Sparse Matrix Ordering Method with a Quantum Annealing Approach and its Parameter Tuning
Quantum annealing realizes quantum computers specialized for combinatorial optimization problems (COPs). A COP is formulated as a Hamiltonian, and quantum annealing obtains a solution by finding the ground state of the Hamiltonian. The ease of finding a solution depends on the weights assigned to th...
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| Vydáno v: | 2021 IEEE 14th International Symposium on Embedded Multicore/Many-core Systems-on-Chip (MCSoC) s. 258 - 264 |
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01.12.2021
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| Abstract | Quantum annealing realizes quantum computers specialized for combinatorial optimization problems (COPs). A COP is formulated as a Hamiltonian, and quantum annealing obtains a solution by finding the ground state of the Hamiltonian. The ease of finding a solution depends on the weights assigned to the cost and constraint functions when formulating the problem. In other words, parameter tuning is essential in solving problems with quantum annealing. In the present paper, the problem of searching an ordering that reduces the fill-in for a sparse direct solver is formulated as a Hamiltonian, and quantum annealing finds the solution to this problem. We discuss the necessity and effectiveness of parameter tuning for solving COPs with quantum annealing. The results after weight tuning show that we can improve the rate of an optimal solution obtained by a maximum of 94% for {5\,\times \,5} matrices, 68% for {6\,\times \,6} matrices, and 27% for {7\,\times \,7} matrices. Moreover, it is shown that giving high weights to the constraints we want to satisfy will not provide an optimal solution. |
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| AbstractList | Quantum annealing realizes quantum computers specialized for combinatorial optimization problems (COPs). A COP is formulated as a Hamiltonian, and quantum annealing obtains a solution by finding the ground state of the Hamiltonian. The ease of finding a solution depends on the weights assigned to the cost and constraint functions when formulating the problem. In other words, parameter tuning is essential in solving problems with quantum annealing. In the present paper, the problem of searching an ordering that reduces the fill-in for a sparse direct solver is formulated as a Hamiltonian, and quantum annealing finds the solution to this problem. We discuss the necessity and effectiveness of parameter tuning for solving COPs with quantum annealing. The results after weight tuning show that we can improve the rate of an optimal solution obtained by a maximum of 94% for {5\,\times \,5} matrices, 68% for {6\,\times \,6} matrices, and 27% for {7\,\times \,7} matrices. Moreover, it is shown that giving high weights to the constraints we want to satisfy will not provide an optimal solution. |
| Author | Komiyama, Tomoko Suzuki, Tomohiro |
| Author_xml | – sequence: 1 givenname: Tomoko surname: Komiyama fullname: Komiyama, Tomoko email: tkomiee@gmail.com organization: Graduate School of Engineering, University of Yamanashi,Ko-fu,Japan – sequence: 2 givenname: Tomohiro surname: Suzuki fullname: Suzuki, Tomohiro email: stomo@yamanashi.ac.jp organization: Graduate School of Engineering, University of Yamanashi,Ko-fu,Japan |
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| Snippet | Quantum annealing realizes quantum computers specialized for combinatorial optimization problems (COPs). A COP is formulated as a Hamiltonian, and quantum... |
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| StartPage | 258 |
| SubjectTerms | Annealing Cost function Costs fill-in Multicore processing parameter tuning Quantum annealing Search problems sparse direct solver Stationary state |
| Title | Sparse Matrix Ordering Method with a Quantum Annealing Approach and its Parameter Tuning |
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