Unitary-circuit semantics for measurement-based computations

TL;DR

This paper introduces an efficient algorithm to convert certain measurement-based quantum computations into equivalent unitary circuit models, aiding in understanding and verifying their quantum transformations without deferred measurement.

Contribution

It provides a novel, efficient method for translating specific measurement-based quantum computations into unitary circuits, bypassing the need for deferred measurement techniques.

Findings

Algorithm successfully converts certain measurement-based computations into unitary circuits

The method operates efficiently without deferred measurement principles

Enables better analysis of quantum transformations in measurement-based models

Abstract

One-way measurement based quantum computations (1WQC) may describe unitary transformations, via a composition of CPTP maps which are not all unitary themselves. This motivates the following decision problems: Is it possible to determine whether a ``quantum-to-quantum'' 1WQC procedure (having non-trivial input and output subsystems) performs a unitary transformation? Is it possible to describe precisely how such computations transform quantum states, by translation to a quantum circuit of comparable complexity? In this article, we present an efficient algorithm for transforming certain families of measurement-based computations into a reasonable unitary circuit model, in particular without employing the principle of deferred measurement.