Classification of the Subgroups of the Two-Qubit Clifford Group

2024/09/22 by Eric Kubischta, Kubischta, Eric, Ian Teixeira +1
Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2409.14624

openalex publication_date 2024/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We perform a complete classification of all 56 subgroups of the two-qubit Clifford group containing the two-qubit Pauli group. We provide generators for these groups using gates familiar to the quantum information community and we reference these groups against the group libraries provided in GAP. We also list several families of groups in higher levels of the two-qubit Clifford hierarchy.

Related

• The Clifford theory of the n-qubit Clifford group
• Embedding the n-Qubit Projective Clifford Group into a Symmetric Group
• Pauli Automorphisms, Clifford Groups, and Local Clifford Groups for Higher-Dimensional Systems
• Controlled not connectivity in the Clifford group
• Quasi-Clifford to qubit mappings