Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent

Fuente: arXiv
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Autori principali: Wu, Zeguan, Li, Mingze, Zheng, Muqing, Wang, Meng, Liu, Junyu, Stein, Samuel, Li, Ang, Chen, Yousu, Liu, Chenxu
Natura: Preprint
Pubblicazione: 2026
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author Wu, Zeguan
Li, Mingze
Zheng, Muqing
Wang, Meng
Liu, Junyu
Stein, Samuel
Li, Ang
Chen, Yousu
Liu, Chenxu
author_facet Wu, Zeguan
Li, Mingze
Zheng, Muqing
Wang, Meng
Liu, Junyu
Stein, Samuel
Li, Ang
Chen, Yousu
Liu, Chenxu
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_12066
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent
Wu, Zeguan
Li, Mingze
Zheng, Muqing
Wang, Meng
Liu, Junyu
Stein, Samuel
Li, Ang
Chen, Yousu
Liu, Chenxu
Quantum Physics
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.
title Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent
topic Quantum Physics
url https://arxiv.org/abs/2605.12066