Dynamic depth quantum approximate optimization algorithm for solving constrained shortest path problem

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for solving NP-hard combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) hardware. However, its performance critically depends on the choice of circuit depth-a parameter that must be specified a priori without clear guidance. In this paper, we introduce a variant of QAOA, called the Dynamic Depth Quantum Approximate Optimization Algorithm (DDQAOA), that addresses the challenge of pre-selecting a fixed circuit depth. Our method adaptively expands circuit depth, starting from and progressing up to , by transferring learned parameters to deeper circuits based on convergence criteria. We tested this approach on 100 instances of the Constrained Shortest Path Problem (CSPP) at 10-qubit and 16-qubit scales, and on 20 additional instances at the 22-qubit scale. DDQAOA achieved competitive approximation ratios and success probabilities with substantially fewer CNOT evaluations than standard QAOA at and In particular, while standard QAOA at achieved results close to our approach, it used 217%, 159.3%, and 315% more CNOT gates for 10-qubit, 16-qubit, and 22-qubit instances, respectively. These results demonstrate that convergence-driven DDQAOA, building on the INTERP parameter-transfer protocol (Zhou et al. ), offers a practical route to applying QAOA to constrained NP-hard problems on near-term devices.