Studies in a random noise model of decoherence

Studies in a random noise model of decoherence We study the effects of noise and decoherence for a double-potential well system, suitable for the fabrication of qubits and quantum logic elements. A random noise term is added to the hamiltonian, the resulting wavefunction found numerically and the density matrix obtained by averaging over noise signals. Analytic solutions using the two-state model are obtained and found to be generally in agreement with the numerical calculations. In particular, a simple formula for the decoherence rate in terms of the noise parameters in the two-state model is reviewed and verified for the full simulation with the multi-level system. The formalism is extended to describe multiple sources of noise or different “dephasing” axes at the same time. Furthermore, the old formula for the “Turing-Watched Pot” effect is generalized to the case where the environmental interactions do not conserve the “quality” in question. Various forms for the noise signal are investigated. An interesting result is the importance of the noise power at low frequency. If it vanishes there is, in leading order, no decoherence. This is verified in a numerical simulation where two apparently similar noise signals, but differing in the power at zero frequency, give strikingly different decoherence effects. A short discussion of situations dominated by low frequency noise is given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Studies in a random noise model of decoherence

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Publisher
Springer US
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Physics; Mathematics, general; Quantum Physics; Physics, general; Theoretical, Mathematical and Computational Physics; Computer Science, general
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-010-0224-8
Publisher site
See Article on Publisher Site

Abstract

We study the effects of noise and decoherence for a double-potential well system, suitable for the fabrication of qubits and quantum logic elements. A random noise term is added to the hamiltonian, the resulting wavefunction found numerically and the density matrix obtained by averaging over noise signals. Analytic solutions using the two-state model are obtained and found to be generally in agreement with the numerical calculations. In particular, a simple formula for the decoherence rate in terms of the noise parameters in the two-state model is reviewed and verified for the full simulation with the multi-level system. The formalism is extended to describe multiple sources of noise or different “dephasing” axes at the same time. Furthermore, the old formula for the “Turing-Watched Pot” effect is generalized to the case where the environmental interactions do not conserve the “quality” in question. Various forms for the noise signal are investigated. An interesting result is the importance of the noise power at low frequency. If it vanishes there is, in leading order, no decoherence. This is verified in a numerical simulation where two apparently similar noise signals, but differing in the power at zero frequency, give strikingly different decoherence effects. A short discussion of situations dominated by low frequency noise is given.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 23, 2011

References

  • On the relaxation of an N-level system under gauss noise
    Khriplovich, I.B.; Sokolov, V.V.

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