在量子计算机上利用虚时演化穷举搜索最优分子几何构型
Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer
AI总结：
本文提出一种基于概率虚时演化的非变分分子几何优化方案，通过将电子态与候选几何构型编码为量子叠加态并利用测量直方图寻找全局能量最小构型，同时给出电路深度标度并验证其可扩展性。
摘要：
我们为第一量子化本征求解器提出了一种非变分的分子几何优化方案，该求解器是近期提出的在量子计算机上利用概率虚时演化（PITE）进行量子化学计算的框架。在该方案中，分子中的电子被视为量子力学粒子，而原子核被视为经典点电荷。我们将电子态和候选分子几何构型同时编码为多量子比特态的叠加，从而获得量子优势。由重复测量结果形成的直方图给出能量曲面的全局最小值。我们证明，对于电子数 n_e，电路深度按 O (n_e^2 poly(log n_e)) 标度，如果额外提供 O (n_e log n_e) 个量子比特，则可将其降低到 O (n_e poly(log n_e))。我们通过数值模拟验证了该方案。这一新的高效方案将有助于在量子计算机上实现实用量子化学的可扩展性。作为该方案的一个特例，仅由带电粒子组成的经典系统也被纳入其中。我们还考察了适用于变分计算的方案，该方案优先考虑为含噪声中等规模量子（NISQ）设备节省电路深度。
英文摘要：
We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, a recently proposed framework for quantum chemistry using the probabilistic imaginary-time evolution (PITE) on a quantum computer. While the electrons in a molecule are treated in the scheme as quantum mechanical particles, the nuclei are treated as classical point charges. We encode both electronic states and candidate molecular geometries as a superposition of many-qubit states, leading to quantum advantage. The histogram formed by outcomes of repeated measurements gives the global minimum of the energy surface. We demonstrate that the circuit depth scales as O (n_e^2 poly(log n_e)) for the electron number n_e, which can be reduced to O (n_e poly(log n_e)) if extra O (n_e log n_e) qubits are available. We corroborate the scheme via numerical simulations. The new efficient scheme will be helpful for achieving scalability of practical quantum chemistry on quantum computers. As a special case of the scheme, a classical system composed only of charged particles is admitted. We also examine the scheme adapted to variational calculations that prioritize saving circuit depths for noisy intermediate-scale quantum (NISQ) devices.
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