The Clifford theory of the n-qubit Clifford group

TL;DR

This paper explores the representation theory of the n-qubit Clifford group by leveraging Clifford theory and the simpler representation theory of the Pauli group, revealing an unexpected correspondence between characters of different qubit numbers.

Contribution

It introduces a novel application of Clifford theory to analyze the representation theory of the n-qubit Clifford group using the Pauli group's simpler structure.

Findings

Discovered a correspondence between irreducible characters of n- and (n+1)-qubit Clifford groups

Provided new insights into the structure of the Clifford group representations

Enhanced understanding of quantum error correction and device characterization

Abstract

The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply the tools of (the coincidentally named) Clifford theory to examine the representation theory of the Clifford group using the much simpler representation theory of the Pauli group. We find an unexpected correspondence between irreducible characters of the n-qubit Clifford group and those of the (n+1)-qubit Clifford group.