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.

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。在固态物理学中，找到相互作用电子系统的正确对称性破坏基态是主要挑战之一。为了帮助在热力学极限方法中找到正确的破坏对称性，可以确定大型但有限相互作用的电子系统的基态，这非常有用。变分哈密顿量 (VHA) 是一种变分混合量子经典算法，特别适用于寻找固态系统的基态，通常不会准备破坏对称状态，除非选择初始状态以显示正确的对称性。在这项工作中，我们讨论了 VHA 的三种变体，旨在找到接近不同阶次之间过渡点的有限系统的对称破坏基态。作为测试用例，我们使用二维哈伯德模型，通过耦合到哈密顿量的外部场明确打破对称性并计算对这些场的响应。对于计算，我们模拟了基于门的量子计算机，并考虑了相移噪声对算法的影响。我们发现三种算法中的两种算法与所考虑参数范围的精确解非常一致。第三种算法仅在一部分参数范围内与精确解一致，但与其他两种算法相比，在去相位方面更稳健。