Demonstrating Circuit Benchmarking for Scalable and Efficient Fidelity Estimation

Determining the fidelity of a quantum circuit on actual quantum devices becomes impractical as the number of qubits increases. Here, we illustrate the theoretical concept of circuit benchmarking, an efficient and scalable protocol for estimating the actual fidelity of a circuit. Furthermore, we demonstrate that circuit benchmarking also offers performance guarantees for another important quantity of interest - the total variation distance (TVD) of a noisy circuit (under randomized compiling) with respect to its ideal distribution. A bound on the TVD enables a bound on the accuracy with which a quantum computer can estimate observables of interest under quantum simulation.