Boyn Jan-Niklas, Lykhin Aleksandr O, Smart Scott E, Gagliardi Laura, Mazziotti David A
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
J Chem Phys. 2021 Dec 28;155(24):244106. doi: 10.1063/5.0074842.
While chemical systems containing hundreds to thousands of electrons remain beyond the reach of quantum devices, hybrid quantum-classical algorithms present a promising pathway toward a quantum advantage. Hybrid algorithms treat the exponentially scaling part of the calculation-the static correlation-on the quantum computer and the non-exponentially scaling part-the dynamic correlation-on the classical computer. While a variety of algorithms have been proposed, the dependence of many methods on the total wave function limits the development of easy-to-use classical post-processing implementations. Here, we present a novel combination of quantum and classical algorithms, which computes the all-electron energy of a strongly correlated molecular system on the classical computer from the 2-electron reduced density matrix (2-RDM) evaluated on the quantum device. Significantly, we circumvent the wave function in the all-electron calculations by using density matrix methods that only require input of the statically correlated 2-RDM. Although the algorithm is completely general, we test it with two classical density matrix methods, the anti-Hermitian contracted Schrödinger equation (ACSE) and multiconfiguration pair-density functional theories, using the recently developed quantum ACSE method for simulating the statically correlated 2-RDM. We obtain experimental accuracy for the relative energies of all three benzyne isomers and thereby demonstrate the ability of the developed algorithm to achieve chemically relevant and accurate results on noisy intermediate-scale quantum devices.
虽然包含数百到数千个电子的化学系统仍超出量子设备的处理能力，但混合量子 - 经典算法为实现量子优势提供了一条有前途的途径。混合算法将计算中呈指数级扩展的部分——静态关联——放在量子计算机上处理，而将非指数级扩展的部分——动态关联——放在经典计算机上处理。虽然已经提出了多种算法，但许多方法对全波函数的依赖限制了易于使用的经典后处理实现的发展。在这里，我们提出了一种量子和经典算法的新颖组合，它根据在量子设备上评估的两电子约化密度矩阵（2-RDM）在经典计算机上计算强关联分子系统的全电子能量。值得注意的是，我们通过使用仅需要输入静态关联的2-RDM的密度矩阵方法，在全电子计算中避开了波函数。尽管该算法具有完全通用性，但我们使用最近开发的用于模拟静态关联2-RDM的量子ACSE方法，用两种经典密度矩阵方法——反厄米收缩薛定谔方程（ACSE）和多组态对密度泛函理论对其进行了测试。我们获得了所有三种苯炔异构体相对能量的实验精度，从而证明了所开发算法在有噪声的中尺度量子设备上获得化学相关且准确结果的能力。
