用于绝热热启动的通用父哈密顿量
Universal Parent Hamiltonians for Adiabatic Warm Starts
浏览论文内容
中文总结 AI 辅助
研究量子系统基态性质计算问题，提出用通用父哈密顿量实现绝热热启动的协议（UPHAWS），以解决绝热态制备中谱隙小的问题，通过实验验证该方法能有效提升绝热路径最小能隙。
中文摘要 AI 辅助
计算量子系统的基态性质是量子计算的一个重要潜在应用。量子相位估计解决基态问题的成功概率与输入态和基态的重叠成正比。局部近似态方法存在正交性灾难，而绝热态制备（ASP）可以以与绝热路径上最小谱隙的平方成反比增长的成本制备良好近似。当初始和目标哈密顿量处于由一阶相变分隔的量子相时，绝热路径上的最小谱隙随系统大小呈指数减小。我们基于选择一个绝热态制备的初始哈密顿量来解决这个问题，其基态与目标基态处于相同量子相。我们开发了一种使用通用父哈密顿量的通用绝热热启动协议（UPHAWS），它可以在任何制备电路已知的状态下初始化ASP。我们使用费曼 - 基塔耶夫时钟哈密顿量作为通用父哈密顿量，用于有和没有中间电路测量的制备电路。我们在一个插值到目标GHZ哈密顿量的$\mathbb{Z}_2$对称矩阵乘积态（MPS）族以及对称键拉伸下的线性$H_6$链上对该框架进行基准测试。对于$H_6$系统，相对于哈特里 - 福克初始化，键维度为4的矩阵乘积态热启动使绝热路径上的最小能隙增加了两倍。为了进行这些经典基准模拟，我们开发了绝热哈密顿量的动量空间截断，这可能具有独立的研究意义。
英文摘要
Computing the ground state properties of quantum systems is an important potential application of quantum computing. The success probability of quantum phase estimation approaches to ground state problems is proportional to the overlap of the input state with the ground state. Local ansatz state approaches suffer from the orthogonality catastrophe, whereas adiabatic state preparation (ASP) can prepare good approximations with a cost growing with the inverse square of the minimum spectral gap along the adiabatic path. When the initial and target Hamiltonians lie in quantum phases separated by a first order phase transition, the minimum spectral gap along the adiabatic path becomes exponentially small as a function of system size. We pursue a solution to this problem based on choosing an initial Hamiltonian for adiabatic state preparation whose ground state lies in the same quantum phase as the target ground state. We develop a protocol for universal adiabatic warm starts with universal parent Hamiltonians (UPHAWS) that can initialize ASP in any state whose preparation circuit is known. We use the Feynman--Kitaev clock Hamiltonian as a universal parent Hamiltonian, for preparation circuits with and without mid circuit measurement. We benchmark the framework on a $\mathbb{Z}_2$-symmetric matrix product state (MPS) family interpolating to a target GHZ Hamiltonian, and on the linear $H_6$ chain under symmetric bond stretching. For the $H_6$ system a bond-dimension-$4$ matrix product state warm-start increases the minimum gap on the adiabatic path by a factor of two relative to the Hartree-Fock initialization. To perform these classical benchmark simulations we develop a momentum-space truncation of the adiabatic Hamiltonian that may be of independent interest.
