最近，美国费米国家加速器实验室的Panagiotis Spentzouris研究小组成功在有限资源的量子计算机上模拟了标量场论。相关成果已于2023年3月3日在国际权威学术期刊《物理评论A》上发表。

该研究小组提出了一种在量子比特计算机上实现${?}^{}$⁴晶格标量场论的量子算法。其中场用离散化的场振幅基表示。演化算子的实现所需要的量子比特数和基本门数与晶格大小成正比。该算法可以在正常相和破缺对称相下，针对大范围的输入参数实现高效的${?}^{}$⁴状态制备。制备状态采用变分演化和绝热演化方法相结合的方法。首先，通过短变分电路制备了包含${?}^{}$⁴自相互作用的局域哈密顿量基态，然后通过绝热地打开晶格点之间的耦合来演化该状态。定义局部哈密顿量的参数是可调整的，并构成了算法的输入。

研究人员提出了一种优化这些参数的方法，以减少状态制备所需的绝热时间。在制备破缺对称态的过程中，通过引入一个在绝热过程中逐渐关闭的辅助外场，可以解决由穿过相变临界线和破缺对称基态简并引起的绝热演化问题。该研究小组证明了在绝热演化过程中外场的时间依赖性对于解决对称性破缺基态简并是很重要的。可以通过使用一个随时间呈指数下降而不是线性下降的场强，将逆误差容差的绝热时间依赖性从二次型降低到线性型。

附：英文原文

Title: Simulating scalar field theories on quantum computers with limited resources

Author: Andy C. Y. Li, Alexandru Macridin, Stephen Mrenna, Panagiotis Spentzouris

Issue&Volume: 2023/03/03

Abstract: We present a quantum algorithm for implementing ${?}^{}$⁴ lattice scalar field theory on qubit computers. The field is represented in the discretized field amplitude basis. The number of qubits and elementary gates required by the implementation of the evolution operator is proportional to the lattice size. The algorithm allows efficient ${?}^{}$⁴ state preparation for a large range of input parameters in both the normal and broken-symmetry phases. The states are prepared using a combination of variational and adiabatic evolution methods. First, the ground state of a local Hamiltonian, which includes the ${?}^{}$⁴ self-interaction, is prepared using short variational circuits. Next, this state is evolved by switching on the coupling between the lattice sites adiabatically. The parameters defining the local Hamiltonian are adjustable and constitute the input of our algorithm. We present a method to optimize these parameters in order to reduce the adiabatic time required for state preparation. For preparing broken-symmetry states, the adiabatic evolution problems caused by crossing the phase transition critical line and by the degeneracy of the broken-symmetry ground state can be addressed using an auxiliary external field which gradually turns off during the adiabatic process. We show that the time dependence of the external field during the adiabatic evolution is important for addressing the broken-symmetry ground state degeneracy. The adiabatic time dependence on the inverse error tolerance can be reduced from quadratic to linear by using a field strength that decreases exponentially in time relative to one that decreases linearly.

DOI: 10.1103/PhysRevA.107.032603

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.107.032603