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QCCQI 2008
Quantum/Classical Control in Quantum Information
QUROPE WORKSHOP QUANTUM/CLASSICAL CONTROL IN QUANTUM INFORMATION: THEORY AND EXPERIMENTS
1320, September 2008, Otranto (Italy)
Abstracts
INVITED
Quantum information processing with electron spin resonance
Arzhang Ardavan
The Clarendon Laboratory, Department of Physics
University of Oxford
Electron spin systems were among the earliest proposed physical embodiments of quantum information processors. We have addressed a range of basic questions surrounding the practicalities of exploiting electron spins as qubits. We have shown that electron spin resonance can be used to perform quantum gates with a very high fidelity. We have studied the prospects for application of various candidate spin systems including N@C60 (a nitrogen atom encapsulated in a fullerene cage), molecular nanomagnets and phosphorus donors in silicon (P:Si). While in molecular nanomagnets magnetic nuclei in the vicinity of the electron qubit provides the dominant decoherence path, we have found that in N@C60 and P:Si nuclear moments can provide a valuable subsidiary resource in a quantum information processor.
QuantumOptical Control of Micromechanical Systems
Markus Aspelmeyer
Institute for Quantum Optics and Quantum Information (IQOQI)
Boltzmanngasse 3
A1090 Vienna
Massive mechanical resonators are now approaching the quantum regime. This opens up not only a spectrum of new applications but also a previously inaccessible parameter range for macroscopic quantum experiments. Quantum optics provides a rich toolbox to prepare and detect quantum states of mechanical systems, in particular by combining nano and micromechanical resonators with highfinesse cavities. I will review our recent experiments in Vienna on laser cooling micromechanical systems towards the quantum ground state via radiation pressure. I will also discuss the prospects and experimental challenges of generating optomechanical entanglement, which is at the heart of Schrdinger's cat paradox, and I will present a scheme for an atommechanics interface that promises a feasible hybrid architecture for quantum information processing.
Continously Monitoring the Quantum Oscillations of an
Electrical Circuit
P. Bertet (1), A. PalaciosLaloy (1), F. Mallet (1), F. Nguyen (1),
A. Korotkov (2), D. Vion (1), D. Esteve (1)
(1) Quantronics Group, SPEC, CEA Saclay, 91191 GifsurYvette CEDEX, FRANCE
(2) Department of Electrical Engineering, University of California
Riverside, California 925210204
Superconducting circuits based on Josephson junctions can be used to realize artificial atoms, with coherence times sufficient to perform interesting atomic physics experiments. They can be strongly coupled to the electromagnetic field of an onchip superconducting resonator, allowing to realize cavity quantum electrodynamics experiments with electrical circuits, giving rise to a new field called Circuit Quantum Electrodynamics (Circuit QED) [1,2]. We have studied the interplay between quantum dynamics and measurement in a Circuit QED setup. In our experiment, we use a transmon, a modified CooperPair Box coupled to a coplanar waveguide cavity which protects it from the environment and allows to reach long enough coherence times. An electromagnetic mode of the cavity is used to measure the qubit state. The photons stored in the cavity progressively extract information about the quantum state of the qubit, and correlatively dephase it. This information is carried by the phase of the electromagnetic field leaking out of the cavity that is measured by homodyne detection. By continuously applying the measuring field during Rabi oscillations of the circuit, we revisit the quantum measurement problem of a mesoscopic quantum electrical circuit [3]. By increasing the average number of photons in the cavity, we observe the transition between the weak measurement and Zeno regimes, both in the time and frequency domains. In the latter case, we discuss how far the experimental results provide a proof of the quantum behavior of the circuit.
[1] A. Blais et al., Phys. Rev. A 69, 062320 (2004)
[2] A. Wallraff et al., Nature 431, 162 (2004)
[3] A. Korotkov and D. Averin, Phys. Rev. B 64, 165310 (2001)
Spin Qubits in Graphene
Guido Burkard
University of Konstanz, Germany
Graphene represents a promising host material for spin qubits, due to the low concentration of nuclear spins and relatively weak spinorbit coupling. In this talk, the challenges and some theoretical solutions forelectron spin qubits localized in graphene quantum dots will be discussed. The most striking differences between graphene and conventional semiconductor materials are (i) the gapless linear electron spectrum in graphene which leads to Klein tunneling, thus preventing electron confinement in electrostatically defined quantum dots in extended twodimensional graphene, and (ii) the valley degeneracy which complicates coherently controlled exchange interactions between adjacent quantum dots.
