Reversibility in the Extended Measurement-based Quantum Computation

TL;DR

This paper explores the extended measurement-based quantum computation model, analyzing conditions for determinism and extending the concept of focused gflow to include measurements in additional planes of the Bloch sphere.

Contribution

It introduces necessary and sufficient conditions for the existence of focused gflow in the extended MBQC model with measurements in multiple planes.

Findings

Extended gflow conditions established

Normal form for focused gflow characterized

Determinism conditions generalized to extended measurements

Abstract

When applied on some particular quantum entangled states, measurements are universal for quantum computing. In particular, despite the fondamental probabilistic evolution of quantum measurements, any unitary evolution can be simulated by a measurement-based quantum computer (MBQC). We consider the extended version of the MBQC where each measurement can occur not only in the (X,Y)-plane of the Bloch sphere but also in the (X,Z)- and (Y,Z)-planes. The existence of a gflow in the underlying graph of the computation is a necessary and sufficient condition for a certain kind of determinism. We extend the focused gflow (a gflow in a particular normal form) defined for the (X,Y)-plane to the extended case, and we provide necessary and sufficient conditions for the existence of such normal forms.