Practical Topological Cluster State Quantum Computing Requires Loss Below 1%

TL;DR

This paper demonstrates that practical topological cluster state quantum computing demands qubit loss rates below 1% to maintain feasible resource overheads, especially when accounting for loss during gates and initialization.

Contribution

It extends loss tolerance analysis to include loss during gates and initialization, establishing the necessity of sub-1% loss rates for efficient topological quantum computing.

Findings

Loss during two-qubit gates and initialization significantly impacts error thresholds.

Achieving practical quantum computing requires qubit loss rates below 1%.

Higher loss rates lead to prohibitive space-time overheads.

Abstract

The surface code cannot be used when qubits vanish during computation; instead, a variant known as the topological cluster state is necessary. It has a gate error threshold of $0.75% and only requires nearest-neighbor interactions on a 2D array of qubits. Previous work on loss tolerance using this code only considered qubits vanishing during measurement. We begin by also including qubit loss during two-qubit gates and initialization, and then additionally consider interaction errors that occur when neighbors attempt to entangle with a qubit that isn't there. In doing so, we show that even our best case scenario requires a loss rate below 1% in order to avoid considerable space-time overhead.