SYNTHESIS OF QUANTUM CIRCUITS FOR d-LEVEL SYSTEMS BY USING COSINE-SINE DECOMPOSITION
We study the problem of designing minimal quantum circuits for any operations on n qudits 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 on whether the partitioning is balanced. We provide a new cosine-sine decomposition based on a balanced partitioning for d-level systems. The produced circuit is not asymptotically optimal except when d is a power of two, but, when the number of qudits n is small, our method can produce the smallest quantum circuit compared to the circuits produced by other synthesis methods. For example, when d = 3 (three-level systems) and n = 2 (two qudits), then the number of two-qudit operations called CINC, which is a generalized versions 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 for the radix-d quantum Fourier transform.
synthesis quantum circuit cosine-sine decomposition (csd) kak decomposition