Permutation-invariant quantum gates on any number of qubits can be implemented exactly via the Tavis-Cummings interaction with a vacuum-initialized oscillator plus global x and z fields.
The first condition follows immediately from Theorem 13, and in the previous subsection, we proved that eachV∈ Vz satisfies the phase constraints in the second condition, Eq.(90)
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Permutation-Invariant N-body gates via Tavis-Cummings Hamiltonian
Permutation-invariant quantum gates on any number of qubits can be implemented exactly via the Tavis-Cummings interaction with a vacuum-initialized oscillator plus global x and z fields.