The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). The practical realization is limited by the complexity of quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices. Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as IBM quantum devices.

变分量子本征求解器 (VQE) 是在噪声中等规模量子器件 (NISQ) 上找到给定哈密顿量本征态的最有前途的算法之一。实际实现受限于量子电路的复杂性。在这里，我们提出了一种降低 VQE 中用于电子结构计算的量子电路复杂性的方法。我们的 ClusterVQE 算法将初始量子比特空间分成簇，这些簇进一步分布在单个（较浅）量子电路上。簇是基于反映量子位之间最大纠缠的互信息获得的，而簇间相关性是通过新的“修饰”哈密顿量考虑的。因此，ClusterVQE 允许通过使用更少的量子位和更浅的电路深度来精确模拟问题，但代价是额外的经典资源，使其成为在 NISQ 设备上进行量子化学模拟的潜在领导者。针对基于量子模拟器的几个分子系统以及 IBM 量子设备进行了原理证明演示。