Abstract

In this talk, I will introduce two tensor-network methods targeting the sampling problem of the Sycamore circuits. The first method computes amplitudes and probabilities for a large number of correlated bitstrings. The obtained results verify the Porter-Thomas distribution of the large and deep quantum circuits of Google and can be used for spoofing the linear cross entropy benchmark of quantum supremacy using a post-sampling approach. The second method can be used to generate one million uncorrelated bitstrings which are sampled from a final distribution of the Sycamore circuit with 53 qubits and 20 cycles. With the approximate state having fidelity of roughly 0.0037. The whole computation has cost about 15 hours on a computational cluster with 512 GPUs. 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.