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arXiv:quant-ph/9604028

Stabilisation of Quantum Computations by Symmetrisation

Adriano Barenco, Berthiaume, Andre`, David Deutsch, ARTUR K. EKERT, Richard Jozsa, Chiara Macchiavello

Published Apr 25, 1996• 18 citations
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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 $\cal SYM$, 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 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.

DOI
10.48550/arxiv.quant-ph/9604028

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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\cal SYMSYM, the symmetric subspace of the full state space of RRR redundant copies of the computer. We describe an efficient algorithm and quantum network effecting SYM\cal SYMSYM--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.
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We propose a method for the stabilization of quantum computations (including quantum state storage). The method is based on the operation of projection into SYM\cal SYMSYM, the symmetric subspace of the full state space of R redundant copies of the computer. We describe an efficient algorithm and quantum network effecting SYM\cal SYMSYM--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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This is a brief description of how to protect quantum states from dissipation and decoherence that arise due to uncontrolled interactions with the environment. We discuss recoherence and stabilisation of quantum states based on two techniques known as "symmetrisation" and "quantum error correction". We illustrate our considerations with the most popular quantum-optical model of the system-environment interaction, commonly used to describe spontaneous emission, and show the benefits of quantum error correction in this case.
All free-space quantum communications require the use of a quantum channel, which transports quantum bits in such a way that the quantum mechanical states of the qubits remain preserved from one end of the channel to the other one. In quantum computing the classical error coding methods could not be used, however we can construct a classical channel with zero redundancy error correction for any unitary channel. In our basically new quantum error correction approach, the classical states are coded into the eigenvectors and unitary transformations. In this paper, we show that with our new algorithm it’s possible to create redundancy-free quantum error correction. We also consider the redundancy-free implementation of a unitary error correcting operator. Our protocol achieves the redundancy-free quantum communication using local unitary operations and unitary matrices. These solutions could be useful for the free-space quantum communication.