Computation on a Noiseless Quantum Code and Symmetrization

Details Computation on a Noiseless Quantum Code and Symmetrization Computation on a Noiseless Quantum Code and Symmetrization

1999-01-16

arxiv.org/abs/quant-ph/9901047v2

Phys. Rev. A 60 (1999) R729

Physics

Quantum Physics

One result added, to appear in Phys. Rev. A (RC) 4 pages LaTeX, no figures

Scientific paper

10.1103/PhysRevA.60.R729

Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant gates. Such gates - if not available from the outset - can be obtained by resorting to a symmetrization with respect to the group generated by ${\cal L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.

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