# quantum computation

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

**Colloquium: Protecting quantum information against environmental noise**

Dieter Suter and Gonzalo A. Álvarez

Rev. Mod. Phys. 88, 041001 (2016)

Published 10 October 2016

Quantum-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.

### 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

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?.

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

**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 | Annalen der Physik – 2013

**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

### Robustness of Spin-Chain State-Transfer Schemes – Springer

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)

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.

### Robustness of spin-chain state-transfer schemes

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.

### Experimental protection of quantum gates against decoherence and control errors | Phys. Rev. A 86, 050301(R) 2012

Experimental protection of quantum gates against decoherence and control errors

Alexandre M. Souza, Gonzalo A. Álvarez, and Dieter Suter

Fakultät Physik, Technische Universität Dortmund, D-44221, Dortmund, Germany

One of the biggest challenges for implementing quantum devices is the requirement to perform accurate quantum gates. The destructive effects of interactions with the environment present some of the most difficult obstacles that must be overcome for precise quantum control. In this work we implement a proof of principle experiment of quantum gates protected against a fluctuating environment and control pulse errors using dynamical decoupling techniques. We show that decoherence can be reduced during the application of quantum gates. High-fidelity quantum gates can be achieved even if the gate time exceeds the free evolution decoherence time by one order of magnitude and for protected operations consisting of up to 330 individual control pulses.

©2012 American Physical Society

### Robust dynamical decoupling | Review Article | Phil. Trans. R. Soc. A 370, 4748 (2012)

#### Review article: Robust dynamical decoupling

Alexandre M. Souza, Gonzalo A. Álvarez and Dieter Suter

Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund, Germany

Abstract

Quantum computers, which process information encoded in quantum mechanical systems, hold the potential to solve some of the hardest computational problems. A substantial obstacle for the further development of quantum computers is the fact that the lifetime of quantum information is usually too short to allow practical computation. A promising method for increasing the lifetime, known as dynamical decoupling (DD), consists of applying a periodic series of inversion pulses to the quantum bits. In the present review, we give an overview of this technique and compare different pulse sequences proposed earlier. We show that pulse imperfections, which are always present in experimental implementations, limit the performance of DD. The loss of coherence due to the accumulation of pulse errors can even exceed the perturbation from the environment. This effect can be largely eliminated by a judicious design of pulses and sequences. The corresponding sequences are largely immune to pulse imperfections and provide an increase of the coherence time of the system by several orders of magnitude.

#### via Robust dynamical decoupling: Phil. Trans. R. Soc. A 370, 4748 (2012).

### Featured in PRA Kaleidoscope for Vol. 85 Iss.5 (May 2012)

Image from “Iterative rotation scheme for robust dynamical decoupling.” [Gonzalo A. Álvarez, Alexandre M. Souza, and Dieter Suter, Phys. Rev. A 85, 052324 (2012)]