Estimation of coherent error sources from stabilizer measurements

Abstract

In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information gained from these measurements to characterize and then counteract a coherent source of errors; that is, to determine all the parameters of an error channel that applies a fixed - but unknown - unitary operation to the physical qubits. Such a channel is generated, e.g., by local stray fields that act on the qubits. We study the case in which each qubit of a given graph state may see a different error channel and we focus on channels given by a rotation on the Bloch sphere around either the ◯, the ŷ, or the ẑ axis, for which analytical results can be given in a compact form. The possibility of reconstructing the channels at all qubits depends nontrivially on the topology of the graph state. We prove via perturbation methods that the reconstruction process is robust and supplement the analytic results with numerical evidence.