Decoherence-Free Subspaces for Quantum Computation

TLDR

Decoherence in quantum computers is modeled via a semigroup framework where error generators correspond to Lie algebra generators, encompassing the spin‑boson model as a special case. The study presents a generic condition for error‑free quantum computation, identifying decoherence‑free subspaces as those spanned by states annihilated by all error generators. These subspaces are shown to be perturbation‑stable and support universal quantum computation.

Abstract

Decoherence in quantum computers is formulated within the Semigroup approach. The error generators are identified with the generators of a Lie algebra. This allows for a comprehensive description which includes as a special case the frequently assumed spin-boson model. A generic condition is presented for error-less quantum computation: decoherence-free subspaces are spanned by those states which are annihilated by all the generators. It is shown that these subspaces are stable to perturbations and moreover, that universal quantum computation is possible within them.