论文标题
使用离散的哈伯德 - 斯特拉托尼维奇转换在量子计算机上的gutzwiller波函数
Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
论文作者
论文摘要
我们提出了一种量子古典混合方案，用于使用离散的Hubbard-Stratonovich转换实现非单身的GutzWiller因子，这使我们能够以仅涉及单个问题的单位旋转的单位性能来表达GutzWiller因子，这是单一涉及单一算法的线性组合，而单位算子则以Auxiliary Fields的成本为代价。为了在辅助场上执行总和，我们介绍了具有互补特征的两种方法。第一种方法采用了非军事电路的线性组合，这使人们能够在量子计算机上概率地准备gutzwiller波函数，而第二种方法则使用重要性采样来随机估计可观察到的物质，类似于经典计算中的量子蒙特卡洛方法。该方案用半填充的费米 - 哈伯德模型的数值模拟证明了这一方案。此外，我们使用实际量子设备执行量子模拟，证明所提出的方案可以在误差栏内重现两点费米 - 哈伯德模型的确切地面能量。
We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary operators involving only single-qubit rotations, at the cost of the sum over the auxiliary fields. To perform the sum over the auxiliary fields, we introduce two approaches that have complementary features. The first approach employs a linear-combination-of-unitaries circuit, which enables one to probabilistically prepare the Gutzwiller wave function on a quantum computer, while the second approach uses importance sampling to estimate observables stochastically, similar to a quantum Monte Carlo method in classical computation. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model. Furthermore, we perform quantum simulations using a real quantum device, demonstrating that the proposed scheme can reproduce the exact ground-state energy of the two-site Fermi-Hubbard model within error bars.
