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arXiv:0911.4368 · Quantum Information Processing

Studies in a random noise model of decoherence

P. Korcyl, J. Wosiek, Leo Stodolsky

Published Jan 22, 2011• 2 citations
arXivHTMLPDF
DOI
10.1007/s11128-010-0224-8

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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. 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.
We study the domain of applicability of the classical telegraph noise model in the study of decoherence in qubits. We investigate the decoherence of a qubit coupled to either a quantum fluctuator, a quantum two-level system (TLS) again coupled to an environment, or to a classical fluctuator modeled by random telegraph noise. In order to do this, we construct a model for the quantum fluctuator where we can adjust the temperature of its environment, and the decoherence rate independently. The model has a well-defined classical limit at any temperature and this corresponds to the appropriate random telegraph process, which is symmetric at high temperatures and becomes asymmetric at low temperatures. We find that the difference in the qubit decoherence rates predicted by the two models depends on the ratio between the qubit-fluctuator coupling and the decoherence rate in the pointer basis of the fluctuator. This is then the relevant parameter, which determines whether the fluctuator, has to be treated quantum mechanically or can be replaced by a classical telegraph process. We also compare the mutual information between the qubit and the fluctuator in the classical and the quantum model.