Stabilization of Quantum Computations by Symmetrization

1997/10/01 by Adriano Barenco, André Berthiaume, David Deutsch +3 · 243 citations
Computer Science · Mathematics · #Algorithm #Artificial intelligence #Combinatorics #Computation #Computer science #Context (archaeology) #Mathematics #Neural Networks and Reservoir Computing #Open quantum system #Physics #Projection (relational algebra) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum computer #Quantum mechanics #Quantum operation #Quantum state #State (computer science) #State space #Subspace topology #Symmetrization #Theoretical computer science #Unitary state

paper · doi:10.1137/s0097539796302452

published in SIAM Journal on Computing 26(5), 1541-1557 (Society for Industrial and Applied Mathematics)

openalex publication_date 1997/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We propose a method for the stabilization of quantum computations (including quantum state storage). The method is based on the operation of projection into \cal SYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an efficient algorithm and quantum network effecting \cal SYM--projection and discuss the stabilizing effect of the proposed method in the context of unitary errors generated by hardware imprecision, and nonunitary errors arising from external environmental interaction. Finally, limitations of the method are discussed.

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