AI 中文总结
该研究基于相空间指令集，证明近似制备大N重旋转不变薛定谔猫态的电路深度下界，对素数N给出最优协议，揭示通用门集制备简单态族效率低及不同通用门集间转换的低效性。
AI 中文摘要
相空间指令集是一种连续变量通用门集，包含单量子比特旋转和单玻色子上依赖量子比特的位移。利用这些门，我们证明制备大N重旋转不变薛定谔猫态的近似电路深度需要Ω(φ(N))，其中φ(N)≳N/log log N为欧拉 totient 函数。对于每个素数N，我们得到了一个达到该电路深度渐近界的协议，当门由哈密顿量演化生成时，该协议具有渐近最优运行时间。我们的结果提供了一个鲜明例子，表明通用门集在制备简单态族时效率低得出人意料，进一步暗示将玻色子电路在不同通用门集之间转换可能极为低效。
英文摘要
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 $\mathrmΩ(φ(N))$ is necessary to approximately prepare a large $N$-fold rotationally invariant Schrödinger cat state; here $φ(N) \gtrsim N/\log\log N$ 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.
Comments22+22 pages, 5+1 figures
