论文标题
发电机坐标方法的量子算法
Quantum algorithms for generator coordinate methods
论文作者
论文摘要
本文讨论了可用于基准分子系统的发电机坐标方法（GCM）的量子算法。由指数运算符定义的GCM形式主义，其通过Fermionic U（n）的发电机定义的指数代数（无代数）提供了使用低深度量子电路探测大子空间的可能性。在目前的研究中，我们说明了用于构建山轮方程的离散形式的量子算法的性能，以进行地面和激发状态能量。我们还将标准GCM公式概括为多产品扩展，当正确探测集体路径时，可以系统地引入更高的等级效应，并在发生生成器状态破坏空间或旋转对称性时提供对称性纯化的基本机制。 GCM量子算法也可以看作是现有变异量子本质体的替代方法，在该量子量子量算法中，多步经典优化算法被单步操作替换，以求解山丘旋转器特征值问题。
This paper discusses quantum algorithms for the generator coordinate method (GCM) that can be used to benchmark molecular systems. The GCM formalism defined by exponential operators with exponents defined through generators of the Fermionic U(N) Lie algebra (Thouless theorem) offers a possibility of probing large sub-spaces using low-depth quantum circuits. In the present studies, we illustrate the performance of the quantum algorithm for constructing a discretized form of the Hill-Wheeler equation for ground and excited state energies. We also generalize the standard GCM formulation to multi-product extension that when collective paths are properly probed, can systematically introduce higher rank effects and provide elementary mechanisms for symmetry purification when generator states break the spatial or spin symmetries. The GCM quantum algorithms also can be viewed as an alternative to existing variational quantum eigensolvers, where multi-step classical optimization algorithms are replaced by a single-step procedure for solving the Hill-Wheeler eigenvalue problem.
