标题： 量子比特耦合簇假设在经典计算机上的优化 显示英文标题

标题： Optimization of the Qubit Coupled Cluster Ansatz on classical computers

摘要： 量子计算的巨大兴趣促使开发了适用于量子硬件的电子结构方法。 然而，量子硬件进展缓慢，迫使研究人员在经典计算机上实现他们的想法，尽管这显然失去了任何“量子优势”。 因此，所谓的受量子启发的方法应运而生。 它们允许从不同的角度看待电子结构问题；然而，要充分利用其潜力，高效的实现是非常可取的。 在这里，我们报告了两种改进迭代量子比特耦合簇（iQCC）方法中振幅优化的方案——这是一种基于量子比特耦合簇（QCC）假设的变分量子本征求解器类型方法。 我们的第一个方案将QCC酉矩阵近似为生成元的对称多项式的总和，直到给定的阶数。 由此产生的能量表达式可以通过阶数参数灵活控制计算复杂度。 它还保证了试验能量及其导数的平滑性，这对于基于梯度的优化策略非常重要。 第二个方案限制了生成QCC酉矩阵的展开空间的大小。 它提供了更好的内存需求控制，但通常可能导致能量估计在振幅变化时出现非平滑变化。 它可以用来将给定振幅集的能量外推到精确的QCC值。 这两种方案相比精确公式，允许包含更多生成元到QCC形式中。 这减少了iQCC方法中的迭代次数和/或提高了准确性。 我们评估了新方案在几个分子系统上的QCC振幅优化能力：N$_2$（16个量子比特）， H$_2$O（36个量子比特），以及三(2-(2,4-二氟苯基)吡啶)铱(III)，（80个量子比特）。 显示英文摘要

摘要： Immense interest in quantum computing has prompted development of electronic structure methods that are suitable for quantum hardware. However, the slow pace at which quantum hardware progresses, forces researchers to implement their ideas on classical computers despite the obvious loss of any "quantum advantage." As a result, the so-called quantum inspired methods emerge. They allow one to look at the electronic structure problem from a different angle; yet, to fully exploit their capacity, efficient implementations are highly desirable. Here we report two schemes for improving the amplitude optimisation in the iterative qubit coupled cluster (iQCC) method -- a variational quantum eigensolver-type approach which is based on the qubit coupled cluster (QCC) Ansatz. Our first scheme approximates the QCC unitary as a sum of symmetrical polynomials of generators up to a given order. The resulting energy expression allows for a flexible control of computational complexity via the order parameter. It also guaranties smoothness of trial energies and their derivatives, which is important for gradient-based optimization strategies. The second scheme limits the size of the expansion space in which the QCC unitary is generated. It provides better control of memory requirements, but in general may lead to the non-smooth variation of energy estimates upon changes in amplitudes. It can be used to extrapolate energies for a given set of amplitudes towards the exact QCC value. Both schemes allow for a larger number of generators to be included into the QCC form compared to the exact formulation. This reduces the number of iterations in the iQCC method and/or leads to higher accuracy. We assess capabilities of the new schemes to perform QCC amplitudes optimization for a few molecular systems: N$_2$ (16 qubits), H$_2$O (36 qubits), and tris(2-(2,4-difluorophenyl)pyridine) iridium(III), (80 qubits).