Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication

TL;DR

This paper explores how transformed cluster states via stochastic local operations can serve as resources for measurement-based quantum computation, identifying conditions for universality and robustness in one and two dimensions.

Contribution

It introduces new classes of transformed cluster states (N-U-N and B-U-B) and demonstrates their potential as universal resources for quantum computation.

Findings

N-U-N states enable quasi-deterministic single-qubit rotations

B-U-B states can be arbitrarily locally pure and probabilistically useful

Two-dimensional N-U-N lattices are universal resources for measurement-based quantum computation

Abstract

We examine cluster states transformed by stochastic local operations and classical communication, as a resource for deterministic universal computation driven strictly by projective measurements. We identify circumstances under which such states in one dimension constitute resources for random length single-qubit rotations, in one case quasi-deterministically (N-U-N states) and in another probabilistically (B-U-B states). In contrast to the cluster states, the N-U-N states exhibit spin correlation functions that decay exponentially with distance, while the B-U-B states can be arbitrarily locally pure. A two-dimensional square N-U-N lattice is a universal resource for quasideterministic measurement-based quantum computation. Measurements on cubic B-U-B states yield two-dimensional cluster states with bond defects, whose connectivity exceeds the percolation threshold for a critical value of the local purity.