“Quantum computers are starting to approach the limit of classical simulation and it is important that we continue to benchmark progress and to ask how difficult they are to simulate. This is a fascinating scientific question.
Recent advances in quantum computing have resulted in two 53-qubit processors: one from our group in IBM and a device described by Google in a paper published in the journal Nature. In the paper, it is argued that their device reached “quantum supremacy” and that “a state-of-the-art supercomputer would require approximately 10,000 years to perform the equivalent task.” We argue that an ideal simulation of the same task can be performed on a classical system in 2.5 days and with far greater fidelity. This is in fact a conservative, worst-case estimate, and we expect that with additional refinements the classical cost of the simulation can be further reduced.
Because the original meaning of the term “quantum supremacy,” as proposed by John Preskill in 2012, was to describe the point where quantum computers can do things that classical computers can’t, this threshold has not been met.
This particular notion of “quantum supremacy” is based on executing a random quantum circuit of a size infeasible for simulation with any available classical computer. Specifically, the paper shows a computational experiment over a 53-qubit quantum processor that implements an impressively large two-qubit gate quantum circuit of depth 20, with 430 two-qubit and 1,113 single-qubit gates, and with predicted total fidelity of 0.2%. Their classical simulation estimate of 10,000 years is based on the observation that the RAM memory requirement to store the full state vector in a Schrödinger-type simulation would be prohibitive, and thus one needs to resort to a Schrödinger-Feynman simulation that trades off space for time.
The concept of “quantum supremacy” showcases the resources unique to quantum computers, such as direct access to entanglement and superposition. However, classical computers have resources of their own such as a hierarchy of memories and high-precision computations in hardware, various software assets, and a vast knowledge base of algorithms, and it is important to leverage all such capabilities when comparing quantum to classical.
When their comparison to classical was made, they relied on an advanced simulation that leverages parallelism, fast and error-free computation, and large aggregate RAM, but failed to fully account for plentiful disk storage. In contrast, our Schrödinger-style classical simulation approach uses both RAM and hard drive space to store and manipulate the state vector. Performance-enhancing techniques employed by our simulation methodology include circuit partitioning, tensor contraction deferral, gate aggregation and batching, careful orchestration of collective communication, and well-known optimization methods such as cache-blocking and double-buffering in order to overlap the communication transpiring between and computation taking place on the CPU and GPU components of the hybrid nodes. Further details may be found in Leveraging Secondary Storage to Simulate Deep 54-qubit Sycamore Circuits.
Our simulation approach features a number of nice properties that do not directly transfer from the classical to quantum worlds. For instance, once computed classically, the full state vector can be accessed arbitrarily many times. The runtime of our simulation method scales approximately linearly with the circuit depth (see Figure 1 above), imposing no limits such as those owing to the limited coherence times. New and better classical hardware, code optimizations to more efficiently utilize the classical hardware, not to mention the potential of leveraging GPU-direct communications to run the kind of supremacy simulations of interest, could substantially accelerate our simulation.
Building quantum systems is a feat of science and engineering and benchmarking them is a formidable challenge. Google’s experiment is an excellent demonstration of the progress in superconducting-based quantum computing, showing state-of-the-art gate fidelities on a 53-qubit device, but it should not be viewed as proof that quantum computers are “supreme” over classical computers.
It is well known in the quantum community that we at IBM are concerned of where the term “quantum supremacy” has gone. The origins of the term, including both a reasoned defense and a candid reflection on some of its controversial dimensions, were recently discussed by John Preskill in a thoughtful article in Quanta Magazine. Professor Preskill summarized the two main objections to the term that have arisen from the community by explaining that the “word exacerbates the already overhyped reporting on the status of quantum technology” and that “through its association with white supremacy, evokes a repugnant political stance.”
Both are sensible objections. And we would further add that the “supremacy” term is being misunderstood by nearly all (outside of the rarified world of quantum computing experts that can put it in the appropriate context). A headline that includes some variation of “Quantum Supremacy Achieved” is almost irresistible to print, but it will inevitably mislead the general public. First because, as we argue above, by its strictest definition the goal has not been met. But more fundamentally, because quantum computers will never reign “supreme” over classical computers, but will rather work in concert with them, since each have their unique strengths.
For the reasons stated above, and since we already have ample evidence that the term “quantum supremacy” is being broadly misinterpreted and causing ever growing amounts of confusion, we urge the community to treat claims that, for the first time, a quantum computer did something that a classical computer cannot with a large dose of skepticism due to the complicated nature of benchmarking an appropriate metric.
For quantum to positively impact society, the task ahead is to continue to build and make widely accessible ever more powerful programmable quantum computing systems that can implement, reproducibly and reliably, a broad array of quantum demonstrations, algorithms and programs. This is the only path forward for practical solutions to be realized in quantum computers.
A final thought. The concept of quantum computing is inspiring a whole new generation of scientists, including physicists, engineers, and computer scientists, to fundamentally change the landscape of information technology. If you are already pushing the frontiers of quantum computing forward, let’s keep the momentum going. And if you are new to the field, come and join the community. Go ahead and run your first program on a real quantum computer today.
The best is yet to come.”