Near-deterministic creation of universal cluster states with probabilistic Bell measurements and 3-qubit resource states

TL;DR

This paper presents a probabilistic method to create universal cluster states for quantum computing using 3-qubit resources and Bell measurements, achieving near-deterministic success with potential for error robustness.

Contribution

It introduces a novel scheme combining probabilistic Bell measurements and percolation theory to generate universal cluster states without feed-forward or long-term memories.

Findings

Achieves near-unity probability of spanning cluster in large lattices

Uses 3-qubit resource states within current experimental capabilities

Offers a potentially error-robust quantum state generation protocol

Abstract

We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward or long-time quantum memories. Borrowing ideas from percolation theory we numerically show that using unambiguous Bell measurements that succeed with 75% success probability, one could build a cluster state with an underlying pyrochlore geometry such that the probability of having a spanning cluster in a chosen direction approaches unity in the limit of an infinite lattice size. The initial resources required for the generation of a universal state in our protocol are 3-qubit cluster states that are within experimental reach and are a minimal resource for a Bell-measurement-based percolation proposal. Since single and multi-photon losses can be detected in Bell measurements, our protocol raises the prospect of a fully error-robust scheme.