Numerical method for finding decoherence-free subspaces and its applications

Abstract

In this work, inspired by the study of semidefinite programming for block-diagonalizing matrix *-algebras, we propose an algorithm that can find the algebraic structure of decoherence-free subspaces (DFS's) for a given noisy quantum channel. We prove that this algorithm will work for all cases with probability one, and it is more efficient than the algorithm proposed by Holbrook, Kribs, and Laflamme [Quant. Inf. Proc. 80, 381 (2003)]. In fact, our results reveal that this previous algorithm only works for special cases. As an application, we discuss how this method can be applied to increase the efficiency of an optimization procedure for finding an approximate DFS.

7 pages, 2 tables

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• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Quantum State Reduction: Generalized Bipartitions from Algebras of Observables
• Minimal noise subsystems
• Exact Model Reduction for Continuous-Time Open Quantum Dynamics
• No-go theorem for environment-assisted invariance in non-unitary dynamics