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The most common error models for quantum computers assume the independence oferrors on different qubits. However, most noise mechanisms have somecorrelations in space. We show how to improve quantum information processingfor few-qubit systems when spatial correlations are present. This starts withstrategies to measure the correlations. Once the correlations have beendetermined, we can give criteria to assess the suitability of candidate quantumcircuits to carry out a given task. This is achieved by defining measures ofdecoherence that are local in Hilbert space, identifying "good" and "bad"regions of the space. Quantum circuits that stay in the "good" regions aresuperior. Finally, we point out ways in which the improvement of few-qubitsystems can be extended to large-scale quantum computation. The basicconceptual theme of the work is the generalization of the concept ofdecoherence-free subspaces in order to treat the case of arbitrary spatialcorrelations.

Error Mitigation in Quantum Computers subject to Spatially Correlated Noise