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Quantum algorithms can be simulated using classical computers, but the typical time complexity of the simulation is exponential. There are some data structures which can speed up this simulation to make it possible to test these algorithms on classical computers using more than a few qubits. One of them is QuIDD by Viamontes et al., which is an extension of the Algebraic Decision Diagram. In this paper, we examine the matrix of Fourier operator and its QuIDD representation. To utilize the structure of the operator we propose two orderings(reversed column variables and even-odd order), both resulting in smaller data structure than the standard one. After that, we propose a new method of storing the Fourier operator, using a weighted decision diagram that further reduces its size. It should be the topic of subsequent research whether the basic operations can be performed efficiently on this weighted structure.

Storing the Quantum Fourier Operator in the QuIDD Data Structure