Quantum Grid Path Planning Using Parallel QAOA Circuits Based on Minimum Energy Principle
Jun Liu
TL;DR
The paper tackles NP-hard grid path planning under NISQ constraints by mapping the problem to a minimum-energy Ising/QUBO formulation and solving it with a pair of parallel QAOA circuits that compute connectivity-energy and path-energy terms. A classical threshold filter on the connectivity circuit enhances state discrimination, and the final solution is assembled via a Hadamard product of the two probability distributions followed by normalization. The authors provide a detailed energy-decomposition framework (E1–E6) for connectivity, demonstrate a 2×3 grid example with explicit Hamiltonians, and show via simulations that parallel circuitry with filtering markedly improves the probability of locating an approximately optimal path, even at depth $p=1$. This approach offers a practical, near-term quantum route for grid path planning on NISQ devices, reducing circuit depth while boosting solution quality and robustness compared to serial implementations.
Abstract
To overcome the bottleneck of classical path planning schemes in solving NP problems and address the predicament faced by current mainstream quantum path planning frameworks in the Noisy Intermediate-Scale Quantum (NISQ) era, this study attempts to construct a quantum path planning solution based on parallel Quantum Approximate Optimization Algorithm (QAOA) architecture. Specifically, the grid path planning problem is mapped to the problem of finding the minimum quantum energy state. Two parallel QAOA circuits are built to simultaneously execute two solution processes, namely connectivity energy calculation and path energy calculation. A classical algorithm is employed to filter out unreasonable solutions of connectivity energy, and finally, the approximate optimal solution to the path planning problem is obtained by merging the calculation results of the two parallel circuits. The research findings indicate that by setting appropriate filter parameters, quantum states corresponding to position points with extremely low occurrence probabilities can be effectively filtered out, thereby increasing the probability of obtaining the target quantum state. Even when the circuit layer number p is only 1, the theoretical solution of the optimal path coding combination can still be found by leveraging the critical role of the filter. Compared with serial circuits, parallel circuits exhibit a significant advantage, as they can find the optimal feasible path coding combination with the highest probability.