Quantum state transfer in disordered spin chains: How much engineering is reasonable? | Quant. Inf. Comm. (2015)
Analia Zwick, Gonzalo A. Álvarez, Joachim Stolze, and Omar Osenda
The transmission of quantum states through spin chains is an important element in the im- plementation of quantum information technologies. Speed and fidelity of transfer are the main objectives which have to be achieved by the devices even in the presence of imperfections which are unavoidable in any manufacturing process. To reach these goals, several kinds of spin chains have been suggested, which differ in the degree of fine-tuning, or engineering, of the system parameters. In this work we present a systematic study of two important classes of such chains. In one class only the spin couplings at the ends of the chain have to be adjusted to a value different from the bulk coupling constant, while in the other class every coupling has to have a specific value. We demonstrate that configurations from the two different classes may perform similarly when subjected to the same kind of disorder in spite of the large difference in the engineering effort necessary to prepare the system. We identify the system features responsible for these similarities and we perform a detailed study of the transfer fidelity as a function of chain length and disorder strength, yielding empirical scaling laws for the fidelity which are similar for all kinds of chain and all dis- order models. These results are helpful in identifying the optimal spin chain for a given quantum information transfer task. In particular, they help in judging whether it is worthwhile to engineer all couplings in the chain as compared to adjusting only the boundary couplings.
Optimized dynamical control of state transfer through noisy spin chains
Analia Zwick, Gonzalo A Álvarez, Guy Bensky and Gershon Kurizki
Focus on Coherent Control of Complex Quantum Systems:
New J. Phys. 16, 065021 (2014).
We propose a method of optimally controlling the tradeoff of speed and fidelity of state transfer through a noisy quantum channel spin-chain. This process is treated as qubit state-transfer through a fermionic bath. We show that dynamical modulation of the boundary-qubits levels can ensure state transfer with the best tradeoff of speed and fidelity. This is achievable by dynamically optimizing the transmission spectrum of the channel. The resulting optimal control is robust against both static and fluctuating noise in the channelʼs spin–spin couplings. It may also facilitate transfer in the presence of diagonal disorder on site energy noise in the channel.
Quantum simulations of localization effects with dipolar interactions
Gonzalo A. Álvarez, Robin Kaiser, Dieter Suter
Quantum information processing often uses systems with dipolar interactions. Here a nuclear spin-based quantum simulator is used to study the spreading of information in such a dipolar-coupled system. While the information spreads with no apparent limits in the case of ideal dipolar couplings, additional perturbations limit the spreading, leading to localization. In previous work [Phys. Rev. Lett. 104, 230403 (2010)], it was found that the system size reaches a dynamic equilibrium that decreases with the square of the perturbation strength. This work examines the impact of a disordered Hamiltonian with dipolar interactions. It shows that the expansion of the cluster of spins freezes in the presence of large disorder, reminiscent of Anderson localization of non-interacting waves in a disordered potential.
Keywords: spin dynamics;dipolar interaction;decoherence;localization;disorder;NMR;long range interactions;quantum information processing
Annalen der Physik
Special Issue on “Quantum Simulations“, featuring review papers written by last year’s Nobel Prize winners describing their foundational work (Wineland and Haroche). Issue edited by: Rainer Blatt, Immanuel Bloch, Ignacio Cirac, Peter Zoller.
Ann. Phys. 525, 833 (2013).
© 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Robustness of Spin-Chain State-Transfer Schemes
Joachim Stolze, Gonzalo A. Álvarez, Omar Osenda, Analia Zwick
in Quantum State Transfer and Network Engineering, edited by G. M. Nikolopoulos and I. Jex (Springer Berlin Heidelberg, 2014), pp. 149–182.
Spin chains are linear arrangements of qubits (spin-1/2 objects) with interactions between nearest or more distant neighbors. They have been considered for quantum information transfer between subunits of a quantum information processing device at short or intermediate distances. The most frequently studied task is the transfer of a single-qubit state. Several protocols have been developed to achieve this goal, broadly divisible into two classes, fully-engineered and boundary-controlled spin chains. We discuss state transfer induced by the natural dynamics of these two classes of systems, and the influence of deviations from the ideal system configuration, that is, manufacturing errors in the nearest-neighbor spin couplings. The fidelity of state transfer depends on the chain length and the disorder strength. We observe a power-law scaling of the fidelity deficit, i.e. the deviation from perfect transfer. Boundary-controlled chains can provide excellent fidelity under suitable circumstances and are potentially less difficult to manufacture and control than fully-engineered chains. We also review other existing theoretical work on the robustness of quantum state transfer as well as proposals for experimental implementation.