Characterizing error propagation in quantum circuits: the Isotropic Index

TL;DR

This paper introduces the Isotropic Index, a new tool to analyze how errors spread in quantum circuits by decomposing error states into isotropic and dis-alignment components, aiding in understanding quantum algorithm degradation.

Contribution

The paper proposes the Isotropic Index and the Isotropic Triangle as novel methods for characterizing error propagation in quantum circuits, providing a new perspective on quantum error analysis.

Findings

The Isotropic Index effectively separates error components in quantum states.

The Isotropic Triangle offers a visual representation of error propagation.

Application examples demonstrate the index's usefulness in analyzing quantum algorithms.

Abstract

This paper presents a novel index in order to characterize error propagation in quantum circuits by separating the resultant mixed error state in two components: an isotropic component, that quantifies the lack of information, and a dis-alignment component, that represents the shift between the current state and the original pure quantum state. The Isotropic Triangle, a graphical representation that fits naturally with the proposed index, is also introduced. Finally, some examples with the analysis of well-known quantum algorithms degradation are given.