AI 中文总结
研究学习与任意费米子多体状态具最大保真度的斯莱特行列式，给出经典和量子算法及硬度下限，表明保真度\(2/3\)是优化格局过渡点，还应用于费米 - 哈伯德模型，为理解费米子多体系统提供算法工具。
AI 中文摘要
学习量子多体状态的紧凑、可解释描述是量子科学中的一项重要任务。我们从哈特里 - 福克方法和不可知断层扫描出发，研究学习与任意费米子多体状态具有最大保真度的斯莱特行列式的任务。给定一个由\(m\)个费米子模式构建的\(n\)费米子波函数，我们提供经典和量子算法，能在\(m^{\text{poly}(n,1/\varepsilon)}\)时间内返回保真度在\(\varepsilon\)内接近最大值的斯莱特行列式。我们证明了匹配的硬度下限，还表明在保真度\(2/3\)以上任何驻点是唯一全局最大值，\(2/3\)是该问题优化格局的过渡点。我们将算法应用于费米 - 哈伯德模型，从神经量子态解中提取最接近的斯莱特行列式。
英文摘要
Learning compact, interpretable descriptions of quantum many-body states is an important task in quantum science. We study the task of learning the Slater determinant with maximum fidelity to an arbitrary fermionic many-body state, with motivation from both Hartree-Fock methods and agnostic tomography. Given an $n$-fermion wavefunction built from $m$ fermionic modes, we provide classical and quantum algorithms returning a Slater determinant with fidelity within $\varepsilon$ of maximal in time $m^{\text{poly}(n,1/\varepsilon)}$. We prove matching hardness lower bounds, assuming standard complexity conjectures, along some parameter axes. Given access to quantum copies, we prove this can be accomplished with $\text{poly}(m,n,1/\varepsilon)$ copies of $ρ$. We also show that above a fidelity of $2/3$ any stationary point is the unique global maximum while below $2/3$ the optimization landscape can have spurious stationary points, and hence $2/3$ marks a transition point in the optimization landscape for this problem. We apply the algorithm to the Fermi-Hubbard model, extracting the closest Slater determinant from neural quantum state solutions. Together, our results provide algorithmic tools with provable guarantees in understanding fermionic many-body systems with classical or quantum simulation.
Comments12 + 14 pages, 9 figures
