U(2) gates are derived, which derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number of unitary operations on arbitrarily many bits.Expand

This work provides an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation, and shows that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorized.Expand

The performance of the quantum Fourier transform (QFT) in the presence of decoherence is analysed and it is shown that as far as the peri-1 values are concerned, for some computations an approximation may imply a better performance.Expand

A simple quantum logic gate, the quantum controlled-NOT, is described, and two possible physical realizations of the gate are discussed, one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole-dipole interaction.Expand

The set of good quantum numbers (including spin variables for the electrons and holes) is found which block-diagonalizes the Coulomb and the optical dipole interactions and provides a convenient labeling scheme for the excited states which allows us to diagonalize nearly entirely analytically the 256 x 256 Hamiltonian.Expand