| 摘要 |
<p><P>PROBLEM TO BE SOLVED: To provide a technique which generates a quantum circuit of polynomial size for executing quantum Fourier transformation F<SB POS="POST">sn</SB>on a symmetrical group S<SB POS="POST">n</SB>. <P>SOLUTION: An orthonormal basis calculation unit 3 calculates orthonormal bases being adapted Gelfand-Tsetlin bases corresponding to respective standard Young tableaux with n boxes. A quantum circuit generation unit 4 performs, with respect to each b, processing of generating a matrix representationρ(g<SB POS="POST">b</SB>) being a direct sum of matrix representationsρ<SB POS="POST">ij</SB>(g<SB POS="POST">b</SB>) where the calculated orthonormal bases are used to represent g<SB POS="POST">b</SB>, and performs, with respect to each i, processing of multiplying column matrices constituting generated matrix representationsρ(g<SB POS="POST">0</SB>),ρ(g<SB POS="POST">1</SB>), toρ(g<SB POS="POST">n-1</SB>) by a prescribed value in order from a column matrix located at the top left and combining the multiplication results to constitute a matrix M<SB POS="POST">ρi</SB>of d<SB POS="POST">ρi</SB>n×d<SB POS="POST">ρi</SB>n, and defines a direct sum of d<SB POS="POST">ρ1</SB>pieces of M<SB POS="POST">ρ1</SB>, d<SB POS="POST">ρ2</SB>pieces of M<SB POS="POST">ρ2</SB>, to d<SB POS="POST">ρan-1</SB>pieces of M<SB POS="POST">ρan-1</SB>, as a matrix G<SB POS="POST">n</SB>. <P>COPYRIGHT: (C)2013,JPO&INPIT</p> |
