Feedback Policies for Measurement-based Quantum State Manipulation

TL;DR

This paper develops feedback control strategies for quantum state manipulation using sequential measurements, demonstrating that feedback significantly enhances success probability and exploring various optimization objectives within a Markovian control framework.

Contribution

It introduces a Markovian feedback policy framework for quantum state manipulation, solving the optimal control problem via dynamical programming and comparing different objective functionals.

Findings

Feedback improves success probability over classical schemes.

Optimal policies can be derived using dynamical programming.

Different objectives like fidelity maximization and arrival time minimization are analyzed.

Abstract

In this paper, we propose feedback designs for manipulating a quantum state to a target state by performing sequential measurements. In light of Belavkin's quantum feedback control theory, for a given set of (projective or non-projective) measurements and a given time horizon, we show that finding the measurement selection policy that maximizes the probability of successful state manipulation is an optimal control problem for a controlled Markovian process. The optimal policy is Markovian and can be solved by dynamical programming. Numerical examples indicate that making use of feedback information significantly improves the success probability compared to classical scheme without taking feedback. We also consider other objective functionals including maximizing the expected fidelity to the target state as well as minimizing the expected arrival time. The connections and differences among these objectives are also discussed.