Clifford Orbits from Cayley Graph Quotients
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909012019118080 |
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| author | Keeler, Cynthia Munizzi, William Pollack, Jason |
| author_facet | Keeler, Cynthia Munizzi, William Pollack, Jason |
| contents | 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 $C_2$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01043 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Clifford Orbits from Cayley Graph Quotients Keeler, Cynthia Munizzi, William Pollack, Jason Quantum Physics High Energy Physics - Theory Group Theory 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 $C_2$, 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. |
| title | Clifford Orbits from Cayley Graph Quotients |
| topic | Quantum Physics High Energy Physics - Theory Group Theory |
| url | https://arxiv.org/abs/2306.01043 |