利用无相位辅助场量子蒙特卡洛提高基于采样的量子对角化的精度与效率
Enhancing the accuracy and efficiency of sample-based quantum diagonalization with phaseless auxiliary-field quantum Monte Carlo
AI总结：
本文提出将无相位辅助场量子蒙特卡洛与基于采样的量子对角化相结合，利用量子硬件获得的截断SQD试探波函数恢复大量相关能并缓解采样冗余，从而提升含噪声量子计算机上电子结构计算的精度与效率。
摘要：
量子选定组态相互作用（QSCI）及其扩展协议——基于采样的量子对角化（SQD）——已成为在含噪声量子计算机上求解电子薛定谔方程的有前景的算法。在QSCI/SQD中，量子线路在量子设备上被重复制备，测量得到的组态构成多体希尔伯特空间的一个子空间，哈密顿量在该子空间内被经典对角化。针对N$_2$的解离以及一个模型$\mathrm{[2Fe-2S]}$团簇（分别关联26个轨道中的10个电子和20个轨道中的30个电子），我们展示了一种非微扰随机方法——无相位辅助场量子蒙特卡洛（ph-AFQMC）——使用从量子硬件获得的截断SQD试探波函数，能够恢复大量（例如O(100) mHa）的相关能，并缓解QSCI/SQD过程中可能存在的采样冗余问题。对ph-AFQMC能量与SQD试探波函数能量方差进行外推，有潜力进一步提高能量精度。
英文摘要：
Quantum Selected Configuration Interaction (QSCI) and an extended protocol known as Sample-based Quantum Diagonalization (SQD) have emerged as promising algorithms to solve the electronic Schrödinger equation with noisy quantum computers. In QSCI/SQD a quantum circuit is repeatedly prepared on the quantum device, and measured configurations form a subspace of the many-body Hilbert space in which the Hamiltonian is diagonalized classically. For the dissociation of N$_2$ and a model $\mathrm{[2Fe-2S]}$ cluster (correlating 10 electrons in 26 orbitals and 30 electrons in 20 orbitals, respectively) we show that a non-perturbative stochastic approach, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), using truncated SQD trial wavefunctions obtained from quantum hardware can recover a substantial amount (e.g., O(100) mHa) of correlation energy and alleviate the possible sampling redundancy of the QSCI/SQD procedure. Extrapolation of the ph-AFQMC energy versus the energy variance of the SQD trial wavefunctions has the potential to further improve the energy accuracy.
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