Error Mitigation in Quantum Computers subject to 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 give criteria to assess the suitability of candidate quantum circuits to carry out a given task. This is achieved by defining measures of decoherence that are local in Hilbert space, identifying "good" and "bad" regions of the space. Quantum circuits that stay in the "good" regions are superior. Finally, we point out ways in which the improvement of few-qubit systems can be extended to large-scale quantum computation. The basic conceptual theme of the work is the generalization of the concept of decoherence-free subspaces in order to treat the case of arbitrary spatial correlations.