Stabilisation of Quantum Computations by Symmetrisation

Abstract

We propose a method for the stabilisation of quantum computations (including quantum state storage). The method is based on the operation of projection into $\mathcal{S}\mathcal{Y}\mathcal{M}$, the symmetric subspace of the full state space of $R$ redundant copies of the computer. We describe an efficient algorithm and quantum network effecting $\mathcal{S}\mathcal{Y}\mathcal{M}$--projection and discuss the stabilising 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.

20 pages LaTeX, 2 postscript figures

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