Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments

Abstract

Today’s experimental noisy quantum processors can compete with and surpass all known algorithms on state-of-the-art supercomputers for the computational benchmark task of Random Circuit Sampling (Boixo et al., 2018, Arute et al., 2019, Wu et al., 2021, Zhu et al., 2022, Morvan et al., 2023). Additionally, a circuit-based quantum simulation of quantum information scrambling (Mi et al., 2021), which measures a local observable, has already outperformed standard full wave function simulation algorithms, e.g., exact Schrodinger evolution and Matrix Product States (MPS). However, this experiment has not yet surpassed tensor network contraction for computing the value of the observable. Based on those studies, we provide a unified framework that utilizes the underlying effective circuit volume to explain the tradeoff between the experimentally achievable signal-to-noise ratio for a specific observable, and the corresponding computational cost. We apply this framework to recent quantum processor experiments of Random Circuit Sampling (Morvan et al., 2023), quantum information scrambling (Mi et al., 2021), and a Floquet circuit unitary (Kim et al., 2023). This allows us to reproduce the results of Ref. (Kim et al., 2023) in less than one second per data point using one GPU.