On the freedom in representing quantum operations

TL;DR

This paper explores the gauge freedom in representing quantum operations, showing how different descriptions can alter perceived errors, and proposes a new figure of merit called mean variation error for better characterization.

Contribution

It introduces the concept of gauge freedom in quantum device representations and proposes a new operational figure of merit to improve device characterization.

Findings

Different valid descriptions can assign errors differently in quantum gate-sets.

Existing figures of merit may be misleading due to gauge freedom.

The mean variation error provides a more consistent measure of quantum gate errors.

Abstract

We discuss the effects of a gauge freedom in representing quantum information processing devices, and its implications for characterizing these devices. We demonstrate with experimentally relevant examples that there exists equally valid descriptions of the same experiment which distribute errors differently among objects in a gate-set, leading to different error rates. Consequently, it can be misleading to attach a concrete operational meaning to figures of merit for individual gate-set elements. We propose an alternative operational figure of merit for a gate-set, the mean variation error, and a protocol for measuring this figure.