用减少误差的$N$ -可表示性条件计算Mott金属-绝缘体跃迁的量子-经典混合算法
Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition
摘要：
分子电子结构的量子算法已经开发出比经典算法更低的计算尺度，但新兴的量子硬件远远不能满足实验实现所需的相干性，连通性和门误差。在这里，我们提出了一类量子经典混合算法，计算能量从一个双电子约化密度矩阵（2-RDM）。2-RDM受$N$可表示性条件约束，该条件用于表示$N$ -电子波函数，其减轻来自量子线路的噪声。我们计算了双态H $_{3}$分解成三个氢原子的强关联解离。混合量子经典计算机将全构型相互作用的能量匹配到0.1 kcal/mol，即“化学准确度”的十分之一，即使在解离的强相关极限下也是如此。此外，计算的单电子RDM的空间局部性表明，量子计算机准确地预测莫特金属-绝缘体转变。
英文摘要：
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate errors required for their experimental realization. Here we propose a class of quantum-classical hybrid algorithms that compute the energy from a two-electron reduced density matrix (2-RDM). The 2-RDM is constrained by $N$-representability conditions, conditions for representing an $N$-electron wavefunction, that mitigates noise from the quantum circuit. We compute the strongly correlated dissociation of doublet H$_{3}$ into three hydrogen atoms. The hybrid quantum-classical computer matches the energies from full configuration interaction to 0.1 kcal/mol, one-tenth of "chemical accuracy," even in the strongly correlated limit of dissociation. Furthermore, the spatial locality of the computed one-electron RDM reveals that the quantum computer accurately predicts the Mott metal-insulator transition.
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