Title: A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model Show Chinese title

Title: 一种在量子计算机上局部模拟强关联费米物质的配方：二维费米-哈伯德模型

Abstract: The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority of quantum computing technologies are built around qubits and discrete gate-based operations, the translation of the physical problem into this framework is a crucial step. This translation will often be device specific, and a suboptimal implementation will be punished by the exponential compounding of errors on real devices. The importance of an efficient mapping is already revealed for models of spinful fermions in two or three dimensions, which naturally arise when the relevant physics relates to electrons. Using the most direct and well-known mapping, the Jordan-Wigner transformation, leads to a non-local representation of local degrees of freedom, and necessities efficient decompositions of non-local unitary gates into a sequence of hardware accessible local gates. In this paper, we provide a step-by-step recipe for simulating the paradigmatic two-dimensional Fermi-Hubbard model on a quantum computer using only local operations. To provide the ingredients for such a recipe, we briefly review the plethora of different approaches that have emerged recently but focus on the Derby-Klassen compact fermion mapping in order to make our discussion concrete. We provide a detailed recipe for an end-to-end simulation including embedding on a physical device, preparing initial states such as ground states, simulation of unitary time evolution, and measurement of observables and spectral functions. We explicitly compute the resource requirements for simulating a global quantum quench and conclude by discussing the challenges and future directions for simulating strongly-correlated fermionic matter on quantum computers. Show Chinese abstract

Abstract: 量子多体系统的模拟，对于量子化学和凝聚态物理而言，是近期量子计算机在容错之前最有前途的应用之一。 然而，由于大多数量子计算技术都是围绕量子比特和离散门操作构建的，将物理问题转化为这一框架是一个关键步骤。 这种转化通常是特定于设备的，不优化的实现会在真实设备上因误差的指数级累积而受到惩罚。 对于二维或三维的带有自旋的费米子模型，高效映射的重要性已经显现出来，这些模型在相关物理涉及电子时自然出现。 使用最直接且广为人知的映射，即Jordan-Wigner变换，会导致局部自由度的非局部表示，并需要将非局部的酉门高效地分解为一系列硬件可访问的局部门。 在本文中，我们提供了一个逐步的方案，在量子计算机上仅使用局部操作来模拟典型的二维费米-哈伯德模型。 为了提供此类方案的要素，我们简要回顾了最近出现的各种不同方法，但为了使讨论具体化，我们重点介绍了Derby-Klassen紧凑费米子映射。 我们提供了一个端到端模拟的详细方案，包括在物理设备上的嵌入、准备初始状态（如基态）、单位时间演化的模拟以及可观测量和谱函数的测量。 我们明确计算了模拟全局量子淬火的资源需求，并通过讨论在量子计算机上模拟强关联费米物质的挑战和未来方向来结束本文。