Measurement-Based Quantum Turing Machines and their Universality

TL;DR

This paper introduces Measurement-based Quantum Turing Machines, formalizing measurement-driven quantum computation and highlighting the role of classical control, to explore universality and resource bounds in quantum computing.

Contribution

It presents a formal model for measurement-based quantum computation, emphasizing classical control and establishing bounds on resources for universality.

Findings

Measurement-based quantum computation is universal.

Classical control is essential in measurement-based schemes.

A formal model bounds the minimal resources for quantum universality.

Abstract

Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In order to formalize these other forms of computation, while pointing out the role and the necessity of classical control in measurement-based computation, and for establishing a new upper bound of the minimal resources needed to quantum universality, a formal model is introduced by means of Measurement-based Quantum Turing Machines.