Preparing ground states with a broken symmetry with variational quantum algorithms
Preparing ground states with a broken symmetry with variational quantum algorithms
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DOI：
10.1088/2058-9565/abe568
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发表时间：
2021-02
影响因子：
6.7
通讯作者：
N. Vogt;S. Zanker;Jan-Michael Reiner;M. Marthaler;T. Eckl;A. Marusczyk
中科院分区：
文献类型：
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作者：
N. Vogt;S. Zanker;Jan-Michael Reiner;M. Marthaler;T. Eckl;A. Marusczyk
近期量子计算机最有前途的应用之一是物理量子系统的模拟，特别是化学和凝聚态物理中的多电子系统。在固体物理学中，找到相互作用电子系统的正确对称破缺基态是一个核心挑战。为了帮助找到正确的破缺对称性的热力学极限方法，允许确定大的，但有限的相互作用电子系统的基态是非常有用的。变分哈密顿量近似（VHA）是一种变分混合量子经典算法，特别适合于寻找固态系统的基态，除非初始态被选择为具有正确的对称性，否则一般不会产生对称性破缺态。在这项工作中，我们讨论了三种变化的VHA旨在找到一个有限的系统接近不同的订单之间的过渡点的突破性的基态。作为一个测试案例，我们使用的二维哈伯德模型，我们打破了对称性明确通过外部场耦合到哈密顿量和计算这些领域的响应。对于计算，我们模拟了基于门的量子计算机，并考虑了失相噪声对算法的影响。我们发现，这三个算法中的两个是在所考虑的参数范围内的精确解很好的协议。第三种算法仅在部分参数范围内与精确解一致，但与其他两种算法相比，在移相方面更鲁棒。
One of the most promising applications for near term quantum computers is the simulation of physical quantum systems, particularly many-electron systems in chemistry and condensed matter physics. In solid state physics, finding the correct symmetry broken ground state of an interacting electron system is one of the central challenges. To help finding the correct broken symmetries in the thermodynamic limit methods that allow to determine the groundstate of large but finite interacting electron systems are very useful. The variational Hamiltonian ansatz (VHA), a variational hybrid quantum-classical algorithm especially suited for finding the ground state of a solid state system, will in general not prepare a broken symmetry state unless the initial state is chosen to exhibit the correct symmetry. In this work, we discuss three variations of the VHA designed to find the symmetry-breaking groundstate of a finite system close to a transition point between different orders. As a test case we use the two-dimensional Hubbard model where we break the symmetry explicitly by means of external fields coupling to the Hamiltonian and calculate the response to these fields. For the calculation we simulate a gate-based quantum computer and also consider the effects of dephasing noise on the algorithms. We find that two of the three algorithms are in good agreement with the exact solution for the considered parameter range. The third algorithm agrees with the exact solution only for a part of the parameter regime, but is more robust with respect to dephasing compared to the other two algorithms.