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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Veröffentlicht in:2021 IEEE 14th International Symposium on Embedded Multicore/Many-core Systems-on-Chip (MCSoC) S. 258 - 264
Hauptverfasser: Komiyama, Tomoko, Suzuki, Tomohiro
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 01.12.2021
Schlagworte:
Annealing
Cost function
Costs
fill-in
Multicore processing
parameter tuning
Quantum annealing
Search problems
sparse direct solver
Stationary state
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Zusammenfassung: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.
DOI:10.1109/MCSoC51149.2021.00045