Influence of Non-Resonant Effects on the Dynamics of Quantum Logic Gates at Room Temperature

We study numerically the influence of non-resonant effects on the dynamics of a single $\pi$-pulse quantum CONTROL-NOT (CN) gate in a macroscopic ensemble of fo ur-spin molecules at room temperature. The four nuclear spins in each molecule r epresent a four-qubit register. The qubits are ``labeled'' by the characteristic frequencies, $\omega_k$, ($k=0$ to 3) due to the Zeeman interaction of the nuclear spins with the magnetic field. The qubits interact with each other through an Ising interaction of strength $J$. T he paper examines the feasibility of implementing a single-pulse quantum CN gate in an ensemble of quantum molecules at room temperature. We determine a paramet er region, $\omega_k$ and $J$, in which a single-pulse quantum CN gate can be i mplemented at room temperature. We also show that there exist characteristic cri tical values of parameters, $\Delta\omega_{cr}\equiv|\omega_{k^\prime}-\omega_k|_{cr}$ and $J_{cr}$, such that for $J<J_{cr}$ and $\Delta\omega_k\equiv|\omega_{k^\prime}-\omega_k|<\Delta\omega_{cr}$, non-resonant effects are sufficient to d estroy the dynamics required for quantum logic operations.