/Neven’s Law (Who Asked for That), D-Wave’s Steady Push, IBM’s Li-O2- Simulation (via Qpute.com)
Neven’s Law (Who Asked for That), D-Wave's Steady Push, IBM’s Li-O2- Simulation

Neven’s Law (Who Asked for That), D-Wave’s Steady Push, IBM’s Li-O2- Simulation (via Qpute.com)

Quantum computing’s (QC) many-faceted R&D train keeps slogging ahead and recently Japan is taking a leading role. Yesterday D-Wave Systems announced it has partnered with a Japanese QC consulting start-up, Sigma-i, to help prime the QC pump. Last week IBM, with Japan-based colleagues, reported advances in simulating lithium-oxide reactivity such that could help advance battery technology. But first, have you heard of Neven’s Law?

Coined for Hartmut Neven, director of the Google Quantum Artificial Intelligence lab – Neven’s Law, among other things, predicts QC will achieve quantum supremacy soon, perhaps 2019. A good article in Quanta Magazine and reprinted in Scientific American tells the story.

Here’s a brief excerpt:

“The doubly exponential rate at which, according to Neven, quantum computers are gaining on classical ones is a result of two exponential factors combined with each other. The first is that quantum computers have an intrinsic exponential advantage over classical ones: If a quantum circuit has four quantum bits, for example, it takes a classical circuit with 16 ordinary bits to achieve equivalent computational power. This would be true even if quantum technology never improved.

“The second exponential factor comes from the rapid improvement of quantum processors. Neven says that Google’s best quantum chips have recently been improving at an exponential rate. (This rapid improvement has been driven by a reduction in the error rate in the quantum circuits. Reducing the error rate has allowed the engineers to build larger quantum processors, Neven said.) If classical computers require exponentially more computational power to simulate quantum processors, and those quantum processors are growing exponentially more powerful with time, you end up with this doubly exponential relationship between quantum and classical machines.”

Apparently, the rule began as an in-house observation before Neven mentioned it in May at the Google Quantum Spring Symposium where he said that quantum computers are gaining computational power relative to classical ones at a “doubly exponential” rate. We’ll defer further sketching of his argument till later in the article. Not everyone (no surprise) agrees with Neven but Google definitely has earned credentials in this space.


D-Wave 2000Q System

First up is D-Wave, which yesterday announced forming a partnership with Sigma-i, a spin-out from Tohoku University. Sigma-i is touted as a “company formed to optimize the world with quantum computing technologies.” Might as well have stretch aspirations. Sigma-i is one of an emerging class of quantum computing consultants. In this instance its expertise is in quantum annealing

“In Japan, many companies look forward to the real-world applications that quantum computing can and will bring,” said Masayuki Ohzeki, CEO of Sigma-i. “This contract couples our quantum expertise with D-Wave’s powerful quantum computing systems, bridging the gap between industry and academia, and ushering in a new era of quantum computing in Japan.”

D-Wave labeled its partnership with Sigma-i as “the biggest commercial, global quantum deal to date – (and) will power increased access to commercial quantum computing systems, paving the way towards a practical quantum future” but didn’t precisely explain what that encompasses. Sigma-I’s roots seem to be part of the Tohoku University Quantum Annealing Research Development (T-QARD) project. Two key Sigma-i offerings include:

  • Application development. Sigma-i will consult with commercial, research and educational institutions in Japan to help them build quantum applications. No mention is made of whether Sigma-I will develop applications (IP) of its own
  • Access D-Wave’s “Cloud”. Sigma-i will act as a sort of concierge ‘portal’ for access to D-Wave’s 2000Q family of products through Leap (cloud platform). It’s unclear if broad training is also offered.

D-Wave says the Sigma-i team is deeply knowledgeable about how to program the D-Wave system and will offer consulting services, “including coding best practices and embedding problems onto the D-Wave system.” In April, Tohoku, D-Wave, and automotive manufacturer Denso reported developing a new algorithm to segment certain problem types into sub-problems more readily solved on the D-Wave system.

