Randomized dynamical decoupling techniques for coherent quantum control

Abstract

The need for strategies able to accurately manipulate quantum dynamics is ubiquitous in quantum control and quantum information processing. We investigate two scenarios where randomized dynamical decoupling techniques become more advantageous with respect to standard deterministic methods in switching off unwanted dynamical evolution in a closed quantum system: when dealing with decoupling cycles which involve a large number of control actions and/or when seeking long-time quantum information storage. Highly effective hybrid decoupling schemes, which combine deterministic and stochastic features are discussed, as well as the benefits of sequentially implementing a concatenated method, applied at short times, followed by a hybrid protocol, employed at longer times. A quantum register consisting of a chain of spin-1/2 particles interacting via the Heisenberg interaction is used as a model for the analysis throughout. II. SYSTEM AND CONTROL SETTINGDynamical decoupling (DD) techniques have been extensively discussed both in the original high-resolution nuclear magnetic resonance (NMR) setting [13] and, more recently, in connection with robust quantum information processing, see for instance [14,15,16] for representative contributions. Assume, for simplicity, an isolated finite dimensional target system S described by a (possibly) time dependent Hamiltonian H 0 (t). The basic idea of DD is to modify the dynamics of S by adding to H 0 (t) an appropriate time-dependent control field H c (t). The overall propagator under the total Hamiltonian and the control propagator in units = 1 are, respectively,, where T indicates time ordering. A transformation to a logical frame that removes H c (t) is commonly performed, leading to a controlled evolution described by *

Long-time electron spin storage via dynamical suppression of hyperfine-induced decoherence in a quantum dot

“…29,30,48,[51][52][53] For cyclic schemes, the relevant error bounds assume convergence of the ME series, thus requiring, in particular, that c T c Ͻ 1, where in our problem c is the highest frequency of the total ͑electron plus nuclei͒ spectrum. For a typical GaAs QD with N ϳ 10 6 bath spins,…”

“…48,[51][52][53] Unlike deterministic schemes, randomized DD is distinguished by the fact that the future control path is not fully known in advance. Analysis is most conveniently carried out in a logical frame that follows the applied control, 48 and by tracking the applied sequence to ensure that appropriate frame compensation can be used to infer the evolution in the physical frame.…”

“…However, for a given evolution time, an effective Hamiltonian and the corresponding leading orders to coherence decay may still be defined directly in terms of the unitary logical-frame propagator. 52,53 In general, protocols with higher leading order tend to give superior performance. However, such a conclusion does not necessarily hold if a randomized protocol is compared to a deterministic one.…”

“…Among all randomized protocols, [51][52][53] we consider a few representative choices. Naive random DD ͑NRD͒ corresponds to changing the control propagator according to a path which is uniformly random with respect to the invariant Haar measure on G. For our system, this means that a X, Y, Z pulse, or a no-pulse is applied with equal probability at every instant t j = j, j =0,1,....…”

Quantum phase estimation algorithm in presence of static imperfections

“…Indeed, our studies presented in this paper show that the static imperfections lead to a significant drop of the computation accuracy and the algorithm success probability. To correct these quantum errors induced by static imperfections in IQPEA we apply the Pauli-random-error-correction (PAREC) method proposed in [13] and tested in various quantum circuits [14,15]. Our results for IQPEA show that the PAREC allows to improve significantly the accuracy of quantum computation.…”