AI 中文总结
该研究提出基于坐标空间简谐振子基的φ⁴模型表述，其单体态矩阵和相互作用张量呈有效带对角结构，可降低量子模拟资源，经数值验证其低能谱与动量空间表述一致。
AI 中文摘要
量子计算为量子场论的模拟提供了极具前景的框架，其计算成本取决于所采用的量子算法和哈密顿量的表示形式。我们研究了基于坐标空间中简谐振子基的φ⁴模型的一种表述，推导了该表述下的格点φ⁴哈密顿量，并分析了所得单体态矩阵和相互作用张量的结构，证明二者均呈现有效带对角结构，可对哈密顿量进行可控截断同时保留低能谱。我们通过将数值对角化得到的低能可观测量与标准简谐振子动量空间表述计算的结果进行比较，验证了该表述的有效性。最后，我们估计了使用二元和一元玻色子-量子比特映射在量子计算机上编码哈密顿量所需的资源，结果表明，利用有效局域性，坐标空间表示可在广泛参数范围内降低量子模拟所需的资源。
英文摘要
Quantum computing provides a promising framework for the simulation of quantum field theories, where the computational cost depends both on the quantum algorithm employed and on the representation of the Hamiltonian. We investigate a formulation of the $ϕ^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $ϕ^4$ Hamiltonian in this representation and analyze the structure of the resulting one-body matrix and interaction tensor. We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian while preserving the low-energy spectrum. We validate this formulation by comparing low-energy observables obtained from numerical diagonalization with those computed in the standard harmonic-oscillator momentum-space representation. Finally, we estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings. By exploiting effective locality, the coordinate-space representation reduces the resources required for quantum simulation over a broad range of parameters.
Comments25 pages, 9 figures
