论文标题
提高量子近似优化的性能，以制备无平移对称性的非平凡量子状态
Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry
论文作者
论文摘要
使用量子近似优化算法（QAOA）对复杂量子状态的变分制备具有根本性的兴趣，并且成为量子计算机的有希望的应用。在这里，我们系统地研究了QAOA在其量子相变的临界点附近准备目标汉密尔顿人的基础状态，并产生Greenberger-Horne-Zeilinger（GHz）状态。我们揭示了QAOA的性能与目标汉密尔顿的转化不变性有关：没有翻译对称性，例如，由于系统中的开放边界条件（OBC）或系统中的随机性，QAOA的效率较低。然后，我们提出了一个由参数化资源哈密顿（PRH-QAOA）协助的广义QAOA，以实现更好的性能。此外，基于PRH-QAOA，我们设计了一个低深度量子电路以外的一维几何形状，以生成具有完美忠诚度的GHz状态。讨论了提出的用于在Rydberg破裂原子上产生GHz状态的方案的实验实现。我们的工作为在没有翻译对称性的可编程量子处理器上执行QAOA铺平了道路，尤其是对于最近开发的使用OBC的二维量子处理器。
The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger-Horne-Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: Without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressed atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.