We show that both problems can be overcome using electrically gated graphene nanoribbons, and show that Klein tunneling can be turned from a nuisance into an advantage for longdistance coupling between spin qubits.
Controlling imperfect systems for quantum information processing
Tommaso Calarco
University of Ulm
Quantum optimal control theory allows for shaping the time dependence of parameters that control the evolution of quantum systems relevant for quantum information processing. Fidelities well above the fault tolerance threshold can be attained in a variety of implementations of quantum gates under ideal conditions. Unfortunately, real experimental setups are always affected by imperfections that limit the performance of actual operations. Examples include anharmonicity in the trapping potentials, noise in the control parameters, limited bandwidth, imperfect pulse calibration, finite temperature, inhomogeneous broadening, all leading to decoherence and gate errors. In this talk I will show how quantum optimal control methods can be applied to tackle each of these implementation challenges, in many cases yielding fidelities beyond the faulttolerance threshold for realistic conditions.
Taming and controlling the nonequilibrium: Apparent relaxation and
information transfer in closed quantum lattice systems
Jens Eisert, M. Cramer, T. Osborne, A. Flesch, U. Schollwoeck
Imperial College London( , Prince Consort Road
SW7 2BZ London, UK
A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. Yet, how and in what sense can closed quantum manybody systems apparently relax to an equilibrium state, without any thermalizing environment? In this talk, we will address this question of the local apparent relaxation of quenched quantum systems in nonequilibrium.( ( Emphasis will be put on a setting where relaxation to a steady state is exact and can be rigorously shown. It is shown that locally, the system will "look relaxed", up to an arbitrarily small predescribed error. Remarkably, in the infinite system limit this relaxation is true for all large times, and no time average is necessary. The argument involves the finite speed of quantum information transfer in quantum lattice systems and quantum central limit theorems. We also discuss implications on entropy scaling in such quenched systems and the difficulty of simulating them using matrixproduct states( ( The final part of the talk will be concerned with numerical work on the strongly interacting case, using tDMRG, supporting an actual experiment using cold bosonic atoms. Here, the key idea is that optical superlattices allow for a period two read out of densities and correlations, providing control, such that relaxation phenomena can be studied without the need of locally addressing individual sites.( (
Singleatom singlephoton interaction
Jrgen Eschner
ICFO The Institute of Photonic Sciences
Castelldefels (Barcelona), Spain
The controlled interaction between single atoms and single photons is the basis for quantum interfaces that coherently connect qubit storage and qubit transmission. I will review a series of experiments where aspects of such interaction have been studied with single trapped ions and single photons, either from the ion's own resonance fluorescence or from a heralded singlephoton source. The results range from the observation of line shifts and mechanical effects of single backreflected fluorescence photons, over indistinguishability of photons from independent atoms, to the study of heralded singlephoton absorption. A possible future perspective of the latter is the realisation of photontoatom entanglement transfer.
Deterministic quantum interface between nonclassical light and room
temperature atomic ensembles
Thomas Fernholz
QUANTOP, Niels Bohr Institute, University of Copenhagen,
Copenhagen, Denmark
N.A.
Controlling errors in superconducting qubits
Gran Johansson
MC2, Chalmers University of Technology
The error rate is the main roadblock On the path towards superconducting multiqubit quantum information processing circuits. In order to circumvent or remove this block we need to learn more about the properties and origin of these errors, as well as tailor errorproof operation schemes.
In this talk, I will present a detailed analysis of the errors appearing in a strongly driven superconducting qubit, and show a quantitative comparison with experiment [1].
Boundary of Quantum Evolution in the Presence of Decoherence
Navin Khaneja
Harvard University, USA
A fundamental problem in coherent spectroscopy and quantum information science is to find limits on how close can an open quantum dynamical system be driven to a target state in the presence of decoherence and what is the optimal excitation that achieves this objective.
In this talk, we discuss some new methods we have developed to compute the reachable set of of open quantum systems. We characterize the structure of this reachable set in the presence of Markovian noise models of decoherence.
Application of these ideas are presented in the context of design of
nuclear magnetic resonance (NMR) experiments that maximize the transfer of coherence between couplet spin pairs in a spin network in the presence of decoherence and optimize the sensitivity of these experiments. We show how these methods can be used to compute limits on fidelity of quantum operations.
