Classical Sampling of Random Quantum Circuits with Bounded Fidelity

Random circuit sampling has become a popular means for demonstrating the superiority of quantum computers over classical supercomputers. While quantum chips are evolving rapidly, classical sampling algorithms are also getting better and better. The major challenge is to generate bitstrings exhibiting an XEB fidelity above that of the quantum chips. Here we present a classical sampling algorithm for producing the probability distribution of any given random quantum circuit, where the fidelity can be rigorously bounded. Specifically, our algorithm performs rejection sampling after the introduced very recently multi-tensor contraction algorithm. We show that the fidelity can be controlled by partially contracting the dominant paths in the tensor network and by adjusting the number of batches used in the rejection sampling. As a demonstration, we classically produced 1 million samples with the fidelity bounded by 0.2%, based on the 20-cycle circuit of the Sycamore 53-qubit quantum chip. Though this task was initially estimated to take 10,000 years on the Summit supercomputer, it took about 14.5 days using our algorithm on a relatively small cluster with 32 GPUs (Tesla V100 16GB). Furthermore, we estimate that for the Zuchongzhi 56-qubit 20-cycle circuit one can produce 1M samples with fidelity 0.066% using the Selene supercomputer with 4480 GPUs (Tesla A100 80GB) in about 4 days.