Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent
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arXiv
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| Autori principali: | , , , , , , , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866916004977704960 |
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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 |