“This contract signals the ongoing growth of our cloud business and the increasing interest in quantum computing worldwide,” according to Vern Brownell, CEO of D-Wave. Back in February, D-Wave announced an 18-month technology roadmap featuring a new underlying fab technology, reduced noise, increased connectivity, 5000-qubit processors, and an expanded toolset for creation of hybrid quantum-classical applications. (See HPCwire article, D-Wave Previews Next-Gen Platform; Debuts Pegasus Topology; Targets 5000 Qubits)


A rendering of IBM Q System One, the world’s first fully integrated universal quantum computing system, currently installed at the Thomas J Watson Research Center. Source: IBM

Last week, IBM and Mitsubishi Chemical reported they had simulated the initial steps of the reaction mechanism between lithium and oxygen in Li-air batteries – the first research of its kind to have been simulated on a quantum computer. Their paper (Computational Investigations of the Lithium Superoxide Dimer Rearrangement on Noisy Quantum Devices) was posted on arXiv last week.

Quantum chemistry has long been a prime target for quantum computing. The new work introduces a method for reducing the complexity of the calculation. Here’s the abstract:

“Currently available noisy intermediate-scale quantum (NISQ) devices are limited by the number of qubits that can be used for quantum chemistry calculations on molecules. We show (the) number of qubits required for simulations on a quantum computer can be reduced by limiting the number of orbitals in the active space. Thus, we have utilized ansätze that approximate exact classical matrix eigenvalue decomposition methods (Full Configuration Interaction).

“Such methods are appropriate for computations with the Variational Quantum Eigensolver algorithm to perform computational investigations on the rearrangement of the lithium superoxide dimer with both quantum simulators and quantum devices. These results demonstrate that, even with a limited orbital active space, quantum simulators are capable of obtaining energy values that are similar to the exact ones. However, calculations on quantum hardware underestimate energies even after the application of readout error mitigation,” according to the paper.

In the recent work, researchers demonstrate the reduction of orbitals used in the calculation to just the “highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) of the stationary points can effectively reduce this problem down to two qubits for the investigation of the complete mechanism of this rearrangement reaction.” The paper is best read in full.

This joint research was made possible through the IBM Q Network Hub at Keio University in Japan. IBM reports, “Only one year into the collaboration, the hub of IBM, Keio, Mitsubishi Chemical, Mitsubishi UFJ Financial Group, and Mizuho Financial Group has not only made progress in practical battery chemistry, but also published work in financial risk analysis, and other fundamental quantum research.”

Like D-Wave, IBM has been aggressively expanding its quantum presence worldwide. In a separate announcement today, Big Blue reported expansion of its IBM Q Network in Europe. The new members, Aalto University, University of Turku, EPFL, University of the Basque Country and The International Iberian Nanotechnology Laboratory “will have direct access to IBM Q Network resources and access to the IBM Q Experience’s publicly available quantum computing systems for teaching, as well as faculty and student research projects that advance quantum information science and explore early applications.”


Quantum supremacy – the notion of a quantum computer performing a task that classical computers cannot – was the first attempts to provide a simple description of the capability that would indicate quantum computing was ready to burst past traditional computing. It was followed by a somewhat less absolute notion, quantum advantage, which is the idea that quantum computers can do a task sufficiently better than classical machine to warrant making the switch. In either case, they are intended to represent a pivotal milestone for QC.

Neven’s idea is that achieving quantum supremacy is not far ahead and that doing so is the natural result of QC’s inherent advantages and quantum device advances – captured in Neven’s Law – as discussed earlier in this article. To demonstrate how quickly the gap is closing writer Kevin Hartnett recounts the experiences of Google AI in his article.

“In December 2018, scientists at Google AI ran a calculation on Google’s best quantum processor. They were able to reproduce the computation using a regular laptop. Then in January, they ran the same test on an improved version of the quantum chip. This time they had to use a powerful desktop computer to simulate the result. By February, there were no longer any classical computers in the building that could simulate their quantum counterparts. The researchers had to request time on Google’s enormous server network to do that,” wrote Hartnett.

You get the idea. QC is catching up and fast is the contention. Sometime last February, Neven reportedly had to request more resources – “We were running jobs comprised of a million processors.”

His notion of a doubly exponential rate is interesting. “Even exponential growth is pretty fast. It means that some quantity grows by powers of 2: 21, 22, 23, 24. The first few increases might not be that noticeable, but subsequent jumps are massive. Moore’s law, the famous guideline stating (roughly) that computing power doubles every two years, is exponential,” explained Hartnett.

Doubly exponential growth is more dramatic – instead of increasing by powers of 2, quantities increase by the power two raised to the power of two (shown below):

We’ll see is Neven’s observation proves true.

Link to Quanta article: https://www.quantamagazine.org/does-nevens-law-describe-quantum-computings-rise-20190618/

Link to Scientific American article: https://www.scientificamerican.com/article/a-new-law-suggests-quantum-supremacy-could-happen-this-year/

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