Smart Scott E, Mazziotti David A
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, United States.
J Chem Theory Comput. 2022 Sep 13;18(9):5286-5296. doi: 10.1021/acs.jctc.2c00446. Epub 2022 Sep 1.
A contracted quantum eigensolver (CQE) finds a solution to the many-electron Schrödinger equation by solving its integration (or contraction) to the two-electron space─a contracted Schrödinger equation (CSE)─on a quantum computer. When applied to the anti-Hermitian part of the CSE (ACSE), the CQE iterations optimize the wave function, with respect to a general product ansatz of two-body exponential unitary transformations that can exactly solve the Schrödinger equation. In this work, we accelerate the convergence of the CQE and its wave function ansatz via tools from classical optimization theory. By treating the CQE algorithm as an optimization in a local parameter space, we can apply quasi-second-order optimization techniques, such as quasi-Newton approaches or nonlinear conjugate gradient approaches. Practically, these algorithms result in superlinear convergence of the wave function to a solution of the ACSE. Convergence acceleration is important because it can both minimize the accumulation of noise on near-term intermediate-scale quantum (NISQ) computers and achieve highly accurate solutions on future fault-tolerant quantum devices. We demonstrate the algorithm, as well as some heuristic implementations relevant for cost-reduction considerations, comparisons with other common methods such as variational quantum eigensolvers, and a Fermionic-encoding-free form of the CQE.
一种收缩量子本征求解器（CQE）通过在量子计算机上求解其到双电子空间的积分（或收缩）——一个收缩薛定谔方程（CSE），来找到多电子薛定谔方程的解。当应用于CSE的反厄米部分（ACSE）时，CQE迭代相对于能精确求解薛定谔方程的两体指数酉变换的一般乘积假设来优化波函数。在这项工作中，我们通过经典优化理论的工具加速CQE及其波函数假设的收敛。通过将CQE算法视为局部参数空间中的优化，我们可以应用拟二阶优化技术，如拟牛顿法或非线性共轭梯度法。实际上，这些算法导致波函数超线性收敛到ACSE的一个解。收敛加速很重要，因为它既能最小化近期中尺度量子（NISQ）计算机上噪声的积累，又能在未来的容错量子设备上实现高精度的解。我们展示了该算法，以及一些与成本降低考虑相关的启发式实现、与变分量子本征求解器等其他常用方法的比较，以及CQE的一种无费米子编码形式。
