发表机构
The University of Tokyo; Quemix Inc.; National Institutes for Quantum Science and Technology (QST)（东京大学; Quemix公司; 国立研究開発法人量子科学技術研究機構）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出利用矩阵乘积态编码高效实现非局域赝势，降低第一量子化量子模拟的电路深度，并通过一维氢原子电离模型验证了其有效性。
AI 中文摘要
基于第一量子化方法的量子模拟在空间和门复杂度上可以低于第二量子化方法。通过采用赝势（pseudopotentials）可以进一步降低这些模拟的门需求，赝势是经典量子化学计算中广泛使用的一种技术，用于减少模拟电子的数量。然而，由于赝势的非局域性，在量子电路中实现赝势仍然具有挑战性。在本研究中，我们提出了一种利用矩阵乘积态（MPS）编码高效实现非局域势的方法。MPS编码使我们能够以电路深度$O(\mathrm{deg}(V_{\mathrm{loc}}) n^{\mathrm{deg}(V_{\mathrm{loc}})} + 8Lnn_{\mathrm{atom}}\chi^2 + 2n^2)$高效实现Trotter步算子，其中$\mathrm{deg}(V_{\mathrm{loc}})$是多项式局域势的阶数，$n_{\mathrm{atom}}$是系统中的原子数，$L$是所有原子中投影函数的最大数量，$n$是用于在一维空间中表示二进制编码波函数的量子比特数。我们通过将该方法应用于由超短激光脉冲驱动的一维氢原子电离模型，证明了该方法的有效性。我们的结果表明，与直接酉分解相比，MPS编码显著降低了所需的电路深度，为实际的第一量子化模拟提供了途径。
英文摘要
Quantum simulations based on first-quantized approaches can offer lower space and gate complexities than second-quantized approaches. The gate requirements for these simulations can be further reduced by employing pseudopotentials, a technique widely used in classical quantum chemistry calculations to decrease the number of simulated electrons. However, implementing pseudopotentials in quantum circuits remains challenging due to their non-local nature. In this study, we proposed a method to efficiently implement non-local potentials using matrix product state (MPS) encoding. MPS encoding allows us to efficiently implement a Trotter step operator with a circuit depth of $O(\mathrm{deg}(V_{\mathrm{loc}}) n^{\mathrm{deg}(V_{\mathrm{loc}})} + 8Lnn_{\mathrm{atom}}χ^2 + 2n^2)$, where $\mathrm{deg}(V_{\mathrm{loc}})$ is the degree of the polynomial local potential, $n_{\mathrm{atom}}$ is the number of atoms in the system, $L$ is the maximum number of projector functions across all atoms, and $n$ is the number of qubits used to represent the binary-encoded wave function in one-dimensional space. We demonstrated the effectiveness of this approach by applying it to a model of the ionization of a one-dimensional hydrogen atom driven by an ultrashort laser pulse. Our results showed that MPS encoding significantly reduces the required circuit depth compared to a direct unitary decomposition, providing a pathway for practical first-quantized simulations.
