Scalable noise characterization of syndrome-extraction circuits with averaged circuit eigenvalue sampling

Characterising the performance of noisy quantum circuits is central to the production of prototype quantum computers and can enable improved quantum error correction that exploits noise biases identified in a quantum device. We develop a scalable noise characterisation protocol suited to characterising the syndrome extraction circuits of quantum error correcting codes, a key component of fault-tolerant architectures. Our protocol builds upon averaged circuit eigenvalue sampling (ACES), a framework for noise characterisation experiments that simultaneously estimates the Pauli error probabilities of all gates in a Clifford circuit and captures averaged spatial correlations between gates implemented simultaneously in the layers of the circuit. By rigorously analysing the performance of noise characterisation experiments in the ACES framework, we derive a figure of merit for their expected performance, allowing us to optimise their experimental design and improve the precision to which we estimate noise given fixed experimental resources. We demonstrate the scalability and performance of our protocol through circuit-level numerical simulations of the entire noise characterisation procedure for the syndrome extraction circuit of a distance-25 surface code with over 1000 qubits. Our results indicate that detailed noise characterisation methods are scalable to near-term quantum devices. We release our code in the form of the Julia package QuantumACES.