Optimized pulses for the perturbative decoupling of a spin and a decoherence bath

Abstract

In the framework of nuclear magnetic resonance, we consider the general problem of the coherent control of a spin coupled to a bath by means of composite or continuous pulses of duration p . We show explicitly that it is possible to design the pulse in order to achieve a decoupling of the spin from the bath up to the third order in p . The evolution of the system is separated in the evolution of the spin under the action of the pulse and of the bath times correction terms. We derive the correction terms for a general time dependent axis of rotation and for a general coupling between the spin and the environment. The resulting corrections can be made to vanish by an appropriate design of the pulse. For and / 2 pulses, we demonstrate explicitly that pulses exist which annihilate the first-and the second-order corrections even if the bath is fully quantum mechanical, i.e., it displays internal dynamics. Such pulses will also be useful for quantum information processing.

Soft-pulse dynamical decoupling with Markovian decoherence

“…(25)] is reduced to only two constants. The parameter υ gives an effective pulse length to first order; it is equal to zero, υ = 0 for ideal δ-inversion pulses (rotation angle φ 0 = π), as well as for Hermitian pulses [53] or other 1st-order self-refocusing pulses [19,52,54]. The parameter υ 2 vanishes for ideal δ-pulses with the rotation angle φ 0 = π/2; for hard inversion pulses [Eq.…”

Optimized pulses for the control of uncertain qubits

“…By expanding the final-time unitary evolution operator generated by H open with respect to t f H e and t f Γ about t f H e = 0 and t f Γ = 0, Pasini et al have identified controlfield criteria necessary to eliminate perturbative first-and second-order effects resulting from the environment Hamiltonian H e and the interaction term S · Γ [15]. Although applicable to multi-polarized controls and general qubit-environment coupling, the methodology developed in this section assumes control-qubit coupling along the z-axis and qubit-environment interaction along the x-axis, i.e.,…”

“…According to the analysis in ref. [15], when [H e , Γ λ ] = 0, for all λ, components η 4 and η 5 can be neglected from the vector constraint.…”

“…For the individual unitary targets considered, despite the similar structures of the resulting OCs for different drift-term magnitudes, their gate distances as a function of the drift magnitude differ dramatically. Section V summarizes the nonlinear control-field criteria developed by Pasini et al for designing control pulses that are robust to decoherence [15]. Our adaptation of these criteria to closed-system unitary control is explained and the hybrid DPC+OCT control problem is posed.…”

“…[4,[11][12][13][14][15][16][17]. In a recent article [15], using a rather general open-system, time-dependent Hamiltonian for one qubit, they derive analytical control-field criteria for π/2-and π-pulses, which, when satisfied, eliminate the first-and second-order errors in the unitary time-evolution operator resulting from qubit-environment interactions. In this work, we refer to these criteria as "decoupling-pulse criteria" (DPC) and to the control fields that satisfy this criteria as "decoupling pulses" (DPs).…”