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IEEE International Conference on Quantum Computing and Engineering (QCE)

CVAE-Guided QAOA Parameter Initialization and Dynamic Injection

Jai Nana, Xinpeng Li, Ning Xie, L.T. Li, Yifan Yu, Qiang Guan, Hailu Xu, Shusen Pu, Shuai Xu, Vipin Chaudhary

Published Aug 30, 2025• 0 citations
Publisher

Abstract

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems that are classically intractable. Careful parameter initialization in QAOA can reduce the number of quantum circuit evaluations required, making it more feasible to run on noisy intermediate-scale quantum (NISQ) devices. In this work, We focus on MaX-Cut, a classic NP-hard optimization problem, and propose a conditional variational autoencoder (CVAE) scheme for generating initial QAOA parameters for the Max-Cut problems based on input graph structures. The CVAE, trained on optimal parameters from 270 ten-node graphs, produces multiple parameter candidates conditioned on 27-dimensional feature vectors that incorporate spectral properties as well as learned embeddings. We evaluate and compare two strategies: direct initialization using the highestconfidence prediction, and dynamic injection which monitors optimization progress and intervenes when needed. On 89 test graphs, the dynamic injection strategy increased successful convergence cases from 41 to 49, reduced mean iteration count by 4.94.

DOI
10.1109/qce65121.2025.10338

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The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems that are classically intractable. Careful parameter initialization in QAOA can reduce the number of quantum circuit evaluations required, making it more feasible to run on noisy intermediate-scale quantum (NISQ) devices. In this work, We focus on MaX-Cut, a classic NP-hard optimization problem, and propose a conditional variational autoencoder (CVAE) scheme for generating initial QAOA parameters for the Max-Cut problems based on input graph structures. The CVAE, trained on optimal parameters from 270 ten-node graphs, produces multiple parameter candidates conditioned on 27-dimensional feature vectors that incorporate spectral properties as well as learned embeddings. We evaluate and compare two strategies: direct initialization using the highestconfidence prediction, and dynamic injection which monitors optimization progress and intervenes when needed. On 89 test graphs, the dynamic injection strategy increased successful convergence cases from 41 to 49, reduced mean iteration count by 4.94.
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The quantum approximate optimization algorithm (QAOA) has numerous promising applications in solving the combinatorial optimization problems on near-term Noisy Intermediate Scalable Quantum (NISQ) devices. QAOA has a quantum-classical hybrid structure. Its quantum part consists of a parameterized alternating operator ansatz, and its classical part comprises an optimization algorithm, which optimizes the parameters to maximize the expectation value of the problem Hamiltonian. This expectation value depends highly on the parameters, this implies that a set of good parameters leads to an accurate solution. However, at large circuit depth of QAOA, it is difficult to achieve global optimization due to the multiple occurrences of local minima or maxima. In this paper, we propose a parameters fixing strategy which gives high approximation ratio on average, even at large circuit depths, by initializing QAOA with the optimal parameters obtained from the previous depths. We test our strategy on the Max-cut problem of certain classes of graphs such as the 3-regular graphs and the Erdös-Rényi graphs.
Graph-based combinatorial optimization problems are computationally challenging for classical optimization techniques due to their NP-hard nature. This paper proposes a novel Quantum-Assisted Hybrid Optimization Algorithm (QAHOA) that integrates the Quantum Approximate Optimization Algorithm (QAOA), spectral graph theory, and classical optimization strategies for graph-based combinatorial optimization. The developed framework uses spectral initialization via the graph Laplacian Fiedler vector to provide structurally informed starting variational parameters, aiming to stabilize the parameter search space and improve convergence trajectories under noisy conditions. The mathematical framework, alongside a convergence analysis to first-order stationary points, is provided to establish theoretical baseline properties. Evaluated on synthetic Erdős–Rényi random graph instances, the current study serves as a preliminary, small-to-medium-scale proof-of-concept. Controlled evaluations demonstrate that the proposed QAHOA achieves marginal yet stable and statistically significant improvements in mean cut values and approximation ratios over classical Greedy heuristics, Simulated Annealing, the standard QAOA, and Warm-Start QAOA. Formal paired hypothesis testing mathematically verifies the stability of the framework, while preliminary 4-qubit hardware executions demonstrate baseline architectural compatibility under physical NISQ noise channels.
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The Quantum Approximate Optimization Approach (QAOA) is a hybrid quantum-classical approach designed for solving NP-hard combinatorial optimization problems on Noisy Intermediate-Scale Quantum (NISQ) devices. This study applies QAOA on a four-node Max-Cut problem to investigate the output between two IBM Quantum backends: ibm_torino (Heron r1) and ibm_brisbane (Eagle r3). The experiment uses fixed variational parameters γ=1.2 and β=2.4 for both backends, with a circuit depth of p=2. The ibm_torino backend always produced the right Max-Cut solutions by giving the right optimal bitstrings (0101 and 1010). The ibm_brisbane backend, on the other hand, sometimes gave the wrong bitstrings more often than the right ones. A hypothesis-driven analysis ascribes this discrepancy to variations in backend architecture, qubit connectivity, and parameter sensitivity, in addition to the simplicity of the unweighted four-node network employed.
The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial variational parameters. Hence, parameter selection for QAOA becomes an active area of research, as bad initialization might deteriorate the quality of the results, especially at great circuit depths. We first discuss the patterns of optimal parameters in QAOA in two directions: the angle index and the circuit depth. Then, we discuss the symmetries and periodicity of the expectation that is used to determine the bounds of the search space. Based on the patterns in optimal parameters and the bounds restriction, we propose a strategy that predicts the new initial parameters by taking the difference between the previous optimal parameters. Unlike most other strategies, the strategy we propose does not require multiple trials to ensure success. It only requires one prediction when progressing to the next depth. We compare this strategy with our previously proposed strategy and the layerwise strategy for solving the Max-cut problem in terms of the approximation ratio and the optimization cost. We also address the non-optimality in previous parameters, which is seldom discussed in other works despite its importance in explaining the behavior of variational quantum algorithms.