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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 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 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.

Abstract:

We describe how physics of computation determines computational complexity. In particular we show how quantum phenomena lead to qualitatively new modes of computation. An ideal quantum computer would allow to face certain tasks out of reach of classical computers, the factorization problem being the most striking example. Experimentally, however, implementation of quantum computation faces some serious difficulties due to an interaction with the environment which causes decoherence. We mention quantum error-correction as a process which can, to some extent, protect quantum computers from unwelcome effects of dissipation and decoherence. This is a brief, introductory review of quantum computation. It is based on [1].

Abstract:

Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an `entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and single-qubit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted message.

Abstract:

We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming and the Gilbert-Varshamov bounds and comment on the practical implementation of quantum codes.