Multi-Tensor Contraction for XEB Verification of Quantum Circuits

Classical Sampling of Random Quantum Circuits with Bounded Fidelity

“…Though the computational cost of our algorithm is similar to the one from [15], the former comes with a rigorous analysis of the fidelity, while the latter is only justified by empirical estimates. Moreover, in the current paper, we also independently confirm our analytical estimates of the fidelity using the verification algorithm from [19].…”

“…In general, for a quantum circuit C, by a standard procedure proposed in [6], to produce multiple independent random samples, one needs to calculate multiple independent batches of amplitudes, which is usually a difficult computing task. However, the multi-tensor simulator from [19] provides a much more efficient way to accomplish this task by utilizing a global cache which can reuse some intermediate tensors to significantly save the computing time. The algorithm from [19] also uses the simulated annealing method to optimize the contraction tree and the list of sliced variables.…”

“…However, the multi-tensor simulator from [19] provides a much more efficient way to accomplish this task by utilizing a global cache which can reuse some intermediate tensors to significantly save the computing time. The algorithm from [19] also uses the simulated annealing method to optimize the contraction tree and the list of sliced variables. Let us remind that a contraction tree [10,21,22] encodes a particular way we perform the contraction for a given tensor network.…”

“…Unfortunately, for a large number of samples the computational cost of this approach is quite high if the batches are calculated independently one by one. At the same time, it was shown recently [19] that by applying the multi-tensor contraction algorithm, which reuses the partial contraction results, one can reduce the computational cost in this case by several orders of magnitude. In fact, it is shown in [19] that not only the sampling task but also the much harder verification task for RQCs, where one needs to find the exact amplitudes for a large collection of uncorrelated bitstrings, can also be solved in several days on a modern supercomputer though it was initially estimated in [6] to take millions of years.…”

“…Update. Recently, after all the experiments in the current paper were already finished we became aware of the work [15], where an approach, very similar to the multi-tensor contraction algorithm from [19], was used in combination with other techniques to significantly reduce the simulation time. Though the computational cost of our algorithm is similar to the one from [15], the former comes with a rigorous analysis of the fidelity, while the latter is only justified by empirical estimates.…”