quantum computation

Rev. Mod. Phys.:Protecting quantum information against environmental noise

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Colloquium: Protecting quantum information against environmental noise

Dieter Suter and Gonzalo A. Álvarez
Rev. Mod. Phys. 88, 041001 (2016)
Published 10 October 2016

RevModPhys.88.041001Quantum-mechanical systems retain their properties so long as the phase of quantum superpositions evolve stably over time. Contact with an environment can disrupt this phase evolution. But for environments that do not exchange energy with the quantum system, strategies exist where the controlled driving of the system can recover or maintain the quantum phase. This Colloquium surveys the host of techniques that are available to “refocus” the phase when disturbed by various forms of classical or quantum environment. While the first such techniques were developed long ago, ideas from quantum information theory have introduced new strategies for accomplishing this goal.

Source: Reviews of Modern Physics – Volume 88 Issue 4

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Quantum state transfer in disordered spin chains: How much engineering is reasonable? | Quant. Inf. Comm. (2015)

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Analia Zwick, Gonzalo A. Álvarez, Joachim Stolze, and Omar Osenda

Quant. Inf. Comput. 15, 582-600 (2015).

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.

via [1306.1695] Quantum state transfer in disordered spin chains: How much engineering is reasonable?.

Comparison of the averaged state transfer fidelity for different quantum state transfer channels. The left hand side panels are boundary controlled spin-chain channels and the right hand side panels are fully engineered perfect state transfer channels. Two kinds of disorder are considered in the plot: Absolute disorder with a perturbation strength proportional to the maximum coupling strength of the spin-chain or relative disorder when the perturbation strength in each spin-spin coupling is relative to its optimal value. For the boundary controlled spin channels, both types of disorder are equivalent since the bulk of the chains contains homogeneous couplings, while for the fully engineered spin-channels they provide different effects on the transfer fidelity. The average is calculated over 1000 disorder realizations. The black contour lines belong to fidelities F = 0.99, 0.95, 0.9, 0.8, 0.7, respectively. The colored symbols show the crossovers between the different systems.
Comparison of the averaged state transfer fidelity for different quantum state transfer channels. The left hand side panels are boundary controlled spin-chain channels and the right hand side panels are fully engineered perfect state transfer channels. Two kinds of disorder are considered in the plot: Absolute disorder with a perturbation strength proportional to the maximum coupling strength of the spin-chain or relative disorder when the perturbation strength in each spin-spin coupling is relative to its optimal value. For the boundary controlled spin channels, both types of disorder are equivalent since the bulk of the chains contains homogeneous couplings, while for the fully engineered spin-channels they provide different effects on the transfer fidelity. The average is calculated over 1000 disorder realizations. The black contour lines belong to fidelities F = 0.99, 0.95, 0.9, 0.8, 0.7, respectively. The colored symbols show the crossovers between the different systems.

Optimized dynamical control of state transfer through noisy spin chains | New Journal of Physics

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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.

via Optimized dynamical control of state transfer through noisy spin chains – Abstract – New Journal of Physics – IOPscience.

Top inset: Spin-channel for state transfer with boundary-controlled couplings. Boundary-controlled spin chain mapped to a non-interacting spinless fermions system. The two boundary spins 0 and N+1 are resonantly coupled to the chain by the fermionic-mode z with a coupling strength J_z*α(t). (a) Spectrum of the effective fermionic system (rectangular bars) which interacts with the bath-modes k (red-even k and blue-odd k vertical lines) with strengths J ̃_k* α(t). Dashed contour: noise spectrum described by the Wigner-semicircle (maximal-disorder) lineshape with a central gap around ω_z. In the central gap, the optimal spectral-filters F_T(ω) generated by dynamical boundary-control with α_p(t) (p = 0 (black dotted), p = 2 (orange thin)) are shown. Bottom inset: a zoom of the tails of the filter spectrum that protect the state transfer against a general noisy bath with a central gap. (b) Infidelity as a function of transfer time T under optimal control (filter) with p = 0 (black dotted) and p = 2 (orange thin).
Top inset: Spin-channel for state transfer with boundary-controlled couplings. Boundary-controlled spin chain mapped to a non-interacting spinless fermions system. The two boundary spins 0 and N+1 are resonantly coupled to the chain by the fermionic-mode z with a coupling strength J_z*α(t). (a) Spectrum of the effective fermionic system (rectangular bars) which interacts with the bath-modes k (red-even k and blue-odd k vertical lines) with strengths J ̃_k* α(t). Dashed contour: noise spectrum described by the Wigner-semicircle (maximal-disorder) lineshape with a central gap around ω_z. In the central gap, the optimal spectral-filters F_T(ω) generated by dynamical boundary-control with α_p(t) (p = 0 (black dotted), p = 2 (orange thin)) are shown. Bottom inset: a zoom of the tails of the filter spectrum that protect the state transfer against a general noisy bath with a central gap. (b) Infidelity as a function of transfer time T under optimal control (filter) with p = 0 (black dotted) and p = 2 (orange thin).

