Concatenated Dynamical Decoupling Pulse Sequences
by
Kaveh Khodjasteh
University of Toronto, Dept. of Physics
Coauthors: Daniel Lidar

The origins of noise and decoherence in the evolution of open quantum system are the uncontrollable interactions of the parts of the system with an environment that normally challenges production or manipulation of quantum states in experimental realizations of quantum information processing. Dynamical decoupling (DD) pulse sequences are feedback free and conceptually simple means of eliminating the unwanted terms of the interaction Hamiltonian in a system (possibly) coupled to an environment or the bath, by applying fast, strong pulses to the system in regularly paced intervals.

DD pulses, has by far been limited to simple models in which the pulses are applied in series and the removal of the undesired interactions depends on the following: (a) the width of the pulses must be small enough so that the evolution of the system during the pulse can be ignored and (b) the time between consecutive pulses has to be much smaller than the time scales of the bath. These conditions restrict the applicability of simple DD pulses, usually known as parity kicks.

In this work we use an analogy with quantum error correction codes and investigate the idea of concatenating dynamical decoupling pulses to obtain further cancellations of the error terms in the Hamiltonian. To this end we develop a series of renormalized Hamiltonians that are used to estimate the strength of the undesired interactions, after applying each layer of dynamical decoupling. The sources of these Hamiltonians will be the errors due to the pulse imperfections (including the effects of the pulse width) and the errors due to the evolution of the bath between the application of pulses. We further present a criteria in terms of the system-bath interaction Hamiltonian strength H_SB, bath's internal Hamiltonian strength H_B, the time between consecutive pulses \tau, and the pulse width t, for the overall usefulness of concatenating dynamical decoupling pulses against decoherence. We also compare these results with the threshold calculations in quantum error correction literature.

Date received: April 26, 2004