Clifford Orbits from Cayley Graph Quotients

• URL: http://arxiv.org/abs/2306.01043v1
• Date: Thu, 1 Jun 2023 18:00:02 GMT
• Title: Clifford Orbits from Cayley Graph Quotients
• Authors: Cynthia Keeler, William Munizzi, Jason Pollack
• Abstract summary: We describe the structure of the $n$-qubit Clifford group $mathcalC_n$ via Cayley graphs. In order to obtain the action of Clifford gates on a given quantum state, we introduce a quotient procedure. We extend our study to non-stabilizer states, including the W and Dicke states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We describe the structure of the $n$-qubit Clifford group $\mathcal{C}_n$ 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 $\mathcal{C}_2$, 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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