A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this work, we present a detailed roadmap on how to simulate a two-dimensional electron gas—cooled to absolute zero and pierced by a strong transversal magnetic field—on a quantum computer. This system describes the setting of the Fractional Quantum Hall Effect (FQHE), one of the pillars of modern condensed matter theory. We give analytical expressions for the two-body integrals that allow for mixing between $N$ Landau levels at a cutoff $M$ in angular momentum and give gate count estimates for the efficient simulation of the energy spectrum of the Hamiltonian on an error-corrected quantum computer. We then focus on studying efficiently preparable initial states and their overlap with the exact ground state for noisy as well as error-corrected quantum computers. By performing an imaginary time evolution of the covariance matrix we find the generalized Hartree-Fock solution to the many-body problem and study how a multi-reference state expansion affects the state overlap. We perform small-system numerical simulations to study the quality of the two initial state Ans"{a}tze in the Lowest Landau Level (LLL) approximation.

中文翻译：

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分数量子霍尔效应的量子模拟路线图

建立量子计算机的主要动机是它提供了一种工具，可以有效地模拟强相关的量子系统。在这项工作中，我们给出了如何在量子计算机上模拟二维电子气的详细路线图，该二维电子气冷却至绝对零并被强横向磁场刺穿。该系统描述了分数量子霍尔效应（FQHE）的设置，该分数是现代凝聚态理论的支柱之一。我们给出了两体积分的解析表达式，该积分允许在$ñ$ 极限水平 $\mathrm{中号}$角动量，并给出门计数估计值，以便在误差校正的量子计算机上有效地模拟哈密顿量的能谱。然后，我们专注于研究有效的可制备初始状态及其与噪声和纠错量子计算机的确切基态的重叠。通过执行协方差矩阵的假想时间演化，我们找到了针对多体问题的广义Hartree-Fock解，并研究了多参考状态扩展如何影响状态重叠。我们执行小型系统数值模拟，以研究最低兰道能级（LLL）近似的两个初始状态Ans“ {a} tze的质量。