提高量子连通矩展开的精度和效率
Improving the accuracy and efficiency of quantum connected moments expansions
摘要：
仍然成熟的噪声中间尺度量子（NISQ）技术面临着可以有效实现的算法的严格限制。在量子化学中，变分量子本征求解器（VQE）算法已经变得无处不在，它使用量子本征解算器的函数形式作为自由度，其参数在量子处理器和其常规对应物之间的反馈回路中变化。或者，一个有前途的新途径已经被基于哈密顿量的矩的扩展的技术的量子变体所揭示，其中两个突出：连接矩扩展（CMX）[Phys. Rev. Lett. 58，53（1987）]和Peeters-Devreese-Soldatov（PDS）泛函[J. Phys. A 17，625（1984）; Int. J. Mod. Phys. B 9，2899]，后者基于标准矩< $H^k$ >。与基于VQE的方法相比，如果量子线路准备与真实基态具有非零重叠的状态，CMX通常收敛到基态能量，而PDS由于是变分的而保证收敛。然而，对于有限的CMX/PDS阶数，电路可能会显著影响能量精度。在这里，我们使用的ADAPT-VQE算法来测试浅电路的建设策略，预计不会妨碍他们的实施在目前的量子硬件，同时授予相当大的精度提高计算的基态能量。我们还表明，我们可以利用这样一个事实，即在连接时刻的条款是高度经常性的不同的权力，导致大量减少必要的测量。通过将该测量缓存与阈值耦合，该阈值确定是否要基于其相关联的标量系数来测量给定项，我们观察到电路实现的数量进一步减少，同时允许可调精度。
英文摘要：
The still-maturing noisy intermediate-scale quantum (NISQ) technology faces strict limitations on the algorithms that can be implemented efficiently. In quantum chemistry, the variational quantum eigensolver (VQE) algorithm has become ubiquitous, using the functional form of the ansatz as a degree of freedom, whose parameters are found variationally in a feedback loop between the quantum processor and its conventional counterpart. Alternatively, a promising new avenue has been unraveled by the quantum variants of techniques grounded on expansions of the moments of the Hamiltonian, among which two stand out: the connected moments expansion (CMX) [Phys. Rev. Lett. 58, 53 (1987)] and the Peeters-Devreese-Soldatov (PDS) functional [J. Phys. A 17, 625 (1984); Int. J. Mod. Phys. B 9, 2899], the latter based on the standard moments <$H^k$>. Contrasting with VQE-based methods and provided the quantum circuit prepares a state with non-vanishing overlap with the true ground state, CMX often converges to the ground state energy, while PDS is guaranteed to converge by virtue of being variational. However, for a finite CMX/PDS order, the circuit may significantly impact the energy accuracy. Here we use the ADAPT-VQE algorithm to test shallow circuit construction strategies that are not expected to impede their implementation in the present quantum hardware while granting sizable accuracy improvement in the computed ground state energies. We also show that we can take advantage of the fact that the terms in the connected moments are highly recurring in different powers, incurring a sizable reduction in the number of necessary measurements. By coupling this measurement caching with a threshold that determines whether a given term is to be measured based on its associated scalar coefficient, we observe a further reduction in the number of circuit implementations while allowing for tunable accuracy.
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