CPQM’s Laboratory for Quantum Information Processing collaborated with “Zhores,” a supercomputing team from CDISE, to imitate Google’s quantum processor. The team discovered a subtle effect in Google’s data by reproducing noiseless data using the same statistics as Google’s most recent experiments. The past work of the Skoltech team revealed this effect, which is called a reachability gap. The numerics showed that Google’s data was at the edge of a density-dependent avalanche. This means that future experiments will need significantly more quantum resources to optimize Quantum approximate. These results were published in the leading journal QuantumQuantum.
Quantum systems have been challenging to emulate since the beginning of numerical computing. However, active research continues to uncover the reasons. Researchers have attempted to change the story because of the apparent inability of a classical computer to emulate a quantum system.
In the 1980s, Richard Feynman (and Yuri Manin) speculated that the unidentified ingredients that make quantum computers challenging to emulate with a traditional computer could be used to create computational resources. A quantum processor, for example, should be able to simulate quantum systems because similar principles govern them.
These early ideas led to Google and other tech giants developing prototypes of long-awaited quantum processors. Modern devices can’t execute complex quantum programs. They are also error-prone. Each calculation must be repeated multiple times to eliminate errors and form approximate results.
One of the most popular applications of quantum processors today is the QuantumQuantum approximate optimization algorithm or QAOA. (pronounced “okay-okay”) Google’s processor was used to test QAOA performance with 23 qubits, three tunable program steps, and a series of dramatic experiments.
QAOA, in its simplest form, is a method that attempts to solve optimization problems using a hybrid computer-quantum co-processor setup. The current limitation of prototypical quantum processors like Google’s Sycamore is that they can only perform noisy and limited operations. A hybrid design can overcome some limitations while obtaining quantum behavior. This makes QAOA attractive.
Skoltech scientists made several discoveries regarding QAOA. For example, see the write-up. One of the most important is a limitation in the application of QAOA. These results show that an optimization problem’s density — the ratio of its variables and constraints — is a significant barrier to finding approximate solutions. Additional resources like quantum co-processor operations can overcome this performance limitation. These discoveries were made using pen and paper and very small emulations. They wanted to determine if the effect they discovered was reflected in Google’s most recent experimental study.
Skoltech’s Quantum Algorithms Lab approached the CDISE supercomputing group led by Oleg Panarin to obtain the enormous computing resources necessary to replicate Google’s quantum chip. Igor Zacharov, a senior researcher in the quantum lab, worked with others to convert the existing emulation into software that allows parallel computation on Zhores. The team created an emulation that outputs identical statistical distributions to Google. It also showed a range at which QAOA performance severely degrades. Further, they found that Google’s data was at the edge of this range. This is beyond what the current state-of-the-art could not produce advantages.
The Skoltech team initially found that reachability deficits — a performance limitation induced by a problem’s constraint-to-variable ratio — were present for a problem called maximum constraint satisfiability. Google, however, considered minimizing graph energy functions. These problems were at the same complexity level, which gave the team the conceptual hope that they could be related. This intuition proved to be correct. The data was collected, and the results revealed that reachability deficiencies create an avalanche effect. This puts Google’s data at the edge of this rapid transition, beyond which longer, more powerful QAOA systems become necessary.
Oleg Panarin is a manager for data and information services at Skoltech. He said: “We are happy to see our computer being pushed to the extreme. This was a challenging project that took a long time. We worked closely with the quantum lab to create this framework. This project is a benchmark for future Zhores demonstrations.
Igor Zacharov is a senior research scientist at Skoltech. He added that “we took existing code from Akshay Vishiwanatahan, the first author of this study, and turned it into parallel programs. We had the same statistics as Google, which was a great moment for everyone. We created a software package to emulate different state-of-the-art quantum processors. It can have as many as 36 qubits.
Akshay Vishwanatahan is a Ph.D. student at Skoltech. He concluded, “Going beyond a few qubits or layers in QAOA wasn’t easy.” Although the in-house emulation software was limited to cases involving toys, this would be a challenging project. I was fortunate to be surrounded by optimistic and high-spirited colleagues, which further motivated me to reproduce Google’s noiseless data. It was a great moment when our data matched Google’s with similar statistical distributions. We were finally able to see the effect’s existence.
