Chemistry and Physics of Quantum Materials (CPQM) Laboratory for Quantum Information Processing has collaborated with Computational and Data Science and Engineering (CDISE) supercomputing team known as ‘Zhores’ to mimic the quantum processor by Google. The collaborative team were able to point out a subtle effect lurking in Google’s data with the reproduction of noiseless data using the same statistics used in Google’s recent experiments, in the results published in the field’s leading journal Quantum.
The subtle effect dubbed the ‘reachability deficit’, discovered by the past researches of the Skoltech team had the numeric confirming that Google’s data was on the edge of a so-called, density-dependent avalanche, an implication that future experiments will require more quantum resources in performing approximate optimization.
Quantum systems had in the past been exceedingly difficult to emulate and this was the inspiration needed for this crop of researchers to unlock the obvious difficulty. Eminent scientists in the 80’s like Richard Feynman and Yuri Manin aware of this difficulty had speculated that the unknown ingredients that may be factored in the imitation difficulty of quantum computers could be used as a computational resource. For instance, a quantum processor should be ideal in the stimulation of quantum systems, as they are governed by the same principles.
The ideas of these veteran scientists prompted Google and other tech giants to create prototype version of quantum processors but the modern devices can only be able to execute simple quantum programs and are error-prone.
One of the most studied applications of these modern day quantum processors is the quantum approximate optimization algorithm, or QAOA (pronounced “kyoo-ay-oh-AY”). Google in a series of dramatic experiments had used its processor to know the performance of QAOA with the use of 23 qubits and three tunable program steps.
The QAOA can be summed up as a process where optimization issues are solved with a hybrid setup that consisted of a computer and a quantum c0-processor. The use of the hybrid setup was to hopefully remove some of the systematic limitations, while still recovering quantum behaviour.
Scientists at Skoltech made a number of discoveries relating to QAOA; prominent among them an affect limits QAOA applicability. The researchers discovered that the ratio between the constraints and variables (density of optimization) could serve as a major barrier to achieving approximate solutions. It hence means that additional resources are required to overcome this performance limitation and the team wanted to see if the effect they recently discovered manifested itself in Google’s recent experimental study.
It is in lieu of this that Skoltech’s quantum algorithms lab approached the CDISE supercomputing team led by Oleg Panarin to have access to the important computing resources needed to imitate the quantum chip by Google.
After several months of collaboration, the team created emulation that outputs data with the same statistical distributions as Google and showed a range of instance densities at which QAOA performance sharply degrades. The team further showed that the data by Google was superimposed at the edge of this range beyond which the current state of the art would not suffice to produce any advantage.
The team also discovered that a performance limitation caused by a problem’s constraint-to-variable ratio known as reachability deficits was present for a kind of problem called maximum constraint satisfiability. The minimization of graph energy functions was however considered by Google. The team knowing that these problems belong to the same complexity class had the inkling and hope that the problems and effects could be related and they were later to be proven right. The data was then generated, with findings clearly showing that a type of avalanche effects are created by reachability deficits, an implication of Google’s data being a precursor to this rapid transition beyond which longer, more powerful QAOA circuits become a necessity.
Oleg Panarin, a manager of data and information services at Skoltech, commented: “We are very pleased to see our computer pushed to this extreme. The project was long and challenging and we’ve worked hand in glove with the quantum lab to develop this framework. We believe this project sets a baseline for future demonstrations of this type using Zhores.”
Igor Zacharov, a senior research scientist at Skoltech, added: “We took existing code from Akshay Vishwanatahan, the first author of this study, and turned it into a program that ran in parallel. It was certainly an exciting moment for all of us when the data finally appeared, and we had the same statistics as Google. In this project, we created a software package that can now emulate various state-of-the-art quantum processors, with as many as 36 qubits and a dozen layers deep.”
Akshay Vishwanatahan, a PhD student at Skoltech, concluded: “Going past a few qubits and layers in QAOA was a significantly challenging task at the time. The in-house emulation software we developed could only address toy-model cases and I initially felt that this project, while an exciting challenge, would prove nearly impossible. Fortunately, I was amidst a group of optimistic and high-spirited peers and this further motivated me to follow through and reproduce Google’s noiseless data. It was certainly a moment of great excitement when our data matched Google’s, with a similar statistical distribution, from which we were finally able to see the effect’s presence.”
Reference: “Reachability Deficits in Quantum Approximate Optimization of Graph Problems” by V. Akshay, H. Philathong, I. Zacharov and J. Biamonte, 30 August 2021, Quantum.