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arXiv:1308.2008 · Physical Review A

Extended techniques for feedback control of a single qubit

Yu‐Guang Yang, X. Y. Zhang, Jing Ma, X. X. Yi

Published Jan 29, 2013• 15 citations
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Abstract

The protection of quantum states is challenging for nonorthogonal states, especially in the presence of noise. Recent research shows that this difficulty can be overcome by feedback control with weak measurements. However, the state-protection schemes proposed recently work optimally only for special quantum states. In this paper, by applying different weak measurements, we extend the idea of the state-protection scheme to include protecting general states. We calculate numerically the optimal parameters and discuss the performance of the scheme. Comparison between this extended scheme and the earlier scheme is also presented.

DOI
10.1103/physreva.87.012333

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The protection of quantum states is challenging for nonorthogonal states, especially in the presence of noise. Recent research shows that this difficulty can be overcome by feedback control with weak measurements. However, the state-protection schemes proposed recently work optimally only for special quantum states. In this paper, by applying different weak measurements, we extend the idea of the state-protection scheme to include protecting general states. We calculate numerically the optimal parameters and discuss the performance of the scheme. Comparison between this extended scheme and the earlier scheme is also presented.
Measurements in quantum mechanics cannot perfectly distinguish all states and necessarily disturb the measured system. We present and analyze a proposal to demonstrate fundamental limits on quantum control of a single qubit arising from these properties of quantum measurements. We consider a qubit prepared in one of two nonorthogonal states and subsequently subjected to dephasing noise. The task is to use measurement and feedback control to attempt to correct the state of the qubit. We demonstrate that projective measurements are not optimal for this task, and that there exists a nonprojective measurement with an optimum measurement strength which achieves the best trade-off between gaining information about the system and disturbing it through measurement backaction. We study the performance of a quantum control scheme that makes use of this weak measurement followed by feedback control, and demonstrate that it realizes the optimal recovery from noise for this system. We contrast this approach with various classically inspired control schemes.
We consider an open quantum system subjected to a noise channel under measurement-based feedback control and two prototypical classes of decoherence channels are considered: phase damping and generalized amplitude damping. Based on quantum trajectory theory, we obtain an extended master equation for the dynamics of the reduced system in the presence of feedback control. For a qubit system we analytically solve this master equation and obtain the solution of the state vector dynamics. Then we propose an effective feedback control scheme for preparing an arbitrary quantum pure state. We also study how to protect two nonorthogonal states effectively, and find that projective measurement with unbiased basis is not optimal for this task, while weak measurement with biased basis could realize the best protection of two nonorthogonal states. Furthermore, the inefficiencies in the feedback process are also discussed.
A goal of the emerging field of quantum control is to develop methods for quantum technologies to function robustly in the presence of noise. Central issues are the fundamental limitations on the available information about quantum systems and the disturbance they suffer in the process of measurement. In the context of a simple quantum control scenario-the stabilization of nonorthogonal states of a qubit against dephasing-we experimentally explore the use of weak measurements in feedback control. We find that, despite the intrinsic difficultly of implementing them, weak measurements allow us to control the qubit better in practice than is even theoretically possible without them. Our work shows that these more general quantum measurements can play an important role for feedback control of quantum systems.
One of the crucial tasks in quantum systems is to reduce the effects of decoherence due to the unavoidable interactions between a system and its environment. Many protection schemes have been proposed recently, among them the weak measurement quantum measurement reversal (WMQMR), weak measurement-based quantum feedback control (QFBC) and quantum feedforward control (QFFC) are reviewed in this paper. By considering weak measurement, the aim is to find a balance between information gain and disturbance of the system caused by the measurement. We classify different types of measurement and give the definition of noise sources and their effects on the state of the system. Finally, we compare and analyze the performance of the discussed protection schemes for different noise sources by numerical simulations.
Although information gain and disturbance in quantum systems are always antagonistic in quantum theory, a recently proposed optimal feedback control system [A. M. Bra\ifmmode \acute{n}\else \'{n}\fi{}czyk, P. E. M. F. Mendonca, A. Gilchrist, A. C. Doherty, and S. D. Bartlett, Phys. Rev. A 75, 012329 (2007)] could reach a trade-off by using weak measurements in the case of pure dephasing noise. We reexamine this approach for stabilizing quantum states in the presence of different noise sources and with respect to different system states. We find that the approach is sensitive to the system state but, for some suitable states, it works well for all typical types of noise sources.
Due to the interaction with the environment, a quantum state is often affected by the different types of noises which becomes to one of the biggest problems for practical quantum computation. We study the possibility of protecting the mixed state of a quantum system that goes through noise by weak measurements and control operations. The aim is to find the optimal measurement strength and control operations and make the input and output states as close as possible. We show that our scheme can effectively protect arbitrary mixed states against typical types of noise sources: amplitude damping, phase damping and amplitude-phase damping. The optimal measurement and control operators are deduced in different bases of the Bloch sphere to find the best control scheme for each type of noise. The effectiveness of our control scheme is demonstrated by simulation results.