Computation on a Noiseless Quantum Code and Symmetrization

Abstract

Let $\mathcal{H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra $\mathcal{L}.$ Suppose $\mathcal{L}$ admits a noiseless quantum code i.e., a subspace $\mathcal{C}\subset \mathcal{H}$ annihilated by $\mathcal{L}.$ We show that a universal set of gates over $\mathcal{C}$ is obtained by any generic pair of $\mathcal{L}$-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 $\mathcal{L}.$ Any computation can then be performed completely within the coding decoherence-free subspace.

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

References in corpus (7)

• Decoherence Free Subspaces for Quantum Computation
• Dynamical Decoupling of Open Quantum Systems
• Quantum Computing
• Noiseless Quantum Codes
• Preserving coherence in quantum computation by pairing quantum bits
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