A very interesting paper from IBM Quantum Computing Team as an answer to the famous leaked preprint of Google regarding quantum supremacy.
Recent advances in quantum computing have resulted in two 53-qubit processors: one from our group in IBM and a device described in the leaked preprint from Google. In the preprint, 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.
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 preprint 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.
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.
A headline that includes some variation of “Quantum Supremacy Achieved” is almost irresistible to print, but it will inevitably mislead the general public.