An introduction to measurement based quantum computation

TL;DR

Measurement based quantum computation uses entangled states and measurements to perform quantum algorithms, offering potential advantages in parallelism over traditional gate-based models.

Contribution

This paper introduces the formalism of measurement based quantum computation, describing its main schemes and exploring their computational capabilities and benefits.

Findings

Demonstrates how measurement based models can perform universal quantum computation

Highlights potential advantages in parallel execution of algorithms

Clarifies relationships between different measurement based models

Abstract

In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the so-called cluster model or one-way quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms.