YZ-plane measurement-based quantum computation: Universality and Parity Architecture implementation

TL;DR

This paper explores measurement-based quantum computation using only YZ-plane measurements, establishing universality and implementing the Parity Architecture with local interactions.

Contribution

It introduces a universal YZ-plane measurement pattern and connects it to XZ-plane patterns, advancing the understanding of measurement restrictions in MBQC.

Findings

YZ-plane measurement patterns can be embedded into local interaction graphs.

Universal YZ-plane measurement patterns are constructed.

The Parity Architecture is extended to YZ-plane measurement-based quantum computation.

Abstract

We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the $YZ$ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal $YZ$-plane-only measurement pattern and establish a connection between $YZ$-plane-only and $XZ$-plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that $YZ$-plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation.