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arXiv:quant-ph/0602191 · IEEE Conference on Nanotechnology (IEEE NANO)

Decoherence of Dynamically Manipulated Qubits

Vladimir Privman A, Dmitry Solenov

Published Jan 1, 2006• 1 citation
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Abstract

We summarize our results on decoherence for short-to intermediate-time dynamics of an externally controlled two-state quantum system—a qubit—interacting with thermal bosonic environment. The developed approximation schemes are illustrated for an adiabatic model with time-dependent gate control, and for a model with rotating-wave gate function.

DOI
10.1109/nano.2006.1717240

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We summarize our results on decoherence for short-to intermediate-time dynamics of an externally controlled two-state quantum system—a qubit—interacting with thermal bosonic environment. The developed approximation schemes are illustrated for an adiabatic model with time-dependent gate control, and for a model with rotating-wave gate function.
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 present an open-loop (bang-bang) scheme to control decoherence in a generic one-qubit quantum gate and implement it in a realistic simulation. The system is consistently described within the spin-boson model, with interactions accounting for both adiabatic and thermal decoherence. The external control is included from the beginning in the Hamiltonian as an independent interaction term. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. The controls are determined exactly from the condition to eliminate decoherence, i.e. to restore unitarity. Numerical simulations show excellent performance and robustness of the proposed control scheme.
We present a rigorous analysis of the phenomenon of decoherence for general N -level quantum systems coupled a reservoir modelled by a thermal bosonic quantum environment. We present an explicit form of the dominant reduced dynamics of open systems. We give explicit results for a spin 1/2 (qubit), including decoherence and thermalization times. Our approach is based on a dynamical theory of quantum resonances. It yields the exact reduced dynamics of the small system and does not involve master equation or van Hove limit approximations. This approach is suitable for a wide variety of systems which are not explicitly solvable, including systems of interacting spins (registers of interacting qubits), for which the coupling between the system and the environment is fixed but small.
We present an open loop (bang-bang) scheme to control decoherence in a quantum NOT gate and implement it in a realistic simulation. The system is consistently described within the spin-boson model, with interactions accounting for both adiabatic and thermal decoherence. The external control is included from the beginning in the Hamiltonian as an independent interaction term. After tracing out the environment modes, reduced equations are obtained for the two-level system in which the effects of both decoherence and external control appear explicitly. The controls are determined exactly from the condition to eliminate decoherence, i.e. to restore unitarity. Numerical simulations show excellent performance and robustness of the proposed control scheme.