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arXiv:1204.6379

Discrete Quantum Control - State Preparation

Jon R. Grice, DAVID A. MEYER

Published Apr 28, 2012• 0 citations
arXivHTMLPDF

Abstract

A discrete-time method for solving problems in optimal quantum control is presented. Controlling the time discretized markovian dynamics of a quantum system can be reduced to a Markov-decision process. We demonstrate this method in this with a class of simple one qubit systems, which are also discretized in space. For the task of state preparation we solve the examples both numerically and analytically with dynamic programming techniques.

DOI
10.48550/arxiv.1204.6379

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Abstract. The fundamental mathematical definitions of the controlled feedback Markov dynamics of quantum-mechanical systems are introduced with regard to the dynamical reduction and filtering of quantum states in the course of quantum measurement in either discrete or continuous real time. The concept of sufficient coordinates for the description of a posteriori quantum states in a given class is introduced and it is proved that they form a classical Markov process with values in either state operators or state vector space. The general problem of optimal control of a quantum-mechanical system is discussed and the corresponding Bellman equation in the space of sufficient coordinates is derived. The results are illustrated in the example of control of the semigroup dynamics of a quantum system that is instantaneously observed at discrete times and evolves between measurement times according to the Schrődinger equation. 1.
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