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Acta Sinica Quantum Optica

Open-loop Control of Non-state-controllable Quantum Systems

Shi Zhong-ke

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Based on Grover algorithm we design a scheme to perform a quantum control task of steering a finite-dimensional bilinear quantum mechanical system,which is basis-state controllable(but may not be state controllable).And investigate the probability of quantum control from an arbitrary state to a target one.A quantum simulation that performs the quantum control task is finally provided.

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Based on Grover algorithm we design a scheme to perform a quantum control task of steering a finite-dimensional bilinear quantum mechanical system,which is basis-state controllable(but may not be state controllable).And investigate the probability of quantum control from an arbitrary state to a target one.A quantum simulation that performs the quantum control task is finally provided.
For finite-dimensional quantum systems, we propose a quantum control scheme based on a multi-step unitary evolution and quantum projective measurements. The objective is to design a control law to steer the system to a target eigenstate of the measurement operator in the least number of steps. Within each control step, unitary evolution and quantum projective measurement are performed in turn until the system reaches the target state. The control process can be modeled as a finite-state Markov chain with an absorbing state. We prove that the controlled system will converge to the target eigenstate with probability one after a finite number of control steps and find a minimal-step-number condition that would steer the system to the target eigenstate in the least number of steps.
In this paper, a new quantum hybrid controller for controlling the strongly eigenstate controllable systems, is designed.For this purpose, a Lyapunov control law is implemented when the target state is in reachable set of the initial state.On the other hand, if the target state is not in the reachable set of the given initial state, based on Grover algorithm, a new interface state that the target state is in its reachable set, will be found and the given initial state is transferred to the new interface state.Then, the new interface state is transferred to the target state, based on a designed Lyapunov control law.A theorem and a new algorithm, for implementing the presented method, is designed.Finally, a simulated example illustrates the applications and advantages of presented method.
Quantum systems can be controlled by other quantum systems in a reversible way, without any information leaking to the outside of the system-controller compound. Such coherent quantum control is deterministic, is less noisy than measurement-based feedback control, and has potential applications in a variety of quantum technologies, including quantum computation, quantum communication, and quantum metrology. Here we introduce a coherent feedback protocol, consisting of a sequence of identical interactions with controlling quantum systems, that steers a quantum system from an arbitrary initial state towards a target state. We determine the broad class of such coherent feedback channels that achieve convergence to the target state, and then stabilize as well as protect it against noise. Our results imply that also weak system-controller interactions can counter noise if they occur with suitably high frequency. We present an example of a control scheme that does not require knowledge of the target state encoded in the controllers, which could be the result of a quantum computation. It thus provides a mechanism for autonomous, purely quantum closed-loop control.