Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms

TL;DR

This paper introduces a framework for detecting and correcting qubit loss errors in fault-tolerant quantum algorithms, improving performance in systems where loss is a dominant noise source.

Contribution

It develops a delayed-erasure decoder for loss errors, integrating loss detection into logical circuits with minimal overhead, and demonstrates performance gains through simulation.

Findings

Significant performance improvement with increased loss fraction

Effective loss detection integrated into syndrome extraction

Shortened circuit depth via gate teleportation reduces overhead

Abstract

Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally-motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis, and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault tolerant quantum computation in systems with loss error detection.