发表机构
Qilimanjaro Quantum Tech（奇力马扎罗量子技术）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明量子电路Born机的纠缠层可为Clifford电路，不提供非稳定子性，其性能与近Haar纠缠器相当，且训练态的非稳定子性来自旋转，并给出最小稳定子Rényi熵的计算方法。
AI 中文摘要
量子电路Born机的纠缠层可以同时提供纠缠和非稳定子性。在这项工作中，我们展示了纠缠层可以是一个Clifford电路，它不提供非稳定子性。我们使用一种架构，其中固定的、不可训练的纠缠器在每一层中被重复使用，仅优化单量子比特旋转。在那里，一个Clifford纠缠器在足够的电路深度下达到与近Haar纠缠器相同的Kullback-Leibler散度，并且跨越从零到Haar典型非稳定子性的纠缠器达到相同的损失，除了自由费米子matchgate纠缠器的一个小偏移。一个掺杂控制，提高纠缠器的非稳定子性，同时保持每个门的纠缠能力不变，使损失保持平坦。使用Clifford纠缠器，训练态的非稳定子性完全来自旋转，这些旋转将训练电路带出稳定子形式体系。我们还展示了，在所有Born分布为给定目标的纯态中，其振幅为概率的正平方根的那个态具有最小的稳定子Rényi熵，因此这个最小值可以在不训练的情况下计算。
英文摘要
The entangling layer of a quantum circuit Born machine can supply both entanglement and nonstabilizerness. In this work we show that the entangling layer can be a Clifford circuit, which supplies no nonstabilizerness. We use an architecture in which a fixed, non-trainable entangler is reused in every layer and only single-qubit rotations are optimized. There, a Clifford entangler reaches the same Kullback--Leibler divergence as a near-Haar one at sufficient circuit depth, and entanglers spanning zero to Haar-typical nonstabilizerness reach the same loss, up to a small offset for a free-fermion matchgate entangler. A doping control that raises the entangler's nonstabilizerness while leaving the entangling power of every gate unchanged leaves the loss flat. With a Clifford entangler the nonstabilizerness of the trained state comes entirely from the rotations, which take the trained circuit outside the stabilizer formalism. We also show that, among all pure states whose Born distribution is a given target, the one whose amplitudes are the positive square roots of the probabilities has the smallest stabilizer Rényi entropy, so this minimum can be computed without training.
