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IEEE Conference on Decision and Control (CDC)

Partial feedback control of quantum systems using probabilistic fuzzy estimator

Chunlin Chen, Gerasimos G. Rigatos, Daoyi Dong, James Lam

Published Dec 1, 2009• 10 citations
Publisher

Abstract

A partial feedback control scheme with a probabilistic fuzzy estimator (PFE) is presented for the robust control of quantum systems. In this scheme, a probabilistic fuzzy simulator is trained to estimate the quantum states for feedback control of quantum systems. Usually, the estimated state is fed back to design a controller. However, when the estimated quantum state is an almost-eigenstate, a projective measurement will be triggered for the quantum system and the measurement results will be fed back to construct the controller and regulate the fuzzy estimator. This scheme is a partial feedback strategy with controlled discontinuous measurement, where the quantum measurement serves as a control tool and is helpful for driving the quantum system to a desired state tracking even in the presence of unknown disturbances and stochastic noises. An example of a two-spin-¿ system is also presented to demonstrate the proposed approach.

DOI
10.1109/cdc.2009.5399492

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A partial feedback control scheme with a probabilistic fuzzy estimator (PFE) is presented for the robust control of quantum systems. In this scheme, a probabilistic fuzzy simulator is trained to estimate the quantum states for feedback control of quantum systems. Usually, the estimated state is fed back to design a controller. However, when the estimated quantum state is an almost-eigenstate, a projective measurement will be triggered for the quantum system and the measurement results will be fed back to construct the controller and regulate the fuzzy estimator. This scheme is a partial feedback strategy with controlled discontinuous measurement, where the quantum measurement serves as a control tool and is helpful for driving the quantum system to a desired state tracking even in the presence of unknown disturbances and stochastic noises. An example of a two-spin-¿ system is also presented to demonstrate the proposed approach.
An approach of control design using fuzzy estimators (FEs) is proposed for quantum systems with uncertainties. Two types of quantum control problems are considered: 1) control of a pure-state quantum system in the presence of uncertainties and 2) control design of quantum systems with initial mixed states and uncertainties. For the first type of tasks, a partial feedback control scheme with an FE is presented to design controllers. In this scheme, an FE is trained to estimate the quantum state for feedback control of a quantum system, and controlled projective measurement is used to assist in controlling the system. For the second type of quantum control tasks, a probabilistic fuzzy estimator (PFE) is trained to estimate the quantum state for control design of a quantum system with an initial mixed state, and a corresponding control algorithm is proposed to design a control law that drives the system from the mixed state to a target pure state. Two examples of two-spin-1/2systems are also presented and analyzed to demonstrate the process of control design and potential applications of the proposed approach.
A hybrid control approach for uncertain quantum systems is proposed using probabilistic fuzzy estimators (PFE) and quantum reinforcement learning (QRL). This hybrid control design involves coherent control with PFE and learning control via QRL. The problems of controlling a quantum system from an initial state to a pointed target state are studied in this paper, where we assume that the initial quantum state is a mixed state and the target quantum state is a controllable pure state within a wavefunction controllable subspace. First, the initial quantum system is controlled coherently with the help of a PFE. When the controlled system is estimated to be likely to collapse to an expected eigen state, trigger the measurement and the quantum system collapses to an eigen state in the wavefuntion controllable subspace with a high probability. Then the quantum system is driven to the target state with admissible controls, where the control sequence is learned and optimized with QRL. An example is presented and analyzed to demonstrate the control process.
We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. Direct feedback may be combined with feedback by estimation, and the resulting combination, performed on a linear system, is closely analogous to classical linear-quadratic-Gaussian control theory with residual feedback.
We present a formulation of feedback in quantum systems in which the best estimates of the dynamical variables are obtained continuously from the measurement record, and fed back to control the system. We apply this method to the problem of cooling and confining a single quantum degree of freedom, and compare it to current schemes in which the measurement signal is fed back directly in the manner usually considered in existing treatments of quantum feedback. The two approaches to feedback are to a certain extent complementary, and they may be combined to achieve the best results. The resulting combined feedback, performed on a linear system, is closely analogous to classical LQG control theory with residual feedback.
Abstract. No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory. Here we study the properties of controlled quantum filtering equations as classical stochastic differential equations. We then develop methods, using a combination of geometric control and classical probabilistic techniques, for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator.
No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is necessarily one with partial observations and can generally be converted into a completely observed control problem for an appropriate quantum filter as in classical stochastic control theory. Here we study the properties of controlled quantum filtering equations as classical stochastic differential equations. We then develop methods, using a combination of geometric control and classical probabilistic techniques, for global feedback stabilization of a class of quantum filters around a particular eigenstate of the measurement operator.