耗散基态制备的局域性与滤波器设计
Locality and filter design for dissipative ground-state preparation
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中文总结 AI 辅助
通过线性规划优化滤波权重、利用利布-罗宾逊界实现局域补丁演化，并在小补丁下保持稳态接近基态，大幅降低耗散基态制备的模拟成本，同时保持高保真度。
中文摘要 AI 辅助
基态制备是量子多体物理、化学和材料科学中的一个基本挑战。耗散态制备技术通过设计一个林德布拉德（Lindbladian）耦合到环境，驱动系统到达其基态，且不需要初始重叠。其成本主要由滤波跳跃算子内部的哈密顿量模拟主导，因为每个跳跃都是耦合算子的海森堡演化副本（即分支）的加权和。我们通过将三个简单观察贯彻到底来降低这一成本。首先，在固定时间网格上，线性规划优化分支权重，在加热响应与电路成本之间进行权衡。其次，利布-罗宾逊（Lieb-Robinson）界允许每个分支在一个半径随其持续时间增长的补丁上演化。第三，如果动力学快速收敛且截断仅轻微改变跳跃，则稳态即使位于比光锥更小的补丁上也仍接近基态。我们通过数值方式验证了我们的方法。在包含81个演化时间点的网格上，优化后的滤波器在相同成本下将最坏情况下的加热响应（即泄漏）降低了超过116倍。在十五个分子和六条链上，在匹配的设计网格泄漏下，成本降低了27%至56%；在匹配成本下，分子泄漏降低了2.9倍至2×10³倍。密度矩阵模拟显示两种滤波器均具有高基态保真度，并且在伊辛（Ising）和哈伯德（Hubbard）链上，较便宜的滤波器在三个或四个位点的补丁上保持了至少0.89的基态布居数。相同的补丁在海森堡（Heisenberg）链上失效，因为其截断误差随补丁尺寸下降更慢，且其林德布拉德能隙比伊辛链小12倍，这表明能隙在补丁可截断程度中起作用。在固定半径下，每个分支的成本变得与系统尺寸无关，从而降低了耗散态制备的成本。
英文摘要
Ground-state preparation is a fundamental challenge in quantum many-body physics, chemistry and materials science. Dissipative state-preparation techniques engineer a Lindbladian coupling to a bath that drives the system to its ground state, needing no initial overlap. Their cost is dominated by the Hamiltonian simulations inside the filtered jump operators, since each jump is a weighted sum of Heisenberg-evolved copies, or branches, of a coupling operator. We reduce this cost by following three simple observations to their logical end. First, on a fixed time grid, linear programming optimises the branch weights, trading the heating response against the circuit cost. Second, Lieb--Robinson bounds let each branch evolve on a patch whose radius grows with its duration. Third, if the dynamics converges quickly and truncation changes the jumps only slightly, the stationary state stays near the ground state even on patches smaller than the light cone. We validate our approach numerically. On a grid of $81$ evolution times, the optimised filter reduces the worst-case heating response, or leakage, more than $116$-fold at equal cost. Across fifteen molecules and six chains, the cost falls by 27 to 56\% at matched design-grid leakage; at matched cost, the molecular leakage falls by a factor of $2.9$ to $2\times10^{3}$. Density-matrix simulations show high ground-state fidelity for both filters, and on Ising and Hubbard chains the cheaper filter keeps a ground-state population of at least $0.89$ on patches of three or four sites. The same patches fail on a Heisenberg chain whose truncation error falls more slowly with patch size and whose Lindbladian gap is 12 times smaller than the Ising chain's, pointing to a role for the gap in how far patches can be truncated. At fixed radius the per-branch cost becomes independent of system size, reducing the cost of dissipative state preparation.
发表机构
- Centre for Quantum Software and Information, School of Computer Science, Faculty of Engineering and Information Technology, University of Technology Sydney（悉尼科技大学工程学院信息技术学院量子软件与信息研究中心）
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