论文标题
多体基态数字量子模拟的加速变异算法
Accelerated variational algorithms for digital quantum simulation of many-body ground states
论文作者
论文摘要
新兴量子模拟器的关键应用之一是模仿多体系统的基础状态，因为它在从凝聚态物理学到材料科学的各个领域都引起了人们的关注。传统上，从模拟的意义上讲，绝热的进化被提议慢慢地进化出一种以基础状态初始化的简单的哈密顿量，以使最终状态成为所需的基础状态。最近，在量子模拟器中还提出了变异方法，以模拟多体系统的基态。在这里，我们首先提供了绝热方法和变异方法与数字量子模拟器所需的量子资源之间的定量比较，即电路的深度和两个Qubit的量子门的数量。我们的结果表明，在这些资源方面，各种方法的要求较小。但是，它们需要通过经典优化杂交，该优化可以缓慢收敛。因此，作为论文的第二个结果，我们通过对变异电路的参数进行良好的初始猜测来提供两种不同的方法来加速经典优化器的收敛。我们表明，这些方法适用于广泛的哈密顿量，并在优化程序方面可显着改善。
One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we first provide a quantitative comparison between the adiabatic and variational methods with respect to required quantum resources on digital quantum simulators, namely the depth of the circuit and the number of two-qubit quantum gates. Our results show that the variational methods are less demanding with respect to these resources. However, they need to be hybridized with a classical optimization which can converge slowly. Therefore, as the second result of the paper, we provide two different approaches for speeding the convergence of the classical optimizer by taking a good initial guess for the parameters of the variational circuit. We show that these approaches are applicable to a wide range of Hamiltonian and provide significant improvement in the optimization procedure.
