Random Stimuli Generation for the Verification of Quantum Circuits

TL;DR

This paper explores methods for generating random stimuli to verify quantum circuits efficiently, demonstrating high error detection rates with minimal stimuli through theoretical analysis and extensive simulations.

Contribution

Introduces and analyzes three schemes for quantum stimuli generation, balancing error detection and efficiency, supported by theoretical and empirical validation.

Findings

High error detection rates achieved with few stimuli

Three schemes offer trade-offs between efficiency and accuracy

Approximately 10^6 simulations across 50,000 benchmarks conducted

Abstract

Verification of quantum circuits is essential for guaranteeing correctness of quantum algorithms and/or quantum descriptions across various levels of abstraction. In this work, we show that there are promising ways to check the correctness of quantum circuits using simulative verification and random stimuli. To this end, we investigate how to properly generate stimuli for efficiently checking the correctness of a quantum circuit. More precisely, we introduce, illustrate, and analyze three schemes for quantum stimuli generation---offering a trade-off between the error detection rate (as well as the required number of stimuli) and efficiency. In contrast to the verification in the classical realm, we show (both, theoretically and empirically) that even if only a few randomly-chosen stimuli (generated from the proposed schemes) are considered, high error detection rates can be achieved for quantum circuits. The results of these conceptual and theoretical considerations have also been empirically confirmed---with a grand total of approximately $10^6$ simulations conducted across 50 000 benchmark instances.