Dynamical description of quantum computing: Generic nonlocality of quantum noise

Abstract

We develop a dynamical non-Markovian description of quantum computing in the weak-coupling limit, in the lowest-order approximation. We show that the long-range memory of the quantum reservoir (such as the ${1/t}^{4}$ one exhibited by electromagnetic vacuum) produces a strong interrelation between the structure of noise and the quantum algorithm, implying nonlocal attacks of noise. This shows that the implicit assumption of quantum error correction theory---independence of noise and self-dynamics---fails in long time regimes. We also use our approach to present pure decoherence and decoherence accompanied by dissipation in terms of the spectral density of the reservoir. The so-called dynamical decoupling method is discussed in this context. Finally, we propose a minimal decoherence model, in which the only source of decoherence is vacuum. We optimize the fidelity of quantum-information processing under the trade-off between the speed of the gate and the strength of decoherence.