Finding the ground-state energy of molecules is an important and challenging computational problem for which quantum computing can potentially find efficient solutions. The variational quantum eigensolver (VQE) is a quantum algorithm that tackles the molecular groundstate problem and is regarded as one of the flagships of quantum computing. Yet, to date, only very small molecules were computed via VQE, due to high noise levels in current quantum devices. Here we present an alternative variational quantum scheme that requires significantly less qubits than VQE. The reduction in the qubit number allows for shallower circuits to be sufficient, rendering the method more resistant to noise. The proposed algorithm, termed variational quantum selected-configuration-interaction (VQ-SCI), is based on: (a) representing the target groundstate as a superposition of Slater determinant configurations, encoded directly upon the quantum computational basis states; and (b) selecting a-priory only the most dominant configurations. This is demonstrated through a set of groundstate calculations of the H₂, LiH, BeH₂, H₂O, NH₃ and C₂H₄ molecules in the sto-3g basis set, performed on IBM quantum devices. We show that the VQ-SCI reaches the full configuration interaction energy within chemical accuracy using the lowest number of qubits reported to date. Moreover, when the SCI matrix is generated ‘on the fly’, the VQ-SCI requires exponentially less memory than classical SCI methods. This offers a potential remedy to a severe memory bottleneck problem in classical SCI calculations. Finally, the proposed scheme is general and can be straightforwardly applied for finding the groundstate of any Hermitian matrix, outside the chemical context.

中文翻译：

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一种量子比特高效的变分选择配置交互方法


找到分子的基态能量是一个重要且具有挑战性的计算问题，量子计算有可能找到有效的解决方案。变分量子特征求解器 （VQE） 是一种解决分子基态问题的量子算法，被认为是量子计算的旗舰产品之一。然而，迄今为止，由于当前量子器件的噪声水平较高，只有非常小的分子是通过 VQE 计算的。在这里，我们提出了一种替代的变分量子方案，它需要的量子比特比特要少得多。量子比特数的减少使较浅的电路就足够了，从而使该方法更耐噪声。所提出的算法称为变分量子选择配置交互 （VQ-SCI），它基于：（a） 将目标基态表示为 Slater 行列式配置的叠加，直接在量子计算基态上编码;（b） 仅选择 a-priory 最主要的配置。通过在 IBM 量子设备上对 sto-3g 基集中的 H₂、LiH、BeH₂、H₂O、NH₃ 和 C₂H₄ 分子进行一组基态计算来证明这一点。我们表明，VQ-SCI 使用迄今为止报道的最少的量子比特数量在化学精度内达到了完整的构型相互作用能。此外，当 SCI 矩阵是“动态”生成的时，VQ-SCI 需要的内存比传统的 SCI 方法少得多。这为经典 SCI 计算中严重的内存瓶颈问题提供了一种潜在的补救措施。 最后，所提出的方案是通用的，可以直接应用于在化学背景之外查找任何厄米特矩阵的基态。