Propagation of generalized Pauli errors in qudit Clifford circuits

TL;DR

This paper introduces an error probability tensor to analyze generalized Pauli errors in qudit Clifford circuits, demonstrating its application in quantum error correction and showing higher-dimensional qudits can outperform qubits in entanglement distribution.

Contribution

It presents a novel error probability tensor framework compatible with qudit stabilizer codes and provides an exact analytical error analysis for qudit repeaters.

Findings

Higher-dimensional qudits can outperform qubits in distributed entanglement.

The error probability tensor effectively tracks error statistics in qudit Clifford circuits.

Analytical solutions for error distribution in qudit repeaters are derived.

Abstract

It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum circuits composed of qudit Clifford gates. Our framework is compatible with qudit stabilizer quantum error-correcting codes. We show how the error probability tensor can be applied in the most general case, and we demonstrate an error analysis of bipartite qudit repeaters with quantum error correction. We provide an exact analytical solution of the error statistics of the state distributed by such a repeater. For a fixed number of degrees of freedom, we observe that higher-dimensional qudits can outperform qubits in terms of distributed entanglement.