Interference and Measurement: Changing amplitude phase information to amplitude magnitude information

TL;DR

This paper explores how quantum interference and measurement can be used to transform phase-encoded information into amplitude magnitude information, aiding in problem-solving without complex phase manipulations.

Contribution

It introduces a method leveraging interference and measurement to extract useful information from phase-encoded quantum states, simplifying quantum algorithms.

Findings

Constructive interference enhances relevant amplitudes.

Destructive interference suppresses irrelevant amplitudes.

Measurement sequences provide insights into solution landscapes.

Abstract

There are quantum procedures that encode the solutions to a problem in the phases of quantum amplitudes. This happens in some quantum optimization algorithms in which the value of a function to be maximized or minimized is represented by a phase. An example of this is the QAOA algorithm for the MaxCut problem in which one encodes the number of edges connecting the sets resulting from a partition of the vertices of a graph into phases of amplitudes of a quantum state. Another is the minimum vertex cover problem in which the number of edges included in the cover is encoded in phases. Here we want to see what can be done if we only use simple aspects of quantum mechanics, interference and measurement, to manipulate the magnitudes of the amplitudes whose phases encode the relevant information. The idea is to use constructive interference to enhance the amplitudes that contain useful information and destructive interference to suppress those that do not. We examine examples, both analytically and numerically. We also show how the results of sequences of measurements can be used to gain information about the landscape of solutions.