Clifford Orbits from Cayley Graph Quotients

2023/06/01 by Cynthia Keeler, Keeler, Cynthia, William Munizzi +3 · 2 citations
Computer Science · #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #High Energy Physics - Theory (hep-th) #Parallel Computing and Optimization Techniques #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2306.01043

openalex publication_date 2023/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We describe the structure of the n-qubit Clifford group C_n via Cayley graphs, whose vertices represent group elements and edges represent generators. In order to obtain the action of Clifford gates on a given quantum state, we introduce a quotient procedure. Quotienting the Cayley graph by the stabilizer subgroup of a state gives a reduced graph which depicts the state's Clifford orbit. Using this protocol for C₂, we reproduce and generalize the reachability graphs introduced in arXiv:2204.07593. Since the procedure is state-independent, we extend our study to non-stabilizer states, including the W and Dicke states. Our new construction provides a more precise understanding of state evolution under Clifford circuit action.

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• Topological Preparation of Non-Stabilizer States and Clifford Evolution in SU(2)₁ Chern-Simons Theory
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