  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
describe an implementation of averaged circuit eigenvalue sampling (ACES), a
general framework for the scalable noise characterisation of quantum circuits.
ACES is capable of simultaneously estimating the Pauli error probabilities of
all gates in a Clifford circuit, and captures averaged spatial correlations
between gates implemented simultaneously in the circuit. By rigorously
analysing the performance of ACES experiments, we derive a figure of merit for
their expected performance, allowing us to optimise ACES experimental designs
and improve the precision to which we estimate noise given fixed experimental
resources. Since the syndrome extraction circuits of quantum error correcting
codes are representative components of a fault-tolerant architecture, we
demonstrate the scalability and performance of our ACES 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 AveragedCircuitEigenvalueSampling.jl.
