Perspectives on Utilization of Measurements in Quantum Algorithms

TL;DR

This paper reviews the fundamental measurement operations in quantum computing, emphasizing their crucial role in quantum algorithms, error mitigation, and circuit modifications, advocating for their broader integration in algorithm design.

Contribution

It provides one of the first comprehensive algorithmic overviews of measurement processes in quantum computing, highlighting their importance beyond traditional roles.

Findings

Measurements are key to accessing quantum computation results.

Measurement-based methods can address quantum computational challenges.

Sophisticated measurement schemes are essential for advanced quantum algorithms.

Abstract

Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a selected set of their applications in quantum algorithms. Our goal is to provide one of the first algorithmic overviews of measurement processes in quantum computing. From the quantum information-theoretical perspective, measurements are either a method to access the result of a quantum computation or a technique to modify a quantum state. We also identify measurement-based methods to solve quantum computational challenges, such as error mitigation and circuit cutting. We discuss three main categories of measurements: performing measurements in static quantum circuits, modifying the quantum state in dynamic quantum circuits via measurements, and addressing challenges in quantum computing with measurements. Based on the reviewed topics, the measurement operations are frequently not at the center of the quantum algorithm design. However, the most novel and error-prone quantum algorithms will likely require sophisticated measurement schemes. Thus, the central message of this article is to broaden the view of measurement operations and highlight their importance at every level of quantum algorithm design.