Quantum simulations of localization effects with dipolar interactions | Annalen der Physik – 2013

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Quantum simulations of localization effects with dipolar interactions

Gonzalo A. Álvarez, Robin Kaiser, Dieter Suter

Abstract:
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).
DOI: 10.1002/andp.201300096

© 2013 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

via Quantum simulations of localization effects with dipolar interactions – Álvarez – 2013 – Annalen der Physik – Wiley Online Library.

Quantum simulations of localization effects with dipolar interactions - Álvarez - 2013 - Annalen der Physik - Wiley Online Library
Time evolution of the cluster-size of correlated spins starting from different initial sates. The experimental data is shown for two different perturbation strengths given in the legend. The solid black squares, red triangles and green rhombuses are evolutions from an uncorrelated initial state. Empty symbols start from an initial state with K0 correlated spins. The insets show the Multiple Quantum Coherence spectrum starting from K0 = 141 as a functions of time for a perturbation strength.

Robustness of Spin-Chain State-Transfer Schemes – Springer

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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.

Abstract

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.

via Robustness of Spin-Chain State-Transfer Schemes – Springer.

Robustness of dynamical decoupling sequences | Phys. Rev. A 87, 042309 (2013)

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Robustness of dynamical decoupling sequences

Mustafa Ahmed Ali Ahmed [1,2], Gonzalo A. Álvarez [1,3], and Dieter Suter [1]
1Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
2Department of Physics, International University of Africa, Khartoum, Sudan
3Department of Chemical Physics, Weizmann Institute of Science, Rehovot, Israel

Active protection of quantum states is an essential prerequisite for the implementation of quantum computing. Dynamical decoupling (DD) is a promising approach that applies sequences of control pulses to the system in order to reduce the adverse effect of system-environment interactions. Since every hardware device has finite precision, the errors of the DD control pulses can themselves destroy the stored information rather than protect it. We experimentally compare the performance of different DD sequences in the presence of an environment that was chosen such that all relevant DD sequences can equally suppress its effect on the system. Under these conditions, the remaining decay of the qubits under DD allows us to compare very precisely the robustness of the different DD sequences with respect to imperfections of the control pulses.

©2013 American Physical Society

via Phys. Rev. A 87, 042309 (2013): Robustness of dynamical decoupling sequences.

Average error per pulse for different DD sequences with delay τ =100μs. The average decay per pulse for different sequences is plotted against the number of pulses. The most conspicuous feature is that CP performs very badly and CPMG very well. The compensated sequences lie between these two extremes, and we find that the higher order sequences (XY8, KDD perform better than the lower order sequences (XY4). For unknown initial conditions, KDD shows the best performance. Under the present conditions, sequences that differ only with respect to time reversal symmetry perform quite similarly.
Average error per pulse for different DD sequences with delay τ =100μs.
The average decay per pulse for different sequences is plotted against the number of pulses. The most conspicuous feature is that CP performs very badly and CPMG very well. The compensated sequences lie between these two extremes, and we find that the higher order sequences (XY8, KDD perform better than the lower order sequences (XY4). For unknown initial conditions, KDD shows the best performance. Under the present conditions, sequences that differ only with respect to time reversal symmetry perform quite similarly.

Robustness of spin-chain state-transfer schemes

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Joachim Stolze, Gonzalo A. Álvarez, Omar Osenda, and Analia Zwick
To appear in Georgios M. Nikolopoulos and Igor Jex, editors:
Quantum State Transfer and Quantum Network Engineering. Springer Series in Quantum Science and Technology, Springer, Berlin 2013.

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.