AI 中文总结
该研究在NISQ设备上，基于GCM提出QuGCM与ADAPT-GCIM方法，结合GC编码策略，成功模拟核系统低能谱，验证了方法的稳健性与硬件兼容性。
AI 中文摘要
基于生成坐标方法（Generator Coordinate Method, GCM），我们在混合量子-经典框架内采用量子GCM（Quantum GCM, QuGCM）在量子设备上模拟核系统的低本征态。生成基态由哈特里-福克（Hartree-Fock, HF）参考态通过对称适配的酉耦合簇（unitary coupled-cluster, UCC）算子激发构造，这些态被制备为非正交量子电路并成对测量，以计算所需的重叠积分和哈密顿核。根据GCM形式主义，所得数据经经典广义本征求解器处理，用于提取系统的能谱。为提升效率并降低电路深度，我们应用自适应生成坐标启发方法（Adaptive Generator Coordinate Inspired method, ADAPT-GCIM），该方法基于能量梯度迭代选择生成激发，从而避免探索整个希尔伯特空间。我们将该实现应用于核系统，具体为采用Reid68势的氘核以及⁶Li和³⁸Ar的壳模型哈密顿量。对于每个系统，QuGCM和ADAPT-GCIM两种方法均得到与经典对角化结果一致的能谱，即使在噪声和有限深度约束下也展现出稳健性。此外，我们比较了费米子编码策略，即独热（one-hot, OH）编码的约旦-维格纳（Jordan-Wigner, JW）变换与格雷码（Gray code, GC）映射，结果显示GC编码可降低电路复杂度并提升多参考态制备过程中的保真度。我们的发现表明，QuGCM和ADAPT-GCIM为模拟关联量子系统提供了一条实用且可扩展的路径，其对噪声的脆弱性更低，且与当前量子硬件的限制兼容性更好。
英文摘要
Based on the Generator Coordinate Method (GCM), we use a Quantum GCM (QuGCM) within a hybrid quantum-classical framework to simulate low-lying eigenstates of nuclear systems on quantum devices. The generator basis states are constructed from Hartree-Fock (HF) reference states, excited via symmetry-adapted unitary coupled-cluster (UCC) operators. These states are prepared as non-orthogonal quantum circuits and measured pairwise to compute the required overlap and Hamiltonian kernels. The resulting data is processed using a classical generalized-eigenvalue solver, following the GCM formalism, to extract the system's energy spectrum. To enhance efficiency and reduce circuit depth, we apply the Adaptive Generator Coordinate Inspired method (ADAPT-GCIM), which iteratively selects generator excitations based on energy gradients, thereby avoiding the need to explore the full Hilbert space. Our implementation is applied to nuclear systems, specifically the deuteron with the Reid68 potential and shell-model Hamiltonians of $^6$Li and $^{38}$Ar. For each system, both the QuGCM and ADAPT-GCIM methods produce energy spectra in agreement with classical diagonalization results, demonstrating robustness even under noise and limited-depth constraints. Additionally, we compare fermionic encoding strategies, specifically Jordan-Wigner (JW) transformations of one-hot (OH) encoding and Gray code (GC) mappings, and show that GC encoding reduces circuit complexity and improves fidelity during multi-reference state preparation. Our findings indicate that QuGCM and ADAPT-GCIM provide a practical and scalable path toward simulating correlated quantum systems, with lesser vulnerability to noise and better compatibility with the limitations of current quantum hardware.
Comments23 pages, 10 figures