Dynamic control ofthermal decoherence
G. Kurizki , G. Gordon , N. Erez and N.BarGill
Weizmann Institute of Science, Rehovot 76100 , Israel
Dynamic control comprised of frequent quantum measurements and rapid phase modulation is shown to counter the effects of thermallyinduced decoherence in quantum systems ranging from atomic qubits through entangled qubit pairs to macroscopic quantum superpositions in BEC. This control relies on the breakdown ofthe Markov and rotatingwave approximations as per the universal principles laid out in our recentpublications .
Observation and dynamics of entanglement
Florian Mintert
Albert Ludwigs University Freiburg, Germany
The direct observation of quantum entanglement is a crucial prerequisite for its control.
We discuss various approaches to monitor and potentially control the time evolution of entanglement in open quantum systems.
Relating convex roof measures to unravellingtechniques of master equations allows to infer timedependent entanglement by observation of the environment only, and suitably chosen observables allow a direct measurement of entanglement on multiple identically prepared quantum states.
Often, the dynamical properties of entanglement depend on both the decoherence mechanism and the initial state.
However, there are quantum channels for which the time evolution of entanglement is basically independent of the initial state, what give rises to a very simple description of dynamical properties of general quantum states.
Using such tools we describe the time evolution of entanglement in open quantum systems of increasing size, and find environment coupling mechanisms that protect entanglement in a natural way.
Strong magnetic coupling between an electronic spin qubit
and a mechanical resonator
Peter Rabl
ITAMP, HarvardSmithsonian Center for Astrophysics,
Cambridge, MA 02138, USA.
Techniques for cooling and manipulating motional states of a nanomechanical resonator are nowadays actively explored, motivated by ideas from quantum information science, testing quantum mechanics for macroscopic objects and potential applications in nanoscale sensing. Here we describe a technique that enables a strong, coherent coupling between a single electronic spin qubit associated with a nitrogenvacancy impurity in diamond and the quantized motion of a nanomechanical resonator. The coupling is achieved by a magnetized tip attached to the freely vibrating end of the resonator that causes oscillating Zeeman shifts of the spin states. Under realistic conditions the shift corresponding to a single quantum of motion can approach 100 kHz and exceed both the electronic spin coherence time ($T_2 \sim 1$ ms) and the intrinsic damping rate, $\kappa = \omega_r/Q$, of high$Q$ mechanical resonators. In this regime, the spin becomes strongly coupled to mechanical motion in direct analogy to strong coupling of cavity QED.
We show how the strong coupling regime can be accessed in a practical setting specifically addressing the issues of fast dephasing ($T_2^* \sim 1 \,\mu$s) of the electronic spin due to interactions with the nuclear spin bath. Under such conditions strong coupling can be achieved by a careful preparation of dressed spin states which are highly sensitive to the motion of a magnetic resonator but insensitive to perturbations from the nuclear spin bath. The resulting JaynesCummings type model allows a coherent transfer of quantum states between the spin and the resonator mode, which in combination with optical pumping and readout techniques for spin states provides the basic ingredients for the generation and detection of various nonclassical states of the mechanical resonator. We discuss in more detail the implementation of continuous and pulsed optical cooling schemes to prepare the resonator close to the quantum ground state and a general strategy for the generation of arbitrary superpositions of resonator states.
QND measurements and quantum state reconstruction in cavity QED
JeanMichel Raimond
Laboratoire Kastler Brossel
Dpartement de physique de l'Ecole Normale Suprieure
24 rue Lhomond, 75005 Paris
Using longlived circular Rydberg atoms as sensitive probes of a quantum field trapped in a highquality superconducting cavity, we perform a Quantum non Demolition measurement of the cavity field photon number. We observe quantum jumps of light when photons are leaking into the environment. The analysis of the jump statistics provides a detailed insight into the cavity field relaxation mechanisms. Quantum Zeno effect occurs when repeated QND measurements compete with the injection of a coherent field in the cavity by a classical source.
By using atoms to perform QND measurements on an ensemble of cavity fields prepared in the same state, we fully reconstruct this state and its Wigner function. We apply this method to coherent states and to nonclassical Fock and `Schrdinger cat' states exhibiting Wigner functions with striking nongaussian features and negative values. We observe in real time the decoherence of a Schrdinger cat, through the progressive decay of the quantum interference features in its Wigner function.
