论文标题
对称增强的变分量子自旋特征者
Symmetry enhanced variational quantum spin eigensolver
论文作者
论文摘要
变分量子古典算法是在近期量子模拟器上实现量子优势的最有希望的方法。在这些方法中，近年来，各种量子量化量引起了很多关注。尽管它对于模拟多体系统的基础状态非常有效，但其对激发状态的概括变得非常需要资源。在这里，我们表明，通过利用哈密顿人的对称性可以大大改善这个问题。改进对于更高的能量本征态更为有效。我们介绍了两种合并对称性的方法。在第一种方法（称为硬件对称性保存）中，所有对称性都包含在电路设计中。在第二种方法中，更新成本函数以包括对称性。硬件对称保留方法确实表现出了第二种方法。但是，将所有对称性集成到电路的设计中可能非常具有挑战性。因此，我们介绍了混合对称性保存方法，其中对称性在电路和经典成本函数之间分配。这允许在防止复杂的电路设计的同时利用对称性的优势。
The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.
