用更少量子比特实现更高精度：量子计算机上量子化学的单粒子基组优化
Better accuracy with fewer qubits: Single-particle basis set optimization for quantum chemistry on quantum computers
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中文总结 AI 辅助
该研究针对近期量子计算机的噪声限制，通过遗传算法优化生成MSTO-kG基组，在相同或更少量子比特数下，可实现优于或相当于6-31G、cc-pVQZ等基组的量子化学计算能量，降低了量子化学计算的量子资源需求。
中文摘要 AI 辅助
尽管近期取得了进展，未来几年量子计算机预计仍将存在显著噪声，这会限制量子化学计算所能使用的轨道数量。然而，即使采用质量尚可的单粒子基组，轨道数量有限的小活性空间也会导致大量相关能损失，因此亟需为量子算法设计中等质量且量子比特效率高的基组。我们采用受遗传算法启发的方法结合激进的优化策略，对现有最小基组进行重新优化，生成了适用于氢（H）至氟（F）原子的改进型最小基组（MSTO-kG基，k=2-11）。在全配置相互作用（FCI）理论水平下，使用我们的MSTO基组计算H至F的基态能量，所得结果与6-31G基组的结果相当，部分情况下甚至更低；对于锂（Li），MSTO基组的性能优于相关一致极化价四重zeta（cc-pVQZ）基组。因此，相较于STO基组，我们的MSTO基组在相同量子比特数下可获得更优的原子能量；相较于更高质量的基组，在更少量子比特数下即可获得更优或相当的能量。对于分子而言，氢分子（H₂）的表现较差，这与文献中早期研究的结论一致；对于其他分子，包括锂二（Li₂）、碳二（C₂）、氢化锂（LiH）、氢化铍（BeH）和氢化铍二（BeH₂），使用我们的基组得到的FCI结果（针对C₂，我们采用组态相互作用单双（CISD）方法）与6-31G基组的结果相当或更优。最后，我们对比了不同基组所需的资源，发现相较于同类基组，MSTO基组在使用变分量子本征求解器（VQE）、量子相位估计算法（QPE）和HHL算法时，既能获得更优的能量，又能减少所需的量子比特数和两量子比特门数量；QPE和HHL的逻辑T门数量也显著降低。总体而言，我们的工作为近期量子计算机上实现更精准且量子比特需求更低的量子化学计算铺平了道路。
英文摘要
In spite of recent advances, quantum computers are expected to be sufficiently noisy in the coming few years to the extent of limiting quantum chemical calculations to relatively small number of orbitals. However, even with reasonable quality single particle basis sets, small active spaces with limited orbitals can result in a significant fraction of correlation energy being lost, motivating the design of moderate quality qubit-efficient basis sets for quantum algorithms. We begin by reoptimizing the existing minimal basis sets using a genetic algorithm-inspired approach in conjunction with aggressive refinement strategies, and generate modified minimal basis sets (MSTO-kG basis; k = 2-11) for atoms from H through F. The ground state energies of H through F using our MSTO bases at FCI level of theory yield ground state energies that are comparable or sometimes even lower than those obtained using 6-31G basis sets. In the case of Li, the MSTO bases surpass the performance of cc-pVQZ bases. Thus, we obtain better atomic energies with same number of qubits relative to STO bases, and better/comparable energies with fewer qubits relative to higher quality bases. In the case of molecules, H2 performs poorly; a finding that is consistent with an earlier work in literature. For other molecules, Li2, C2, LiH, BeH and BeH2, the FCI results (except C2 for which we employ CISD) from our bases are comparable to/outperform those from 6-31G basis. Finally, we compare the resources required between different bases and find that MSTO bases yield better energies than the competing basis sets while incurring fewer qubits and two-qubit gates with VQE, QPE, and HHL. The logical T-gate counts are also found to be considerably lower for QPE and HHL respectively. Overall, our work paves way for more accurate yet less qubit-hungry quantum chemical calculations using near-term quantum computers.
