Solving the Sampling Problem of the Sycamore Quantum Circuits

We study the problem of generating independent samples from the output distribution of Google's Sycamore quantum circuits with a target fidelity, which is believed to be beyond the reach of classical supercomputers and has been used to demonstrate quantum supremacy. We propose a method to classically solve this problem by contracting the corresponding tensor network just once, and is massively more efficient than existing methods in generating a large number of uncorrelated samples with a target fidelity. For the Sycamore quantum supremacy circuit with 53 qubits and 20 cycles, we have generated 1 ×10⁶ uncorrelated bitstrings s which are sampled from a distribution P ^(s )=|ψ ^(s )|² , where the approximate state ψ ^ has fidelity F ≈0.0037 . The whole computation has cost about 15 h on a computational cluster with 512 GPUs. The obtained 1 ×10⁶ samples, the contraction code and contraction order are made public. If our algorithm could be implemented with high efficiency on a modern supercomputer with ExaFLOPS performance, we estimate that ideally, the simulation would cost a few dozens of seconds, which is faster than Google's quantum hardware.