Simple pulses for universal quantum computation with a HeisenbergABABchain

Recently, Levy has shown that quantum computation may be performed using an $\mathrm{ABAB}\dots$ chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational “gates” may be achieved purely by manipulating the spin-spin interaction: he proposes using “spin-resonance” techniques involving modulating the interaction strength at high frequency. Here, we establish an alternative: it is possible to perform the elementary gates via simple, nonoscillatory switching of the interaction strength. This approach removes a time “bottle neck” in Levy’s scheme, so that all elementary operations may now be performed within a time scale of order $ħ{/(E}_A-E_B).\mathrm{}$