBM identified three key segments in which they expect open-source developers
to create a base for those working higher up the software stack:

Quantum-kernel developers create the
high-performing quantum circuits at the lowest level (i.e. closest to the
hardware). IBM will release the Qiskit runtime environment later in 2021. It
will increase the capacity to run more circuits faster, and to store quantum
programs so that others may run them as a service. A wider variety of circuits
will also be made available.

Quantum-algorithm developers leverage those
circuits to develop quantum algorithms that surpass classical computing solutions.
IBM’s Circuit Composer[clxxii]
has a customizable set of tools that allow developers to build, visualize, and
run quantum circuits on quantum hardware or simulators.

Quantum-model developers apply these algorithms
to real-world use cases to develop quantum models for optimization, chemistry,
physics, machine learning, and so forth.

By 2023, IBM
plans to offer families of pre-built runtimes in the domains of natural
science, optimization, machine learning, and finance. These will be callable
from a cloud-based API. Beyond 2025, IBM has a vision of
frictionless quantum computing, where developers and users will no longer need to concern themselves
with the hardware. The usage and creation of open-source tool and converting
these to run native in the cloud are key components of IBM’s quantum roadmap.

Honeywell Roadmap

When it released the Model H1 QC in 2020, Honeywell also provided
a high-level roadmap for successor QCs, up the “large scale” Model H5 in 2030.[clxxiii]
The roadmap mentions the technologies that Honeywell expect to add with every
generation, but it is not specific on the number of qubits that will be

IonQ Roadmap

This quantum startup released a roadmap in December 2020.

In the roadmap IonQ introduced a new metric, Algorithmic
Qubits (AQ), while rejecting IBM’s Quantum Volume (QV) metric for the reason
that it will become unusable when QCs become large. AQ takes the log 2 base of
QV. According to IonQ, AQ represents the number of “useful” encoded
qubits in a particular QC and therefore is a good proxy for the ability to
execute real quantum algorithms for a given input size. AQ is smaller than QV,
for instance, IBM’s quantum computing roadmap has a 1,121-qubit system in 2023,
which would be equal to an AQ of 65.

IonQ aims to have a 64 AQ machine by 2025, a 384 AQ machine
by 2027, and a 1024 machine by 2028.[clxxiv] 

The High-level View

In a recent report,[clxxv]
BCG estimated the total benefit of quantum computing across all industries to
reach $450 billion to $850 billion by 2050 (roughly evenly split between
revenue and cost improvements.) BCG also estimated the impact and timeline for
the financial industry: The first applications expected will be quantum
annealers for optimization, expected over the next 3 – 5 years. In the 5 –
10-year horizon, shallow quantum approximate optimization algorithms (QADA) are
expected, with convex optimizers and full-scale quantum heuristics only
expected at least a decade or two out. But even during the noisy
intermediate-scale quantum (NISQ) era, when high error rates will limit what
QCs can do, quantum-inspired algorithms and hybrid approaches (of quantum and
classical computing) may create significant value for institutions and help
them and prepare for the big quantum advances yet to come.

It is therefore advisable not to over-generalize from the
assessment that full-scale fault-tolerant QCs are decades away to assert that
no real-world applications are possible in the First Wave, defined as the next
3-5 years. Indeed, particular areas of finance, such as portfolio optimization,
lend themselves well to what early quantum hardware and software are already
able to do. The rapid progress made on early working quantum technologies, in
particular annealing, suggests that optimization solutions are feasible in the
short run. In the second wave, improved risk analytics have the potential to
move risk management from a defensive to an offensive trading strategy.


A summary of the expected impact of quantum computing on the
finance industry compiled from various sources is presented in Table 2 below.

Table SEQ Table * ARABIC2. Expected
Impact of Quantum Computing on Finance over Time


First Wave (<5 yrs.)


Second Wave (5 – 10 yrs.)

Third Wave (a decade +)

Technology Status

NISQ era of
noisy machines, most still <100 qubits and low quantum volume.

algorithms can run on classical computers.

solutions that are part classical, part quantum.

coherence times on quantum annealers.

Qubits in the
thousands allow for partial error correction.

Most cloud
services providers offer access to quantum computing, “quantum-as-a-service.”

machines with tens of thousands of qubits. Full-scale fault tolerance (as
decoherence is controlled via quantum error correction) gives broad quantum
advantage. But only 2,000 – 5,000 operational machines exist worldwide.

New Finance Applications

portfolio optimization algorithms run on either classical or QCs.

forecasting and risk assessments that better predict black swan events.

New standards
for post-quantum cryptography to replace current encryption techniques (RSA,
AES 256)

risk assessments e.g. for quant hedge funds.


based on post-quantum cryptography.

Finance-industry Impact

computing becomes a competitive differentiator. Income gains from portfolio optimization
up to $0.5bn.

Income gains
from portfolio optimization and risk analytics beyond $5bn.

$40 billion
to $70 billion in operating income to banks and other financial services from
all quantum applications.

Applications in Other Industries

simulations for pharma and material science.

neural networks.

Transport and
supply chain network optimization.

Auto and
aircraft computational fluid dynamics.

De novo drug
discovery and design with large biologics.

materials, extension of market life of patents.

McKinsey, IBM, Honeywell, IonQ, NEC, WEF)


Full-scale quantum computers that fulfil all the breathless
media predictions for the technology are still at least a decade or more away.
It will take that long to increase the number of useable qubits into the
thousands while carrying a full error-correction overhead, which will consume
most of the qubits absent any other breakthroughs. However, there are several
niche QC applications available at present that can deliver near-term business
value despite the limits of the current hardware. The financial industry is
best-placed of all industries to be a first mover because the types of
probabilistic optimizations possible with already-proven quantum technology are
directly applicable to valuable finance problems such as portfolio
optimization. This explains the level of activity and investment in the
technology by many of the largest financial institutions in the world.

A range of portfolio-optimization applications from
quantum-inspired algorithms that run on classical digital hardware to hybrid
and full quantum algorithms are available from a growing ecosystem of hardware
and software vendors. In contrast to previous revolutionary technologies, access
to quantum computing is widely available over the cloud, often at no or low
cost. That both broadens and accelerates the adoption of the technology.

Given the extent of public information on activity and
progress with portfolio optimization, it is likely, even plausible, that there
are already financial-services companies using quantum technology to guide
their trading strategies. It would be easy for a company to do this quietly
since no hardware purchase is necessary. It only requires vendor relationships,
cloud access, and internal modeling expertise.

A number of pathways for financial institutions to get
involved in the technology can be discerned from publicly-available cases and
from the way the industry ecosystem is taking shape. For example, as a first
move an institution could try out quantum-inspired portfolio-optimization
algorithms running on classical hardware, and then graduate to running
portfolio-optimization algorithms on quantum hardware over the cloud. That
could build internal expertise in the use of the technology while proving the
concept. Afterwards, there are opportunities to make larger and more aggressive
investments, including taking a stake in quantum startups, or joining a
consortium. The extent of the commitment will be determined by whether the
organization only wants to try out the technology, shape the development of the
technology, or own the technology.

The risk of not exploring quantum computing technology at
all seems to exceed the relatively modest cost of exploration at this point.
Quantum engineers and physicists are in high demand and in short supply, a fact
that is driving many of the current participants to build up teams now. Given
the scarcity of human resources with quantum computing expertise, those institutions
who are first to build up quantum computing teams may be able to lock in their
advantage for years. The internal capability-building dimension should not be
an afterthought but be matched to the corporate strategy, and aligned with the
organization’s technology strategy.

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