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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.12394 |
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| _version_ | 1866913944828903424 |
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| author | Altelarrea-Ferré, Erik Barberà-Rodríguez, Júlia Jansen, David Acín, Antonio |
| author_facet | Altelarrea-Ferré, Erik Barberà-Rodríguez, Júlia Jansen, David Acín, Antonio |
| contents | We introduce excited local quantum annealing (ExcLQA), a classical, physics-inspired algorithm that extends local quantum annealing (LQA) to identify excited states of classical Ising Hamiltonians. LQA simulates quantum annealing while constraining the quantum state to remain in a product state and uses a gradient-based approach to find approximate solutions to large-scale quadratic unconstrained binary optimization problems. ExcLQA extends this framework by adding a penalty term in the cost function to target excited states, with a single hyperparameter that can be tuned via binary search to set the desired penalization level. We benchmark ExcLQA on the shortest vector problem (SVP), a fundamental lattice problem underlying the security of many postquantum cryptographic schemes. Solving an SVP instance can be mapped to identifying the first excited state of a Hamiltonian, with approximate solutions located among nearby excited states. Our results show that ExcLQA manages to solve SVP instances up to rank 46, and outperforms the Metropolis-Hastings algorithm in solved ratio, number of shots, and approximation factor in the tested instances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12394 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians Altelarrea-Ferré, Erik Barberà-Rodríguez, Júlia Jansen, David Acín, Antonio Quantum Physics We introduce excited local quantum annealing (ExcLQA), a classical, physics-inspired algorithm that extends local quantum annealing (LQA) to identify excited states of classical Ising Hamiltonians. LQA simulates quantum annealing while constraining the quantum state to remain in a product state and uses a gradient-based approach to find approximate solutions to large-scale quadratic unconstrained binary optimization problems. ExcLQA extends this framework by adding a penalty term in the cost function to target excited states, with a single hyperparameter that can be tuned via binary search to set the desired penalization level. We benchmark ExcLQA on the shortest vector problem (SVP), a fundamental lattice problem underlying the security of many postquantum cryptographic schemes. Solving an SVP instance can be mapped to identifying the first excited state of a Hamiltonian, with approximate solutions located among nearby excited states. Our results show that ExcLQA manages to solve SVP instances up to rank 46, and outperforms the Metropolis-Hastings algorithm in solved ratio, number of shots, and approximation factor in the tested instances. |
| title | Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.12394 |