By Masanori Ohya, N. Watanabe
ISBN-10: 9812566147
ISBN-13: 9789812566140
Accardi, Ohya, Watanabe. (eds.) Quantum info and computing (WS, 2006)(ISBN 9812566147)(398s)_CsQc_
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Additional info for Quantum information and computing
Sample text
A quantum computer 1 ' 2 ' 3 performs parallel computations by operating a unitary transformation on the quantum states of N qubits. The explicit form of unitary operator depends on the problem to be solved, and the construction of such a unitary operator is one of the crucial tasks in the quantum computation (QC). Barenco et al. 4 showed that any unitary operations can be expressed as compositions of single-qubit and two-qubit Controlled-Not (CNOT) gates. In principle, QC is accomplished by performing these gates piece by piece.
By noticing t h a t t h e Ising interactions need n o t b e controlled, we can express this process in t h e form U(t) = « ! 8. I. Chuang and N. A. Gershenfeld, M. Kubinec, and D. Leung, Proc. R. Soc. London, Ser. A 454, 447 (1998) 9. D. R. Yamaguchi, and Y. Yamamoto, Phys. Rev. Lett. 89, 017901 (2002). 10. S. Hill and W. K. Wootters, Phys. Rev. Lett. jp The problem of existence and uniqueness of a state of a joint system, when its restrictions to subsystems are specified, is studied for a Fermion system, where a novel feature as compared with Boson or spin systems is non-commutativity between algebras of subsystems located at disjoint regions. • • • <8> Vjv, (3) where Wj = Mj(£), Vi = v,(0) are local unitary operators acting on t h e i-th qubit a t t h e time t a n d t = 0, expressing t h e effect of local manipulation d u e to external high-frequency pulses applied at each time. Here, by noticing t h a t [vi,Tf+li+2] = 0 a n d [ui,Tf_2i_i\ = 0, we rewrite Eq. (3) in such a way U(t) = (iti Quantum information and computing by Masanori Ohya, N. Watanabe
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