{"title":"二元线性规划的量子约束生成框架","authors":"András Czégel, Boglárka G.-Tóth","doi":"10.1140/epjqt/s40507-025-00364-z","DOIUrl":null,"url":null,"abstract":"<div><p>We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general purpose, standalone solvers for ILP. However, to consider them practically useful, we expect them to overperform the current state of the art classical solvers. That expectation is unfair to quantum algorithms: in classical ILP solvers, after many decades of evolution, many different algorithms work together as a robust machine to get the best result. This is the approach we would like to follow now with our quantum ‘solver’ solutions. In this study we wrap any suitable quantum optimization algorithm into a quantum informed classical constraint generation framework. First we relax our problem by dropping all constraints and encode it into an Ising Hamiltonian for the quantum optimization subroutine. Then, by sampling from the solution state of the subroutine, we obtain information about constraint violations in the initial problem, from which we decide which coupling terms we need to introduce to the Hamiltonian. The coupling terms correspond to the constraints of the initial binary linear program. Then we optimize over the new Hamiltonian again, until we reach a feasible solution, or other stopping conditions hold. Since one can decide how many constraints they add to the Hamiltonian in a single step, our algorithm is at least as efficient as the (hybrid) quantum optimization algorithm it wraps. We support our claim with results on small scale minimum cost exact cover problem instances.</p></div>","PeriodicalId":547,"journal":{"name":"EPJ Quantum Technology","volume":"12 1","pages":""},"PeriodicalIF":5.6000,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-025-00364-z","citationCount":"0","resultStr":"{\"title\":\"A quantum constraint generation framework for binary linear programs\",\"authors\":\"András Czégel, Boglárka G.-Tóth\",\"doi\":\"10.1140/epjqt/s40507-025-00364-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general purpose, standalone solvers for ILP. However, to consider them practically useful, we expect them to overperform the current state of the art classical solvers. That expectation is unfair to quantum algorithms: in classical ILP solvers, after many decades of evolution, many different algorithms work together as a robust machine to get the best result. This is the approach we would like to follow now with our quantum ‘solver’ solutions. In this study we wrap any suitable quantum optimization algorithm into a quantum informed classical constraint generation framework. First we relax our problem by dropping all constraints and encode it into an Ising Hamiltonian for the quantum optimization subroutine. Then, by sampling from the solution state of the subroutine, we obtain information about constraint violations in the initial problem, from which we decide which coupling terms we need to introduce to the Hamiltonian. The coupling terms correspond to the constraints of the initial binary linear program. Then we optimize over the new Hamiltonian again, until we reach a feasible solution, or other stopping conditions hold. Since one can decide how many constraints they add to the Hamiltonian in a single step, our algorithm is at least as efficient as the (hybrid) quantum optimization algorithm it wraps. We support our claim with results on small scale minimum cost exact cover problem instances.</p></div>\",\"PeriodicalId\":547,\"journal\":{\"name\":\"EPJ Quantum Technology\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":5.6000,\"publicationDate\":\"2025-05-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://epjquantumtechnology.springeropen.com/counter/pdf/10.1140/epjqt/s40507-025-00364-z\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EPJ Quantum Technology\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1140/epjqt/s40507-025-00364-z\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPJ Quantum Technology","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1140/epjqt/s40507-025-00364-z","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPTICS","Score":null,"Total":0}
A quantum constraint generation framework for binary linear programs
We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general purpose, standalone solvers for ILP. However, to consider them practically useful, we expect them to overperform the current state of the art classical solvers. That expectation is unfair to quantum algorithms: in classical ILP solvers, after many decades of evolution, many different algorithms work together as a robust machine to get the best result. This is the approach we would like to follow now with our quantum ‘solver’ solutions. In this study we wrap any suitable quantum optimization algorithm into a quantum informed classical constraint generation framework. First we relax our problem by dropping all constraints and encode it into an Ising Hamiltonian for the quantum optimization subroutine. Then, by sampling from the solution state of the subroutine, we obtain information about constraint violations in the initial problem, from which we decide which coupling terms we need to introduce to the Hamiltonian. The coupling terms correspond to the constraints of the initial binary linear program. Then we optimize over the new Hamiltonian again, until we reach a feasible solution, or other stopping conditions hold. Since one can decide how many constraints they add to the Hamiltonian in a single step, our algorithm is at least as efficient as the (hybrid) quantum optimization algorithm it wraps. We support our claim with results on small scale minimum cost exact cover problem instances.
期刊介绍:
Driven by advances in technology and experimental capability, the last decade has seen the emergence of quantum technology: a new praxis for controlling the quantum world. It is now possible to engineer complex, multi-component systems that merge the once distinct fields of quantum optics and condensed matter physics.
EPJ Quantum Technology covers theoretical and experimental advances in subjects including but not limited to the following:
Quantum measurement, metrology and lithography
Quantum complex systems, networks and cellular automata
Quantum electromechanical systems
Quantum optomechanical systems
Quantum machines, engineering and nanorobotics
Quantum control theory
Quantum information, communication and computation
Quantum thermodynamics
Quantum metamaterials
The effect of Casimir forces on micro- and nano-electromechanical systems
Quantum biology
Quantum sensing
Hybrid quantum systems
Quantum simulations.