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arXiv:quant-ph/0202141 · Journal of Physics A Mathematical and General

Robust control of decoherence in realistic one-qubit quantum gates

V. Protopopescu, R Perez, C D Helon, J Schmulen

Published Feb 12, 2003• 21 citations
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Abstract

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.

DOI
10.1088/0305-4470/36/8/314

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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 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.
We present an open-loop (bang–bang) scheme which drives an open two-level quantum system to any target state, while maintaining quantum coherence throughout the process. The control is illustrated by a realistic simulation for both adiabatic and thermal decoherence. In the thermal decoherence regime, the control achieved by the proposed scheme is qualitatively similar, at the ensemble level, to the control realized by the quantum feedback scheme of Wang, Wiseman and Milburn (2001 Phys. Rev. A 64 063810) for the spontaneous emission of a two-level atom. The performance of the open-loop scheme compares favourably against the quantum feedback scheme with respect to robustness, target fidelity and transition times.
A linear coupling model of a spin system with bosonic modes is a typical model to theoretically evaluate decoherence. In this contribution, we consider a dynamical control of decoherence of entanglement in a spin system consisting of an electron spin and nuclear spins (namely, a spin bus system) coupled with bosons whose modes are in resonance with individual spins. Numerical simulations show that bang-bang pulses with a realistic duty ratio can suppress decoherence considerably in an entangled two-qubit system. Simulation results indicate one phenomenon: a very large, as well as very small, dissipation rate of bosons results in a small decoherence.
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.