Optimal schedule of multi-channel quantum Zeno dragging with application to solving the k-SAT problem

TL;DR

This paper analyzes multi-channel quantum Zeno dragging with generalized measurements, optimizing the process to efficiently prepare states and solve problems like k-SAT, providing theoretical bounds and control strategies.

Contribution

It introduces a detailed analysis and optimization of multi-channel Zeno dragging using generalized measurements for quantum state preparation and problem solving.

Findings

Derived analytical upper bounds on convergence time.

Applied optimal control to minimize dragging schedule duration.

Provided a theoretical framework for designing quantum algorithms using Zeno dragging.

Abstract

Quantum Zeno dragging enables the preparation of common eigenstates of a set of observables by frequent measurement and adiabatic-like modulation of the measurement basis. In this work, we present a deeper analysis of multi-channel Zeno dragging using generalized measurements, i.e. simultaneously measuring a set of non-commuting observables that vary slowly in time, to drag the state towards a target subspace. For concreteness, we will focus on a measurement-driven approach to solving k-SAT problems as examples. We first compute some analytical upper bounds on the convergence time, including the effect of finite measurement time resolution. We then apply optimal control theory to obtain the optimal dragging schedule that lower bounds the convergence time, for low-dimensional settings. This study provides a theoretical foundation for multi-channel Zeno dragging and its optimization, and also serves as a guide for designing optimal dragging schedules for quantum information tasks including measurement-driven quantum algorithms.