费米子组态相互作用表象的指数级更精确量子模拟
Exponentially More Precise Quantum Simulation of Fermions in the Configuration Interaction Representation
摘要：
我们提出了一个量子算法的分子系统的模拟，是渐近更有效的比以前所有的算法在文献中的主要问题参数。与以前的工作一样[Babbush等人，New Journal of Physics 18，033032（2016）]，我们采用最近开发的用于模拟哈密顿演化的技术，使用截断的泰勒级数来获得具有所需精度的倒数的对数标度。本文的算法包括模拟下的甲骨文稀疏，第一个量子化表示的分子哈密顿被称为配置相互作用（CI）矩阵。我们构造和查询CI矩阵Oracle，以允许以比经典数值方法更高效的指数方式进行分子积分的实时计算。波函数的二次量子化表示需要$\widetilde{\cal O}(N)$量子位，其中$N$是单粒子自旋轨道的数量，而CI矩阵表示需要$\widetilde{\cal O}(η)$量子位，其中$η\ll N$是目标分子中的电子数量。我们表明，我们的算法的门数规模最多为$\widetilde{\cal O}(η^2 N^3 t)$。
英文摘要：
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New Journal of Physics 18, 033032 (2016)], we employ a recently developed technique for simulating Hamiltonian evolution, using a truncated Taylor series to obtain logarithmic scaling with the inverse of the desired precision. The algorithm of this paper involves simulation under an oracle for the sparse, first-quantized representation of the molecular Hamiltonian known as the configuration interaction (CI) matrix. We construct and query the CI matrix oracle to allow for on-the-fly computation of molecular integrals in a way that is exponentially more efficient than classical numerical methods. Whereas second-quantized representations of the wavefunction require $\widetilde{\cal O}(N)$ qubits, where $N$ is the number of single-particle spin-orbitals, the CI matrix representation requires $\widetilde{\cal O}(η)$ qubits where $η\ll N$ is the number of electrons in the molecule of interest. We show that the gate count of our algorithm scales at most as $\widetilde{\cal O}(η^2 N^3 t)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
