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Laser Physics Letters

Optimal measurement-based feedback control on noisy quantum systems

Cheng-Cheng Liu, Ting-Sheng Wei, Jiadong Shi, Zhiyong Ding, Juan He, Tao Wu, Liu Ye

Published Oct 15, 2021• 0 citations
Publisher

Abstract

Abstract A quantum system will both lose and gain excitation through interaction with the environment in a non-zero temperature environment. In this paper, we investigate how a feedback control scheme utilizing weak measurement stabilizes a quantum state which suffers from an environment with finite temperature. Our study has shown that compared with the conventional ‘do-nothing’ and ‘Helstrom’ schemes, this method is much more useful for suppressing decoherence in a generalized amplitude damping (GAD) noise channel. Additionally, for a quantum state, we give the expression of optimum measurement strength, correction angle and the general analytic expression for the optimum fidelity. Additionally, the maximum value of the fidelity improvement can be achieved by controlling the measurement strength, correction angle and the special initial state of the system. More importantly, we find that this approach can not only be helpful for suppressing decoherence in the GAD channel, but can also play a significant role in the amplitude damping noise channel. This phenomenon reveals that in non-zero temperature noise channels, the feedback control scheme via weak measurement can be better for stabilizing a quantum state.

DOI
10.1088/1612-202x/ac2b95

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Abstract A quantum system will both lose and gain excitation through interaction with the environment in a non-zero temperature environment. In this paper, we investigate how a feedback control scheme utilizing weak measurement stabilizes a quantum state which suffers from an environment with finite temperature. Our study has shown that compared with the conventional ‘do-nothing’ and ‘Helstrom’ schemes, this method is much more useful for suppressing decoherence in a generalized amplitude damping (GAD) noise channel. Additionally, for a quantum state, we give the expression of optimum measurement strength, correction angle and the general analytic expression for the optimum fidelity. Additionally, the maximum value of the fidelity improvement can be achieved by controlling the measurement strength, correction angle and the special initial state of the system. More importantly, we find that this approach can not only be helpful for suppressing decoherence in the GAD channel, but can also play a significant role in the amplitude damping noise channel. This phenomenon reveals that in non-zero temperature noise channels, the feedback control scheme via weak measurement can be better for stabilizing a quantum state.
In practical application, since quantum entanglement is inevitably destroyed by thermal noise resulted from environment, protecting entanglement from decoherence in thermal bath environment becomes a critically important issue in the field of quantum information. In this work, we propose a scheme to protect the tripartite Greenberger–Horne–Zeilinger (GHZ) entanglement state subjected to the generalized amplitude damping (GAD) channel based on the quantum technique of weak measurement (WM) and quantum measurement reversal (QMR). By optimizing the strengths of WM and QMR, the decoherence caused by the channel can be effectively suppressed. The results show that after performing the optimal pre- and post-channel weak measurement, the negativity of the GHZ state can be effectively improved with a certain probability, and the phenomenon of sudden death can be delayed to a certain degree. This scheme can be applied to the decoherence suppression of GAD channel at finite temperature.
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.
The study of system evolution in generalized amplitude damping is of great significance in quantum information science and quantum computing. As an important quantum noise channel, the generalized amplitude damping channel can describe the general phenomenon of the energy dissipation effect in quantum systems at finite temperature. In this paper, we study the use of weak measurement and reversal to protect the entanglement of X-type systems in generalized amplitude damping channels, and give an experimental scheme. The results show that the closer to zero the temperature environment, the better the protection effect of weak measurement and reversal, but the lower the success rate. Therefore, when choosing an experimental environment, it is important to consider not only the temperature factor but also the probability of success. Because all quantum systems work at finite temperatures, it is hoped that the study of generalized amplitude damping channels can help design more robust quantum algorithms and protocols to improve the efficiency and stability of quantum information processing.
When a quantum system interacts with its environment, the so-called decoherence effect will normally destroy the coherence in the quantum state and the entanglement between its subsystems. We propose a feedback control strategy based on quantum weak measurements to protect coherence and entanglement of the quantum state against environmental disturbance. For a one-qubit quantum system under amplitude damping and dephasing decoherence channels, our strategy can preserve the coherence based on the measured information about the population difference between its two levels. For a two-qubit quantum system disentangled by independent amplitude damping and dephasing decoherence channels, the designed feedback control can preserve coherence between the ground state and the highest excited states by tuning the coupling strength between the two qubits, and at the same time minimize the loss of entanglement between the two qubits. As a consequence of dynamic symmetry, the generalization of these results derives the concept of control-induced decoherence-free observable subspace, for which several criteria are provided.
A qubit which is prepared in one of two non-orthogonal states and subjected to bit-flipping noise is considered. The objective is to use measurement and feedback control to correct the state of the qubit. Three classical schemes using projective measurements, i.e. discrimination and re-preparation, do nothing and random preparation, have been discussed, and are not optimal with respect to a performance which is quantified by the average fidelity of the corrected state compared to the initial state. In addition, one quantum scheme using a non-projective measurement with an optimum measurement strength achieves the best trade-off between gaining information about the system and disturbing it through measurement back-action. The performance of a quantum control scheme outperforms the classical schemes. Furthermore, no universal corrected scheme is 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.