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 SYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an e#cient algorithm and quantum network e#ecting SYM--projection and discuss the stabilising e#ect 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. 1 Introduction Any realistic model of computation must conform to certain requirements imposed not by the mathematical properties of the model but by the laws of physics. Computations which require an exponentially increasing precision or exponential amount of time, space, energy or any other physical resource are normally regarded as unrealistic and intractable. Any actual computational process is subject to unavoidab...