Quotienting the Cayley graph of the Clifford group by a quantum state's stabilizer subgroup produces a graph of the state's Clifford orbit.
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Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.
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Clifford Orbits from Cayley Graph Quotients
Quotienting the Cayley graph of the Clifford group by a quantum state's stabilizer subgroup produces a graph of the state's Clifford orbit.
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Magic and Non-Clifford Gates in Topological Quantum Field Theory
Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.