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arXiv:1508.02121 · The proceedings of the IEEE Conference on Control Applications/The proceedings of the ... IEEE Conference on Control Applications

Quantum filter for a non-Markovian single qubit system

Shibei Xue, M. R. James, Alireza Shabani, Valery Ugrinovskii, Ian R. Petersen

Published Sep 1, 2015• 6 citations
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Abstract

In this paper, a quantum filter for estimating the states of a non-Markovian qubit system is presented in an augmented Markovian system framework including both the qubit system of interest and multi-ancillary systems for representing the internal modes of the non-Markovian environment. The colored noise generated by the multi-ancillary systems disturbs the qubit system via a direct interaction. The resulting non-Markovian dynamics of the qubit is determined by a memory kernel function arising from the dynamics of the ancillary system. In principle, colored noise with arbitrary power spectrum can be generated by a combination of Lorentzian noises. Hence, the quantum filter can be constructed for the qubit disturbed by arbitrary colored noise and the conditional state of the qubit system can be obtained by tracing out the multi-ancillary systems.

DOI
10.1109/cca.2015.7320609

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In this paper, we utilize a feedback strategy to stabilize a single qubit in a non-Markovian environment with a Lorentzian spectrum. The non-Markovian single qubit is represented in an augmented system model, where an ancillary system is introduced as the internal mode of the environment to generate Lorentzian noise. The density matrix of the single qubit can be estimated by using an augmented-system-based quantum stochastic master equation. Then a feedback controller can be driven by the estimates to stabilize the qubit in a target state. Simulations show the feedback strategy can provide effective control of the non-Markovian single qubit.
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