We present a map from the travelling salesman problem (TSP), a prototypical NP-complete combinatorial optimisation task, to the ground state associated with a system of many-qudits. Conventionally, the TSP is cast into a quadratic unconstrained binary optimisation (QUBO) problem, that can be solved on an Ising machine. The size of the corresponding physical system's Hilbert space is $2^{N^2}$, where $N$ is the number of cities considered in the TSP. Our proposal provides a many-qudit system with a Hilbert space of dimension $2^{N\log_2N}$, which is considerably smaller than the dimension of the Hilbert space of the system resulting from the usual QUBO map. This reduction can yield a significant speedup in quantum and classical computers. We simulate and validate our proposal using variational Monte Carlo with a neural quantum state, solving the TSP in a linear layout for up to almost 100 cities.
翻译:我们从旅行销售员问题(TSP)上展示了一张地图,这是一个原型的NP-完整的组合优化任务,到一个与多种量子系统相关的地面状态。 通常,TSP被抛入一个可以由 Ising 机器解决的无限制的二进制优化(QUBO)问题。 相应的物理系统Hilbert 空间的大小为 $2 ⁇ N ⁇ 2}, 其中美元是 TSP 考虑的城市数量。 我们的建议提供了一个拥有一个具有Hilbert 尺寸空间的多个量子系统, 2 ⁇ N\log_2N$, 大大小于通常的QUBO 地图产生的系统Hilbert 空间的维度。 这一减少可以大大加速量子计算机和古典计算机的步伐。 我们用一个神经量度状态来模拟和验证我们的提案, 将TSP用近100个城市的线性布局解决 TSP 。