Preparing approximate $N$-fold cat states with the phase space instruction set

• URL: http://arxiv.org/abs/2608.07696v1
• Date: Fri, 07 Aug 2026 18:38:41 GMT
• Title: Preparing approximate $N$-fold cat states with the phase space instruction set
• Abstract summary: We show that a universal gate set is surprisingly inefficient at preparing a simple family of states.<n>We also imply that converting bosonic circuits between different universal gate sets can be extremely inefficient.
• Score: 12.338455427628562
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The phase space instruction set is a continuous-variable universal gate set involving single-qubit rotations and qubit-dependent displacements on a single boson. Using these gates, we prove that a circuit depth $\mathrmΩ(\varphi(N))$ is necessary to approximately prepare a large $N$-fold rotationally invariant Schrödinger cat state; here $\varphi(N) \gtrsim N/\log\log N$ is the Euler totient function. A protocol saturating this asymptotic bound on circuit depth is obtained for every prime number $N$. This protocol has an asymptotically optimal runtime, when the gates are generated by Hamiltonian evolution. Our results provide a sharp example where a universal gate set is surprisingly inefficient at preparing a simple family of states, and further imply that converting bosonic circuits between different universal gate sets can be extremely inefficient.

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