This quantum state reconstruction opens fascinating perspectives for detailed nonclassical state studies and investigations of decoherence processes.
A realtime synchronization feedback for singleatom
frequency standards
Pierre Rouchon
Mines ParisTech
Centre Automatique et Systemes,
60, bd. SaintMichel, 75272 Paris Cedex 06, France,
HYPERLINK "mailto:pierre.rouchon@ensmp.fr"pierre.rouchon@ensmp.fr
Simple feedback loops, inspired from extremumseeking, are proposed to lock a probefrequency to the transition frequency of a single quantum system following quantum MonteCarlo trajectories. A 3level system is considered here: it appears in coherence population trapping and optical pumping. For this system, the feedback algorithm is shown to beconvergent in the following sense: the probe frequency converges in average towards the systemtransition one and its standard deviation can be made arbitrarily small. Closedloop simulations illustrate robustness versus jumpdetection efficiency and modeling errors.
This joined work with Mazyar Mirrahimi from INRIA, was partially supported by the Agence Nationale de la Recherche (ANR), Projet Blanc CQUID number 06313957.
Control Paradigms for Quantum Engineering.
Sonia Schirmer
Dept. of Maths & Statistics, University of Kuopio, Finland
Dept. of Applied Maths & Theoretical Physics, University of Cambridge, UK
This would include a sort of overview of the different approaches to quantum control from (openloop) Hamiltonian engineering to feedback control either based on a (discrete or continuous) measurement record or coherent feedback, some their applications, and problems, and some recent results, including various aspects of our recent work, e.g., on the application of simple bangbang control schemes to improve information transfer in spin chains to a critical, comparative analysis of timedomain optimal control algorithms and alternatives such as frequency domain optimization, we're
currently working on. Timepermitting I might also say something about the need for system identification, especially effective and efficient
protocols for control Hamiltonian tomography.
Watching (de) coherence and quantum noise in mesoscopic many body systems
Joerg Schmiedmayer
Atominstitut der stereichischen Universitten, TUWien
Quantum coherence and Quantum noise, together with the probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. Coherence can be observed in interference experiments, but the full characterization of the noise, which in manybody systems quantum can reveal the nonlocal correlations and entanglement of underlying manybody states remained elusive.
In the talk I will present experiments interfering two 1 dimensional quantum gases, which reveal how the coherence slowly dies under the influence of quantum and thermal noise [1]. To reveal the nature of the fluctuations we generalize the standard homodyne measurement of quantum optics to the analysis of interference of two fluctuating quantum systems. The full distribution function of the shot to shot variation of the interference patterns contains information about the higher order correlation functions and reveals the nature of the noise. In our experiments we clearly distinguish between contributions of fundamental quantum noise and thermal noise [2].
In an outlook we will discuss how experiments can be extended and combined with high efficient atom counting to further characterize the quantum states of mesoscopic many body systems.
This work was supported by the European Union MC network AtomChips, integrated project SCALA, the DIP the FWF and the Wittgenstein Prize.
[1] S. Hofferberth et al. Nature 449, 324 (2007);
[2] S. Hofferberth et al. Nature Physics 4, 489 (2008)
Challenges of Optimal Control in Closed and Open Systems:
From Quantum CISC Compilation to Decoherence Protection
Thomas SchulteHerbrggen
Technical University Munich, Department of Chemistry
D85747 GarchingMunich, Germany
Optimal controls in closed and open Markovian as well as nonMarkovian quantum systems are shown to cut errors by an order of magnitude in realistic settings.
As an application, we exploit the cuttingedge highspeed parallel cluster HLRBII (with a total LINPACK performance of 63.3 TFlops/s) to present a quantum CISC compiler. Its timeoptimised or decoherence protected complex instruction sets (CISC) comprise multiqubit interaction modules with up to 10 qubits. We show how to assemble these CISC modules in a scalable way for largescale quantum computation (~100 qubits). Extending the restricted instruction set (RISC) of universal gates by optimised complex multiqubit instruction sets thus paves the way to fight decoherence in realistic settings.  We also discuss the relation between timeoptimal and relaxation optimised controls and in view of quantum CISC compilation with errorprotected building blocks.
The methods are developed within a theoretical framework of gradient flows on Riemannian manifolds expoiting the structure of Lie groups and semigroups. Based on a Lie semialgebraic analysis of quantum dynamical Master equations, we develop concepts of controllability of open quantum systems.
