Fidelity decay and error accumulation in random quantum circuits

Abstract: We present a comprehensive analysis of fidelity decay and error accumulation in faulty quantum circuit models. Our work devises an analytical bound for the average fidelity between desired and faulty output states, accounting for errors that may arise during the implementation of two-qubit gates and multi-qubit permutations. It is shown that fidelity decays exponentially with both circuit depth and the number of qubits raised to an architecture-dependent power, and determine the decay rates as a function of the two types of errors. Furthermore, we establish a robust linear relationship between fidelity and the heavy output frequency used in Quantum Volume tests to benchmark quantum processors, under the considered errors protocol. These findings pave the way for predicting the behavior of fidelity in the presence of specific errors and offer insights into the best strategies for increasing Quantum Volume.