Quantum-Inspired Optimization through Qudit-Based Imaginary Time Evolution
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914179773890560 |
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| author | Åsgrim, Erik M. Awan, Ahsan Javed |
| author_facet | Åsgrim, Erik M. Awan, Ahsan Javed |
| contents | Imaginary-time evolution has been shown to be a promising framework for tackling combinatorial optimization problems on quantum hardware. In this work, we propose a classical quantum-inspired strategy for solving combinatorial optimization problems with integer-valued decision variables by encoding decision variables into multi-level quantum states known as qudits. This method results in a reduced number of decision variables compared to binary formulations while inherently incorporating single-association constraints. Efficient classical simulation is enabled by constraining the system to remain in a product state throughout optimization. The qudit states are optimized by applying a sequence of unitary operators that iteratively approximate the dynamics of imaginary time evolution. Unlike previous studies, we propose a gradient-based method of adaptively choosing the Hermitian operators used to generate the state evolution at each optimization step, as a means to improve the convergence properties of the algorithm. The proposed algorithm demonstrates promising results on Min-d-Cut problem with constraints, outperforming Gurobi on penalized constraint formulation, particularly for larger values of d. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum-Inspired Optimization through Qudit-Based Imaginary Time Evolution Åsgrim, Erik M. Awan, Ahsan Javed Quantum Physics Emerging Technologies Imaginary-time evolution has been shown to be a promising framework for tackling combinatorial optimization problems on quantum hardware. In this work, we propose a classical quantum-inspired strategy for solving combinatorial optimization problems with integer-valued decision variables by encoding decision variables into multi-level quantum states known as qudits. This method results in a reduced number of decision variables compared to binary formulations while inherently incorporating single-association constraints. Efficient classical simulation is enabled by constraining the system to remain in a product state throughout optimization. The qudit states are optimized by applying a sequence of unitary operators that iteratively approximate the dynamics of imaginary time evolution. Unlike previous studies, we propose a gradient-based method of adaptively choosing the Hermitian operators used to generate the state evolution at each optimization step, as a means to improve the convergence properties of the algorithm. The proposed algorithm demonstrates promising results on Min-d-Cut problem with constraints, outperforming Gurobi on penalized constraint formulation, particularly for larger values of d. |
| title | Quantum-Inspired Optimization through Qudit-Based Imaginary Time Evolution |
| topic | Quantum Physics Emerging Technologies |
| url | https://arxiv.org/abs/2512.04710 |