Research Paper

Solving tiling puzzles with quantum annealing

By Asa Eagle, Takumi Kato, Yuichiro Minato

To solve tiling puzzles, such as “pentomino” or “tetromino” puzzles, we need to find the correct solutions out of numerous combinations of rotations or piece locations. Solving this kind of combinatorial optimization problem is a very difficult problem in computational science, and quantum computing is expected to play an important role in this field. In this article, we propose a method and obtained specific formulas to find solutions for tetromino tiling puzzles using a quantum annealer. In addition, we evaluated these formulas using a simulator and using actual hardware DW2000Q.

Arxiv Preprint

Finding Hadamard matrices by a quantum annealing machine

By Andriyan Bayu Suksmono, Yuichiro Minato

Finding a Hadamard matrix (H-matrix) among the set of all binary matrices of corresponding order is a hard problem. We propose a method to formulate the Hamiltonian of finding H-matrix problem and address its implementation limitation on existing quantum annealing machine (QAM) that allows up to only 2 interacting qubits, whereas the problem naturally introduces higher order terms. For an M-order H-matrix, such a limitation increases the complexity from O(M^2) to O(M^3), which makes the formulation of the Hamiltonian too exhaustive to do by hand. We use symbolic computing techniques to manage this problem. Three related cases are discussed: (1) finding N<M orthogonal binary vectors, (2) finding M orthogonal binary vectors which is equivalent to finding a H-matrix, and (3) finding N-deleted vectors of an M-order H-matrix. Tentative solutions of the problems by a 2-body simulated annealing software, the D-Wave’s neal, and on an actual quantum annealing hardware by using D-Wave quantum annealer DW2000Q, are also discussed.

Arxiv Preprint

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