Error metric for non-trace-preserving quantum operations

TL;DR

This paper introduces a new error metric for non-trace-preserving quantum operations that bounds the trace distance and is useful for analyzing errors in quantum computing protocols, especially in postselected and fault-tolerant contexts.

Contribution

The paper proposes a novel error metric for non-trace-preserving quantum operations that is compatible with the diamond distance and applicable to practical quantum computing scenarios.

Findings

Leakage errors scale worse than expected in neutral-atom quantum computers.

The metric effectively analyzes errors in lossy beam splitters and nondeterministic gates.

It provides insights into error propagation and thresholds in fault-tolerant quantum computing.

Abstract

We study the problem of measuring errors in non-trace-preserving quantum operations, with a focus on their impact on quantum computing. We propose an error metric that efficiently provides an upper bound on the trace distance between the normalized output states from imperfect and ideal operations, while remaining compatible with the diamond distance. As a demonstration of its application, we apply our metric in the analysis of a lossy beam splitter and a nondeterministic conditional sign-flip gate, two primary non-trace-preserving operations in the Knill-Laflamme-Milburn protocol. We then turn to the leakage errors of neutral-atom quantum computers, finding that these errors scale worse than previously anticipated, implying a more stringent fault-tolerant threshold. We also assess the quantum Zeno gate's error using our metric. In a broader context, we discuss the potential of our metric to analyze general postselected protocols, where it can be employed to study error propagation and estimate thresholds in fault-tolerant quantum computing. The results highlight the critical role of our proposed error metric in understanding and addressing challenges in practical quantum information processing.