论文标题
具有双重分解的哈密顿的随机量子Krylov方案
A stochastic quantum Krylov protocol with double factorized Hamiltonians
论文作者
论文摘要
我们提出了一类随机量子Krylov对角化（RQKD）算法，能够使用适度的量子资源需求解决本本征估计问题。与以前的实时进化量子krylov子空间方法相比，我们的方法表示时间演化运算符，$ e^{ - i \ hat {h}τ} $，作为单位型的线性组合，随后使用随机抽样程序来减少电路深度要求。虽然我们的方法适用于任何具有可快速的子组件的哈密顿量，但我们专注于其应用于明确的双重分子电子结构哈密顿量。为了证明所提出的RQKD算法的潜力，我们为具有基于电路的状态向量模拟器的各种分子系统提供了数值基准，从而实现了基态能量误差小于1〜kcal〜kcal〜mol $^{ - 1} $，而均高于低位的确定性trottertertertertertertertertersuki decounctions coultive Decormess timuse suilds forciption-lastige。
We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov subspace methods, our approach expresses the time evolution operator, $e^{-i\hat{H} τ}$, as a linear combination of unitaries and subsequently uses a stochastic sampling procedure to reduce circuit depth requirements. While our methodology applies to any Hamiltonian with fast-forwardable subcomponents, we focus on its application to the explicitly double-factorized electronic-structure Hamiltonian. To demonstrate the potential of the proposed rQKD algorithm, we provide numerical benchmarks for a variety of molecular systems with circuit-based statevector simulators, achieving ground state energy errors of less than 1~kcal~mol$^{-1}$ with circuit depths orders of magnitude shallower than those required for low-rank deterministic Trotter-Suzuki decompositions.
