发表机构
The University of Melbourne; Los Alamos National Laboratory（墨尔本大学; 洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出SCENT协议，通过谱聚类构建纠缠最小化树张量网络，结合张量交叉插值高效制备多变量量子态，在200量子比特电路上以少量CNOT门实现高保真度，优于矩阵乘积态方法。
AI 中文摘要
Quantics张量列在量子启发计算和量子态制备领域引起了强烈关注。这些方法通过将连续函数的振幅编码表示为矩阵乘积态（MPS）来近似连续函数，对于单变量函数极为有效，但在处理多变量函数时迅速变得具有挑战性，因为线性链拓扑导致高度纠缠的量子比特之间距离较大。我们通过引入SCENT（用于纠缠最小化树的谱聚类）来克服这一限制。SCENT是一种利用可高效计算的成对纠缠度量来确定合适的树张量网络（TTN）结构的协议，该结构随后可通过张量交叉插值（TCI）高效近似；我们发现它显著优于MPS方法，并改进了先前的TTN方法。然后我们将这些优化的TTN应用于态制备，引入了一种基于环境张量方法的近似电路编译方法，而不会显著牺牲整体精度。重要的是，TTN固有的规范自由度可在该方法中直接利用，从而在给定电路深度下实现更高的保真度。我们在量子化学和金融投资组合优化的典型态制备问题上演示了这一量子态制备流程。在我们的旗舰演示中，我们将一个具有长程、非最近邻变量间相关性的20变量概率分布编码到200量子比特的态制备电路中，使用仅43284个CNOT门，保真度误差为$7.44\ imes 10^{-9}$；深度和保真度可以权衡，允许同一分布以仅5584个CNOT门制备到误差$10^{-3}$。
英文摘要
Quantics tensor trains are attracting intense interest for quantum-inspired computing and quantum state preparation. These methods, which approximate continuum functions by representing their amplitude encoding as a matrix product state (MPS), are exceedingly powerful for univariate functions but rapidly become challenging when handling multivariate functions, since the linear chain topology leads to a large distance between highly-entangled qubits. We overcome this limitation by introducing SCENT (Spectral Clustering for Entanglement miNimizing Trees). SCENT is a protocol that utilizes efficiently-computable pairwise entanglement metrics to determine a suitable tree tensor network (TTN) structure, which can then be efficiently approximated using tensor cross-interpolation (TCI); we find that it substantially outperforms MPS methods and improves upon previous TTN methods. We then apply these optimized TTNs to state preparation, introducing an approximate circuit compilation method based on environment-tensor methods without significantly conceding overall accuracy. Importantly, the inherent gauge freedom of TTNs can be directly exploited in this method, resulting in higher fidelity at a given circuit depth. We demonstrate this quantum state-preparation pipeline on archetypal state-preparation problems in quantum chemistry and financial portfolio optimization. In our flagship demonstration, we encode a 20-variable probability distribution with long-ranged, non-nearest neighbor inter-variable correlations in a 200-qubit state-preparation circuit with infidelity $7.44\times 10^{-9}$ using only 43284 CNOTs; depth and fidelity can be traded, allowing the same distribution to be prepared to infidelity $10^{-3}$ with as few as 5584 CNOTs.
Comments34 pages, 14 figures
