论文标题
使用Rydberg Atom阵列使用任意连接的量子优化
Quantum optimization with arbitrary connectivity using Rydberg atom arrays
论文作者
论文摘要
基于Rydberg Atom阵列的可编程量子系统最近已用于用于量子优化算法的硬件有效测试[Ebadi等，Science，376，1209（2022）]，具有数百个Qubits。特别是，在所谓的单位磁盘图上的最大独立集问题被证明是在这种量子系统中有效地编码的。在这里，我们扩展了可以在Rydberg数组中有效地编码的问题类别，通过构造从各种问题到单位磁盘图上的最大加权独立集问题，最多最多的Quadratic开销。我们分析了几个示例，包括：具有任意连通性的图表上的最大加权独立集，具有任意或限制连接性的二进制二进制优化问题以及整数分解。小型系统大小的数值模拟表明，解决映射问题的绝热时间尺度与原始问题的时间量表密切相关。我们的工作为使用Rydberg Atom阵列提供了一种蓝图，以解决与硬件几何形状施加的限制之外，以任意连接性解决了广泛的组合优化问题。
Programmable quantum systems based on Rydberg atom arrays have recently been used for hardware-efficient tests of quantum optimization algorithms [Ebadi et al., Science, 376, 1209 (2022)] with hundreds of qubits. In particular, the maximum independent set problem on so-called unit-disk graphs, was shown to be efficiently encodable in such a quantum system. Here, we extend the classes of problems that can be efficiently encoded in Rydberg arrays by constructing explicit mappings from a wide class of problems to maximum weighted independent set problems on unit-disk graphs, with at most a quadratic overhead in the number of qubits. We analyze several examples, including: maximum weighted independent set on graphs with arbitrary connectivity, quadratic unconstrained binary optimization problems with arbitrary or restricted connectivity, and integer factorization. Numerical simulations on small system sizes indicate that the adiabatic time scale for solving the mapped problems is strongly correlated with that of the original problems. Our work provides a blueprint for using Rydberg atom arrays to solve a wide range of combinatorial optimization problems with arbitrary connectivity, beyond the restrictions imposed by the hardware geometry.
