发表机构
University of Innsbruck（因斯布鲁克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明浅深度下通过共享经典随机性可实现量子生成模型中幺正与信道模型的严格可扩展表征分离，MBQC可自然实现所需随机性，数值实验验证了分析结果。
AI 中文摘要
近期量子硬件限制了电路深度，且通常对量子生成模型施加几何局域连通性，这限制了浅度幺正玻恩模型可访问的输出分布。在幺正量子玻恩模型中引入随机性可提升所得信道模型的经验生成性能，且对于受限的小规模架构，已证明其能表征比幺正对应模型严格更大的分布族。然而，这种随机性是否能在固定浅深度下对任意大系统提供可证明的分离仍未解决。本文中，我们表明共享经典随机性（一种来自纠缠理论的相对弱资源）足以在对应浅度幺正玻恩模型之上建立这种严格的可扩展表征分离。更具体地说，我们在有界连通性的浅度幺正电路（后续计算基测量）中加入空间分离的局域泡利操作，其联合应用由单个经典采样的随机比特控制。所得浅度信道模型在经典输出分布中产生长程关联，这是任何具有有界连通性的纯幺正浅度模型都无法复现的。对于一维最近邻架构，用纯幺正模型复现此类分布在最坏情况下需要深度Ω(N)。我们进一步证明，基于测量的量子计算（MBQC）可通过对随机测量结果的适当调整，为所需的共享经典随机性提供自然实现。基于MBQC的生成模型的数值实验支持了这些分析结果。
英文摘要
Near-term quantum hardware limits circuit depth and often imposes geometrically local connectivity for quantum generative models, restricting the output distributions accessible to shallow unitary Born models. Introducing stochasticity into a unitary quantum Born model can improve the empirical generative performance of the resulting channel model and, for a restricted small-scale architecture, has been proven to represent a strictly larger family of distributions than its unitary counterpart. However, whether such randomness provides a provable separation at fixed shallow depth for arbitrarily large systems has remained open. Here, we show that shared classical randomness, a comparatively weak resource from entanglement theory, is sufficient to establish such a strict scalable representational separation over the corresponding shallow unitary Born model. More specifically, we augment bounded-connectivity shallow unitary circuits, followed by computational-basis measurements, with spatially separated local Pauli operations, whose joint application is controlled by a single classically sampled random bit. The resulting shallow-depth channel model generates long-range correlations in the classical output distribution that no purely unitary shallow-depth model with bounded connectivity can reproduce. For one-dimensional nearest-neighbour architectures, reproducing such distributions with a purely unitary model can require depth $Ω(N)$ in the worst case. We further show that measurement-based quantum computation (MBQC) provides a natural implementation of the required shared classical randomness through suitable adaptation of the random measurement outcomes. Numerical experiments on MBQC-based generative models support the analytical results.
Comments33 pages, 9 figures
