Centre for Computational Science, Department of Chemistry, University College London, LondonWC1H 0AJ, United Kingdom.
Department of Physics and Astronomy, Tufts University, Medford, Massachusetts02155, United States.
J Chem Theory Comput. 2023 Feb 14;19(3):808-821. doi: 10.1021/acs.jctc.2c00910. Epub 2023 Jan 23.
Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilize even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning of the molecular Hamiltonian into two parts: one that is and can be solved classically, supplemented by a component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed (CS-VQE); however, there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz, a parametrized quantum state over which we optimize during VQE; it is not initially clear how a splitting of the Hamiltonian should be reflected in the CS-VQE ansätze. We propose a "noncontextual projection" approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator and demonstrate chemically precise ground state energy calculations for a suite of small molecules at a significant reduction in the required qubit count and circuit depth.
量子化学是嘈杂的中等规模量子（NISQ）设备的一个有前途的应用。然而，量子计算机迄今为止未能为真正具有科学意义的问题提供解决方案，需要算法上的进步才能充分利用当今现有的适度 NISQ 机器。我们讨论了一种基于分子哈密顿量的两部分划分的基态能量估计方法：一部分是可以用经典方法求解的 ，通过变分量子本征求解器（VQE）例程获得的量子修正来补充 部分。这种方法被称为 （CS-VQE）；然而，在将其部署到 NISQ 设备之前，还有一些障碍需要克服。我们在这里解决的问题是变分量子本征求解（VQE）中优化的变分量子本征态的假设，在 VQE 中，我们对其进行优化；最初不清楚哈密顿量的分裂应该如何反映在 CS-VQE 假设中。我们提出了一种“非上下文投影”方法，该方法通过在稳定子形式主义中重新表述 CS-VQE 得到了阐明。这定义了从全电子结构问题到上下文子空间的假设限制，并促进了 CS-VQE 的实现，该实现可以部署在 NISQ 设备上。我们使用量子模拟器验证了非上下文投影假设，并演示了对一系列小分子的化学精确基态能量计算，所需的量子比特数和电路深度显著减少。