Longtime relaxation of superconducting qubits
V.S. Shumeiko
Chalmers University of Technology
Control of qubit decoherence requires detailed knowledge of dissipative interaction with the bath. We theoretically investigate relaxation of superconducting qubits beyond BlochRedfield approximation.
For macroscopic (charge and flux) qubits we find exponential suppression of longtime nonMarkovian relaxation tails originating from the bath spectral edges. The effect is analyzed using superoperator diagrammatic technique and selfconsistent Born approximation. For microscopic (Andreev level) qubits we find very slow, nonexponential in time relaxation. The phenomenon is explained by many body effects that add nonlinear terms to the BlochRedfield equation.
Openloop quantum error control: From dynamical decoupling to dynamically corrected universal quantum gates
Lorenza Viola
Department of Physics and Astronomy,
Dartmouth College, 6127 Wilder Laboratory,
Hanover, New Hampshire 03755, USA
Dynamical decoupling methods provide a powerful approach to decoherence control in quantum information processing which is significantly less resourceintensive than quantum error correcting codes. While decoupling schemes for preserving quantum information are theoretically well characterized and are acquiring a growing experimental significance, combining dynamical decoupling with nontrivial quantum gates is significantly more challenging from a quantum control standpoint. General procedures introduced in [1] operate under unrealistic assumptions, including unbounded control strengths and, typically, the need for appropriate encodings. In this talk, I will describe how to overcome the above shortcomings by exploiting recently introduced dynamically corrected gates [2], which achieve substantially higher fidelity than uncorrected gates while using only realistic control resources. The basic idea is to exploit knowledge about relationships between errors of gates in a primitive set to obtain composite gates where decoherence is removed to leading order. Illustrative examples will be presented.
Support from the National Science Foundation is gratefully acknowledged.
[1] L. Viola, S. Lloyd, and E. Knill, Phys. Rev. Lett. 83, 4888 (1999).
[2] K. Khodjasteh and L. Viola, ''Dynamically errorcorrected gates for universal quantum computation,'' submitted (2008).
Experimental inhibition of decoherence on flying qubits
via bangbang control
David Vitali
Dipartimento di Fisica
Universita' di Camerino
In recent years the interest in the storage and manipulation of quantum systems has furthered new strategies for maintaining their coherence. Photons interact weakly with the surroundings. Even so decoherence may significantly affect their polarization state during the propagation within dispersive media because of the unavoidable presence of more than a single frequency in the envelope of the photon pulse. We report here on a nearly complete suppression of the polarization decoherence in a ring cavity obtained by properly retooling for the photon qubit the bangbang protection technique already employed for nuclear spins and nuclearquadrupole qubits. Our results show that the bangbang control can be profitably extended to all quantum information processes involving flying polarization qubits.
Controlling Photons, Qubits and their Interactions in Circuit
Quantum Electrodynamics (QED)
Andreas Wallraff
Department of Physics, ETH Zurich
CH8093 Zurich, Switzerland
In our lab, we are able control the interaction of microwave photons and qubits on the level of individual quanta. We perform novel quantum information processing and quantum optics experiments in superconducting electronic circuits [1,2]. In the resonant regime, we observe the coherent exchange of a single or multiple photons between an onchip cavity and a qubit [2,3]. We also investigate the resonant and nonresonant coupling of a controlled number of photons to single or multiple qubits. These processes are useful in the context of quantum communication, for example for coupling remote qubits via a quantum bus [4]. In circuit QED, long coherence times, high fidelity qubit state control and readout [5], also allow us to explore quantum geometric phases and their use for information processing [6].
