Quantum state reduction for universal measurement based computation

TL;DR

This paper demonstrates that many known universal resource states for measurement-based quantum computation can be reduced to the cluster state through local measurements, simplifying proofs of universality and aiding the search for new resource states.

Contribution

It introduces a state reduction scheme that simplifies proofs of universality and facilitates discovering new resource states for measurement-based quantum computation.

Findings

Most known resource states can be reduced to the cluster state

The reduction scheme simplifies proofs of universality

It enables exploration of new resource states, including deformations of known states

Abstract

Measurement based quantum computation (MBQC), which requires only single particle measurements on a universal resource state to achieve the full power of quantum computing, has been recognized as one of the most promising models for the physical realization of quantum computers. Despite considerable progress in the last decade, it remains a great challenge to search for new universal resource states with naturally occurring Hamiltonians, and to better understand the entanglement structure of these kinds of states. Here we show that most of the resource states currently known can be reduced to the cluster state, the first known universal resource state, via adaptive local measurements at a constant cost. This new quantum state reduction scheme provides simpler proofs of universality of resource states and opens up plenty of space to the search of new resource states, including an example based on the one-parameter deformation of the AKLT state studied in [Commun. Math. Phys. 144, 443 (1992)] by M. Fannes et al. about twenty years ago.