Control of molecular systems with very few phases

Single-step controlled-NOT logic from any exchange interaction

“…By adopting such restriction we were able to isolate a special subalgebra L 0 of su(4), given in Eq. (8), that contains a central element. The fifteen-dimensional problem was then reduced to a nonlinear system of "only" seven first-order differential equations, one of which completely separated from the others.…”

“…Controllability of quantum mechanical systems has been the subject of numerous investigations in the last several years [1][2][3][4][5][6][7][8][9][10][11]. An important contribution by Khaneja et al on time-optimal control [3,7] has led to the development of rf-pulse sequences for NMR-spectroscopy with nearly ideal performance [12].…”

Parameter differentiation and quantum state decomposition for time varying Schrödinger equations

“…Note that because of the last row of (25) the presentation of ad A is not skew-symmetric, like it would have been had we chosen the Gell-Mann basis. For su (3), the basis of the adjoint representation is Inserting the coefficients of the characteristic polynomials (26) into (10), one gets from (15) and (16) the following values for the β and, from (11), the exponentials are:…”

Monotonically Convergent Algorithms for Bounded Quantum Controls

“…Theoretical results: No definitive theoretical results are available to date about the relationship between the possibility of control and the magnitude of the control fields to be used. Promising advances seem to be possible as a byproduct of constructive controllability analysis as in (Ramakrishna et al, 2002;Ramakrishna et al, 2000a;Ramakrishna et al, 2000b;Ramakrishna, 2001;Schirmer et al, 2002).…”

“…In the continuation of this work, we present here a new algorithm that, in addition to conserving the monotonicity properties mentioned above allows for finding controls within a-priori given lower and upper bounds. Indeed, such controls can help understand the practical relationships that exists between the intensity of the control field and the quality of the control; we refer to (Ramakrishna et al, 2002;Ramakrishna et al, 2000a;Ramakrishna et al, 2000b;Ramakrishna, 2001;Schirmer et al, 2002) for alternative strategies that use constructive procedures and that could also be instrumental to obtaining information of the same nature.…”