发表机构
Duale Hochschule Baden-Württemberg Stuttgart（巴登-符腾堡州双元高等教育学院斯图加特分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究用张量网络VQE求解相对论标量束缚态的Bethe-Salpeter方程，发现该问题在测试范围内经典可解，但首次量化了BSE振幅纠缠并建立了泡利哈密顿量框架，为未来量子优势研究奠定基础。
AI 中文摘要
我们提出了一种基于门电路的量子计算方法，用于求解两个有质量相对论标量粒子通过梯子近似标量交换相互作用的束缚态的齐次Bethe-Salpeter方程（hBSE）。在Wick旋转到欧几里得空间并进行O(4) S波分波投影后，hBSE被简化为一个维度为N = 2^n的对称矩阵特征值问题。我们将所得的哈密顿量分解为n量子比特泡利算符之和，并使用矩阵乘积态（MPS）张量网络拟设，通过变分量子本征求解器（VQE）进行求解。对于N=16（n=4量子比特），与经典对角化相比，VQE恢复最大特征值（该特征值编码束缚所需的最小耦合常数）的平均相对误差优于1%。对BSE振幅的纠缠分析显示，在测试的尺寸范围内，纠缠度较低且呈面积律行为，这为MPS拟设提供了动机。对三个独立障碍的关键分析——指数级泡利算符开销、近似尺寸无关的低纠缠度以及所测试拟设的VQE梯度尺度递减（与更大n时常见的贫瘠高原问题一致）——揭示出这里研究的特定问题处于经典可解区域：在测试范围内，它可由低键维张量网络很好地描述，并能被MPS/Lanczos方法高效处理。据我们所知，这一负面结果首次在量子比特编码中对BSE振幅进行了纠缠量化，为未来BSE变体建立了泡利哈密顿量框架，并指出二维闵可夫斯基空间BSE、N体束缚态和非梯子核是物理上动机明确的扩展方向，在这些方向中真正的量子优势可能变得可行。
英文摘要
We present a gate-based quantum computing solution of the homogeneous Bethe-Salpeter equation (hBSE) for the bound state of two massive relativistic scalar particles interacting via ladder-approximation scalar exchange. After Wick rotation to Euclidean space and O(4) S-wave partial-wave projection, the hBSE is reduced to a symmetric matrix eigenvalue problem of dimension N = 2^n. We decompose the resulting Hamiltonian into a sum of n-qubit Pauli operators and solve it with the Variational Quantum Eigensolver (VQE) using a Matrix Product State (MPS) tensor-network ansatz. For N=16 (n=4 qubits), the VQE recovers the maximum eigenvalue - which encodes the minimum coupling constant for binding - to better than 1 % mean relative error compared to classical diagonalization. Entanglement analysis of the BSE amplitude shows low, area-law-like entanglement over the tested sizes, which motivates the MPS ansatz. A critical analysis of three independent barriers - exponential Pauli overhead, approximately size-independent low entanglement, and decreasing VQE gradient scales for the tested ansatz, consistent with generic barren-plateau concerns at larger n - reveals that the specific problem studied here lies in a classically tractable regime: over the tested range it is well described by low-bond-dimension tensor networks and efficiently handled by MPS/Lanczos methods. This negative result provides, to our knowledge, the first entanglement quantification of the BSE amplitude in qubit encoding, establishes the Pauli Hamiltonian framework for future BSE variants, and identifies 2D Minkowski-space BSE, N-body bound states, and non-ladder kernels as physically motivated extensions where genuine quantum advantage may become plausible.
Journal refEur. Phys. J. A 62, 192 (2026)
DOI：10.1140/epja/s10050-026-01957-7
