The Gauge Theory of Measurement-Based Quantum Computation

TL;DR

This paper introduces a gauge theory framework for measurement-based quantum computation, linking quantum measurement processes to gauge fields and transformations, and providing a new theoretical foundation for understanding MBQC's global properties.

Contribution

It establishes a gauge theory perspective for MBQC, connecting measurement randomness and computation output to gauge transformations and holonomies, and relates entanglement structures to gauge concepts.

Findings

MBQC's output is a gauge field holonomy.

Measurement basis adaptation is a gauge transformation.

Gauge theory characterizes SPT entanglement resources.

Abstract

Measurement-Based Quantum Computation (MBQC) is a model of quantum computation, which uses local measurements instead of unitary gates. Here we explain that the MBQC procedure has a fundamental basis in an underlying gauge theory. This perspective provides a theoretical foundation for global aspects of MBQC. The gauge transformations reflect the freedom of formulating the same MBQC computation in different local reference frames. The main identifications between MBQC and gauge theory concepts are: (i) the computational output of MBQC is a holonomy of the gauge field, (ii) the adaptation of measurement basis that remedies the inherent randomness of quantum measurements is effected by gauge transformations. The gauge theory of MBQC also plays a role in characterizing the entanglement structure of symmetry-protected topologically (SPT) ordered states, which are resources for MBQC. Our framework situates MBQC in a broader context of condensed matter and high energy theory.