Synthesis of quantum circuits for d-level systems by using cosine-sine decomposition

Authors:
Yumi Nakajima;Yasuhito Kawano;Hiroshi Sekigawa;Masaki Nakanishi;Shigeru Yamashita;Yasuhiko Nakashima
Affiliations:
NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Atsugi, Kanagawa, Japan and Graduate School of Information Science, Nara Institute of Science and Technology, Ik ...;NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Atsugi, Kanagawa, Japan;NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Atsugi, Kanagawa, Japan;Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma, Nara, Japan;Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma, Nara, Japan;Graduate School of Information Science, Nara Institute of Science and Technology, Ikoma, Nara, Japan
Venue:
Quantum Information & Computation
Year:
2009

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Abstract

We study the problem of designing minimal quantum circuits for any operations on nqudits by means of the cosine-sine decomposition. Our method is based on a divide-and-conquer strategy. In that strategy, the size of the produced quantum circuit depends onwhether the partitioning is balanced. We provide a new cosine-sine decomposition basedon a balanced partitioning for d-level systems. The produced circuit is not asymptoticallyoptimal except when d is a power of two, but, when the number of qudits n is small, ourmethod can produce the smallest quantum circuit compared to the circuits produced byother synthesis methods. For example, when d = 3 (three-level systems) and n = 2 (twoqudits), then the number of two-qudit operations called CINC, which is a generalizedversions of CNOT, is 36 whereas the previous method needs 156 CINC gates. Moreover,we show that our method is useful for designing a polynomial-size quantum circuit forthe radix-d quantum Fourier transform.