Phase transition of computational power in the resource states for one-way quantum computation

TL;DR

This paper investigates how qubit losses in the preparation of 2D cluster states impact their usefulness for quantum computation, revealing a phase transition at the percolation threshold affecting computational power.

Contribution

It introduces a polynomial-time algorithm for resource concentration above the threshold and demonstrates classical simulability below it, highlighting a phase transition in entanglement and computational capability.

Findings

Polynomial-time resource concentration above threshold

Classical simulability of faulty lattice below threshold

Exponential change in entanglement at the phase transition

Abstract

We study how heralded qubit losses during the preparation of a two-dimensional cluster state, a universal resource state for one-way quantum computation, affect its computational power. Above the percolation threshold we present a polynomial-time algorithm that concentrates a universal cluster state, using resources that scale optimally in the size of the original lattice. On the other hand, below the percolation threshold, we show that single qubit measurements on the faulty lattice can be efficiently simulated classically. We observe a phase transition at the threshold when the amount of entanglement in the faulty lattice directly relevant to the computational power changes exponentially.