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

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. Additionally, a circuit-based quantum simulation of quantum information scrambling, which measures a local observable, has already outperformed standard full wave function simulation algorithms, such as, exact Schrodinger evolution and Matrix Product States (MPS). Nevertheless, this experiment has not yet surpassed tensor network contraction for computing the value of the observable.

In my presentation I will review the concept of circuit volume and how it can be used to explain the tradeoff between the experimentally achievable signal-to-noise ratio for a specific observable, and the corresponding computational cost. I will also describe the application of the circuit volume to recent quantum processor experiments of Random Circuit Sampling, quantum information scrambling, and a Floquet circuit unitary.