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Russian Scientists Investigate the Limits of Google's Quantum Processor Using a Supercomputer

The Laboratory for Quantum Information Processing at CPQM has collaborated with the CDISE supercomputer team "Zhores" to emulate Google's quantum processor. The team was able to identify a subtle effect lurking in Google's data by reproducing noiseless data using the same statistics as Google's recent experiments. The Skoltech team previously discovered this effect, dubbed a reachability deficit. The numerical analysis confirmed that Google's data was on the verge of a density-dependent avalanche, implying that future experiments will require significantly more quantum resources to perform quantum approximate optimization. Quantum, the field's preeminent journal, publishes the findings.


Since the dawn of numerical computing, quantum systems have appeared to be exceedingly difficult to emulate, though the precise reasons for this continue to be a source of active research. Nonetheless, the apparent inability of a classical computer to emulate a quantum system prompted several researchers to rewrite the story.


In the early 1980s, scientists such as Richard Feynman and Yuri Manin speculated that the unknown ingredients that make quantum computers difficult to emulate with a classical computer could be used as a computational resource. A quantum processor, for example, should be capable of simulating quantum systems, as they are governed by the same fundamental principles.


These early concepts eventually resulted in Google and other technology giants developing prototypes of the long-awaited quantum processors. These modern devices are prone to errors; they can only execute the simplest quantum programs, and each calculation must be repeated multiple times to average out the errors and form an approximation.


The quantum approximate optimization algorithm, or QAOA (pronounced "kyoo-ay-oh-AY"), is one of the most studied applications of these modern quantum processors. Google examined the performance of QAOA using 23 qubits and three tunable program steps in a series of dramatic experiments.


In a nutshell, QAOA is a method for solving optimization problems approximately using a hybrid setup consisting of a classical computer and a quantum co-processor. At the moment, prototypical quantum processors such as Google's Sycamore are limited to noisy and limited operations. The goal of a hybrid setup is to overcome some of these systematic limitations while still recovering quantum behavior to exploit, which makes approaches such as QAOA particularly appealing.


Skoltech scientists have recently made a number of significant discoveries regarding QAOA; for example, see this write-up. Among them is an effect that severely restricts the applicability of QAOA. They demonstrate that the density of an optimization problem — the ratio of its constraints to variables — acts as a significant impediment to obtaining approximate solutions. To overcome this performance constraint, additional resources in terms of operations performed on the quantum coprocessor are required. These discoveries were made with a pen and a piece of paper, as well as very small emulations. They were curious as to whether the effect they discovered recently manifested itself in Google's recent experimental study.


Skoltech's quantum algorithms lab then approached Oleg Panarin's CDISE supercomputing team for the substantial computing resources required to emulate Google's quantum chip. Senior Research Scientist Dr. Igor Zacharov of the Quantum Laboratory collaborated with several others to transform existing emulation software into a form that enables parallel computation on Zhores. After several months of work, the team succeeded in creating an emulation that produces data with the same statistical distributions as Google and demonstrated a range of instance densities below which QAOA performance degrades significantly. Additionally, they demonstrated that Google's data is on the cusp of this range, beyond which the current state of the art is incapable of producing any advantage.


Initially, the Skoltech team discovered that reachability deficits — a performance constraint induced by a problem's constraint-to-variable ratio — existed for a class of problems known as maximum constraint satisfiability. Google, on the other hand, considered graph energy function minimization. Due to the fact that these problems share the same complexity class, the team gained conceptual hope that the problems, and eventually the effect, could be related. This intuition proved to be accurate. The data was generated, and the findings demonstrated unequivocally that reachability deficits cause an avalanche effect, putting Google's data on the verge of this rapid transition, beyond which longer, more powerful QAOA circuits become necessary.


Oleg Panarin, Skoltech's manager of data and information services, stated, "We are overjoyed to see our computer pushed to its limits." The project was lengthy and difficult, and we developed this framework in collaboration with the quantum lab. We believe that this project establishes a benchmark for future Zhores-based demonstrations of this type.”


“We took existing code from Akshay Vishwanatahan, the study's first author, and turned it into a parallel program,” added Igor Zacharov, a senior research scientist at Skoltech. When the data finally appeared and we had the same statistics as Google, it was an exciting moment for all of us. We developed a software package for emulating various state-of-the-art quantum processors with up to 36 qubits and a dozen layers.”


According to Akshay Vishwanatahan, a PhD student at Skoltech, "moving beyond a few qubits and layers in QAOA was a significant challenge at the time." Our in-house emulation software was limited to toy-model scenarios, and I initially believed that this project, while exciting, would prove nearly impossible. Fortunately, I was surrounded by a group of optimistic and upbeat peers, which further motivated me to replicate Google's noiseless data. It was an exciting moment when our data matched Google's, with a similar statistical distribution, allowing us to finally see the effect."

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