Dynamical description of quantum computing: Generic nonlocality of quantum noise

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.