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arXiv · 2605.12066

Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent

Zeguan Wu·Mingze Li·Muqing Zheng·Meng Wang·Junyu Liu·Samuel Stein·Ang Li·Yousu Chen·Chenxu Liu
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Abstract

Quantum Hamiltonian Descent (QHD) is a continuous optimization algorithm based on simulating a time-dependent quantum Hamiltonian whose potential energy encodes the objective function and whose kinetic energy promotes exploration through quantum interference and tunneling. While QHD is formulated for unconstrained optimization, many real-world optimization problems are constrained and highly nonconvex. In this paper, we benchmark AL-QHD, a hybrid framework that embeds QHD within the Augmented Lagrangian Method (ALM), thereby solving a sequence of unconstrained subproblems while using ALM to enforce constraints. We evaluate AL-QHD on standard nonconvex test functions and use iterative refinement to improve solution accuracy at fixed per-run qubit cost. We also perform a gate-based resource analysis on ACOPF-derived power system subproblems constructed from power-network data to estimate the quantum-computer scale required for practical applications. Resource estimates on Texas7k-derived ACOPF instances show steep hard-gate scaling, reaching $\sim 4.46 \times 10^7$ entangling gates in a NISQ-oriented model and $\sim 9.42 \times 10^8$ T gates in a fault-tolerant model at $\sim 5.3 \times 10^2$ active variables. These results suggest that AL-QHD is a useful framework for studying constrained nonconvex optimization with QHD, but that practical ACOPF-scale applications would likely require large-scale fault-tolerant quantum hardware.

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Zeguan Wu, Mingze Li, Muqing Zheng, Meng Wang, Junyu Liu, Samuel Stein, Ang Li, Yousu Chen, Chenxu Liu. 2026-05-12. Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent. https://arxiv.org/abs/2605.12066

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