Error Mitigation in the Presence of Spatially Correlated Noise

The most common error models for quantum computers assume the
independence of errors on different qubits. However, most noise mechanisms
have some correlations in space. We show how to improve quantum information
processing for few-qubit systems when spatial correlations are present. This starts
with strategies to measure the correlations. Once the correlations have been
determined, we can define decoherence measures that are local in Hilbert space.
These measures yield criteria to assess the ability of different candidate
quantum circuits to carry out a given task with high fidelity. We show that
these criteria work in few-qubit systems. Finally, we point out ways in which
error mitigation in few-qubit systems can be extended to large-scale quantum
information processing.