Topological One-Way Quantum Computation on Verified Logical Cluster States

TL;DR

This paper proposes a fault-tolerant topological one-way quantum computation scheme using verified logical cluster states, achieving high noise thresholds and scalable resource requirements.

Contribution

It introduces a verification-based construction of logical cluster states that enhances noise thresholds and scalability in topological quantum computing.

Findings

Achieves a noise threshold of around 5%.

Uses localized postselection within star clusters.

Requires resource overhead comparable to existing schemes.

Abstract

We present a scheme to improve the noise threshold for the fault-tolerant topological one-way computation with a constant overhead. Certain cluster states of finite size, say star clusters, are constructed with logical qubits through an efficient verification process to achieve high fidelity. Then, the star clusters are connected near-deterministically with verification to form a three-dimensional cluster state to implement the topological one-way computation. The necessary postselection for verification is localized within the star clusters, ensuring the salability of computation. This scheme works with a high error rate $ \sim 1 % $ and reasonable resources comparable to or less than those for the other fault-tolerant schemes, suggesting potentially a noise threshold higher than 5%.