Performance of Domain-Wall Encoding in Digital Ising Machine
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913655282466816 |
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| author | Kikuchi, Shuta Takahashi, Kotaro Tanaka, Shu |
| author_facet | Kikuchi, Shuta Takahashi, Kotaro Tanaka, Shu |
| contents | To tackle combinatorial optimization problems using an Ising machine, the objective function and constraints must be mapped onto a quadratic unconstrained binary optimization (QUBO) model. While QUBO involves binary variables, combinatorial optimization problems frequently include integer variables, which require encoding by binary variables. This process, known as binary-integer encoding, includes various methods, one of which is domain-wall encoding - a recently proposed approach. Experiments on a quantum annealing machine have demonstrated that domain-wall encoding outperforms the commonly used one-hot encoding in terms of objective function value and the probability of obtaining the optimal solution. In a digital Ising machine, domain-wall encoding required less computation time to reach optimal solutions compared to one-hot encoding. However, its practical effectiveness in digital Ising machines remains unclear. To address this uncertainty, the performance of one-hot and domain-wall encoding methods was evaluated on a digital Ising machine using the quadratic knapsack problem (QKP). The comparison focused on the dependency of penalty coefficient and sensitivity to computation time. Domain-wall encoding demonstrated a higher feasible solution rate when relative penalty coefficients for the two constraint terms were adjusted, a strategy not commonly used in previous studies. Additionally, domain-wall encoding obtained higher performance practical evaluation metrics for QKPs with large knapsack capacities compared to one-hot encoding. Furthermore, it was observed to be more sensitive to computation time than one-hot encoding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11198 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Performance of Domain-Wall Encoding in Digital Ising Machine Kikuchi, Shuta Takahashi, Kotaro Tanaka, Shu Statistical Mechanics To tackle combinatorial optimization problems using an Ising machine, the objective function and constraints must be mapped onto a quadratic unconstrained binary optimization (QUBO) model. While QUBO involves binary variables, combinatorial optimization problems frequently include integer variables, which require encoding by binary variables. This process, known as binary-integer encoding, includes various methods, one of which is domain-wall encoding - a recently proposed approach. Experiments on a quantum annealing machine have demonstrated that domain-wall encoding outperforms the commonly used one-hot encoding in terms of objective function value and the probability of obtaining the optimal solution. In a digital Ising machine, domain-wall encoding required less computation time to reach optimal solutions compared to one-hot encoding. However, its practical effectiveness in digital Ising machines remains unclear. To address this uncertainty, the performance of one-hot and domain-wall encoding methods was evaluated on a digital Ising machine using the quadratic knapsack problem (QKP). The comparison focused on the dependency of penalty coefficient and sensitivity to computation time. Domain-wall encoding demonstrated a higher feasible solution rate when relative penalty coefficients for the two constraint terms were adjusted, a strategy not commonly used in previous studies. Additionally, domain-wall encoding obtained higher performance practical evaluation metrics for QKPs with large knapsack capacities compared to one-hot encoding. Furthermore, it was observed to be more sensitive to computation time than one-hot encoding. |
| title | Performance of Domain-Wall Encoding in Digital Ising Machine |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2410.11198 |