Dynamic Depth Quantum Approximate Optimization Algorithm for Solving Constrained Shortest Path Problem

TL;DR

This paper introduces a dynamic depth variant of QAOA that adaptively increases circuit depth to improve solution quality for the constrained shortest path problem on NISQ devices, reducing gate usage.

Contribution

The paper proposes DDQAOA, an adaptive method that dynamically adjusts circuit depth during optimization, enhancing performance over standard QAOA on quantum hardware.

Findings

DDQAOA outperforms standard QAOA in approximation ratios and success probabilities.

DDQAOA requires fewer CNOT gates than fixed-depth QAOA for similar results.

The approach is effective on 10 and 16 qubit instances of CSPP.

Abstract

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 is critically dependent on the selection of the circuit depth a parameter that must be specified a priori without clear guidance. In this paper, we introduce a variant of QAOA called dynamic depth Quantum Approximate Optimization Algorithm (DDQAOA) that resolves the challenge of pre selecting a fixed circuit depth. Our method adaptively expands circuit depth, starting from p = 1 and progressing up to p = 10, 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. Our DDQAOA achieved superior approximation ratios and success probabilities with fewer CNOT gate evaluations than the standard QAOA for p = 3, 5, 10, and 15. In particular, while standard QAOA at p = 15 achieved results close to our approach, it used 217% and 159.3% more CNOT gates for 10 qubit and 16 qubit instances, respectively. This demonstrates the performance and practical applicability of DDQAOA to solve combinatorial optimization problems on near term devices.