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arXiv:cond-mat/0405694

Studies of Short-Time Decoherence for Evaluation of Quantum Computer Designs

Vladimir Privman A, Denis Tolkunov

Published May 29, 2004• 0 citations
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Abstract

We review our recent results on short time approximations, with emphasis on applications for which the system-environment interactions involve a general non-Hermitian system operator and its conjugate. We evaluate the onset of decoherence at low temperatures in open quantum systems. The developed approach is complementary to Markovian approximations and appropriate for evaluation of quantum computing schemes. Example of a spin system coupled to a bosonic heat bath is discussed.

DOI
10.48550/arxiv.cond-mat/0405694

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We review our recent results on short time approximations, with emphasis on applications for which the system-environment interactions involve a general non-Hermitian system operator and its conjugate. We evaluate the onset of decoherence at low temperatures in open quantum systems. The developed approach is complementary to Markovian approximations and appropriate for evaluation of quantum computing schemes. Example of a spin system coupled to a bosonic heat bath is discussed.
A short-time approximation is developed for system-environmental bath mode interactions involving a general non-Hermitian system operator $\ensuremath{\Lambda}$ and its conjugate ${\ensuremath{\Lambda}}^{\ifmmode\dagger\else\textdagger\fi{}}$ in order to evaluate the onset of decoherence at low temperatures in quantum systems interacting with the environment. The developed approach is complementary to Markovian approximations and appropriate for the evaluation of quantum computing schemes. An example of a spin system coupled to a bosonic heat bath via $\ensuremath{\Lambda}\ensuremath{\propto}{\ensuremath{\sigma}}_{\ensuremath{-}}$ is worked out in detail.
We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.
We study the stability of the coherence of a state of a quantum system under the effect of an interaction with another quantum system at short time. We find an expression for evaluating the order of magnitude of the time scale for the onset of instability as a function of the initial state of both involved systems and of the sort of interaction between them. As an application we study the spin-boson interaction in the dispersive interaction regime, driven by a classical field. We find, for this model, that the behavior of the time scale for the onset of instability, with respect to the boson bath temperature, changes depending on the intensity of the classical field.