Fair Sampling Error Analysis on NISQ Devices

Abstract

We study the status of fair sampling on Noisy Intermediate Scale Quantum (NISQ) devices, in particular the IBM Q family of backends. Using the recently introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate fair sampling circuits to solve six problems of varying difficulty, each with several optimal solutions, which we then run on twenty backends across the IBM Q system. For a given circuit evaluated on a specific set of qubits, we evaluate: how frequently the qubits return an optimal solution to the problem, the fairness with which the qubits sample from all optimal solutions, and the reported hardware error rate of the qubits. To quantify fairness, we define a novel metric based on Pearson’s χ 2 test. We find that fairness is relatively high for circuits with small and large error rates, but drops for circuits with medium error rates. This indicates that structured errors dominate in this regime, while unstructured errors, which are random and thus inherently fair, dominate in noisier qubits and longer circuits. Our results show that fairness can be a powerful tool for understanding the intricate web of errors affecting current NISQ hardware.

Quantum Volume in Practice: What Users Can Expect From NISQ Devices

“…Other NISQ benchmarks, such as CLOPS for quantifying execution speed, should also continue to be evaluated in order to provide additional context for the performance of these backends. Another future research area is to quantify the correlation between NISQ benchmarks (such as QV) and error metrics such as aggregate error [45], [23], cross-talk, and average qubit fidelity. On average it is clear that error rates, as well as connectivity and compilers, are the primary factors impacting NISQ device performance.…”

Multi-round QAOA and advanced mixers on a trapped-ion quantum computer

“…Fairness of the sampling result can be quantified as the discrepancy between the ideal ground state distribution Q 2 and the experimentally measured ground state distribution Q 1 , which is obtained by post-selecting out all ground states from 4000 experimental shots. The first method we adopt is the 'shots to reject' method, proposed in reference [32], which is constructed based on the chi-squared (χ 2 ) test. By re-sampling from Q 1 , the goal is to compute the number of samples, N * , needed to reject the null hypothesis H 0 at a selected significance level.…”

“…Other important tasks relying on fair sampling include satisfiability-based membership filters [24][25][26], proportional model sampling [27], machine learning [28,29], and sampling the ground states of arbitrary classical spin Hamiltonians [30,31]. Although in theory G-QAOA fairly samples ground states at any p, the total probability of finding ground states increases with p. While previous works have experimentally demonstrated one round of G-QAOA in Hamiltonian optimization problems on unweighted graphs [32,33], we apply G-QAOA to both weighted and unweighted graph problems up to p = 2 on arbitrary graphs, and quantitatively evaluate the experimental fair sampling results.…”

Entropic property of randomized QAOA circuits

“…The entropy values of these pseudo-Boltzman distributions turned out to be higher than for random states with the same energy. Another output distribution property being theoretically and experimentally studied in the QAOA context (for Grover Mixer-QAOA) is 'fair sampling': uniformity of sampling among optimal solutions [19][20][21].…”