[1] A. Blais et al., Phys. Rev. A 69, 062320 (2004)
[2] A. Wallraff et al., Nature (London) 431, 162 (2004)
[3] J. Fink et al., Nature (London) in print (2008)
[4] J. Majer et al., Nature (London) 449, 443 (2007)
[5] A. Wallraff et al., Phys. Rev. Lett. 95, 060501 (2005)
[6] P. Leek et al., Science 318, 1889 (2007)
Coherent control of decoherence
Ian Walmsley, Matthijs Branderhorst, Piotr Wasylczyk, Pablo Londero,
Department of Physics, University of Oxford, Clarendon Laboratory,
Parks Rd., Oxford, OX1 3PU, UK
Constantin Brif, Herschel Rabitz
Department of Chemistry, Princeton University,
Princeton,NJ, 08544, USA
Robert Kosut
SCSolutions Inc., 1261 Oakmead Parkway,
Sunnyvale, CA, 90089, USA
Coherent control of quantum systems uses the constructive or destructive interference between pathways to manipulate the evolution of the system. The success of any coherent manipulation of the dynamics depends on maintaining the quantum phase relationships between the different parts of the system. The inevitable interaction of any real system with its environment will corrupt the unitary evolution and prevent the coherent control from reaching its objective. Usually, manipulation of quantum interference presupposes that the system under control does not experience significant dissipation by coupling to an uncontrolled environment.
An interesting possibility is to use the principles of coherent control itself to counteract decoherence. Here we show that coherent control can mitigate the effect of the environment. We demonstrate experimentally the ability to control the rate of quantum dephasing using closed loop methods, and show some general principles that have broad application. We chose a simple initial problem: maintaining the coherence of the excited quantum state, without trying to achieve a particular function with it.[1]
Among the simplest physical system that exhibits the salient effects is a diatomic molecule. Here the system is the vibrational mode of the internuclear motion in the excited electronic state, which is dephased by coupling to the rotational degree of freedom. A key element enabling control is the identification of a simple surrogate representing the coherence of the system state. The visibility of fluorescence quantum beats from an excited diatomic molecule provides such a signature. We show that the beat visibility may be adaptively raised from below the experimental noise to approximately four times the noise level by shaping the vibrational mode of the molecule, leading to the counter intuitive result that more coherence, in the sense of a superposition of a larger number of bare system eigenstates, generates a state that is more robust to interactions with the environment.[2]
This system also provides a suitable model to test the concepts of quantum process tomography for a highdimensional system. We have applied concepts of convex optimization to the problem of estimation of the decoherence process operators, and we show how size of the estimation problem can be significantly reduced by using prior knowledge of the process, which is available in most real systems.
These results provide a new route to creating controlled coherence in a system when decoherence is present, by showing the tools of coherent control may themselves be used to inhibit dephasing. Because decoherence is ubiquitous, this is an important issue, and it is perhaps surprising that closed loop coherent control is effective for this application.
Reference
1.C. Brif, H. Rabitz, S. Wallentowitz and I. A. Walmsley, Decoherence of molecular vibrational wave packets: Observable manifestations and control criteria, Phys. Rev. A, 63, 063404 (2001)
2. M. Branderhorst, P. Londero, P. Wasylczyk, C. Brif, R. Kosut, H. Rabitz and I. A. Walmsley Coherent Control of Decoherence, Science, 320, 638 (2008)
Novel experimental building blocks for quantum information processing with trapped ions
Christof Wunderlich1
1Fachbereich Physik, Universitt Siegen
57068 Siegen, Germany
Laser cooled atomic ions confined in an electrodynamic cage have been used successfully for quantum information processing (QIP) [1]. Carrying out quantum logic operations with sufficient accuracy to achieve scalable faulttolerant quantum computing, however, is still tied to experimental obstables. One of the experimental challenges encountered is the use of laser light for coherently driving ionic resonances that serve as qubits. This laser light needs to be stable against variations in frequancy, phase, and amplitude over the course of a quantum computation or simulation. Also, the intensity profile of the laser beam, its pointing stability, and diffraction effects need to be controlled. Spontaneous scattering of laser light poses a fundamental limit for the coherence time of a quantum manybody state.
Here, we report on the first demonstration of coupling internal and motional states of trapped atomic ions using radiofrequency instead of laser radiation [2]. This is prerequisite for implementing multiqubit quantum gates using rf or microwave radiation [3]. In addition, individual addressing of trapped ions is demonstrated by tuning the frequency of rf radiation instead of focussing laser light to a spot size much smaller than the distance between neighboring ions. These demonstrations represent two crucial experimental steps on the route towards realizing a concept for iontrap based quantum computing and simulations where only rf or microwave radiation, instead of laser light, is employed for coherent manipulation.
Also, singlequbit quantum gates, develped using optimal control theory, are experimentally implemented with trapped Yb+ ions [4]. These quantum gates are robust against expeirmental and intrinsic system imperfections and represent, at the same time, building blocks for multiqubit gates. A systematic study of the experimental performance of example pulses base on optimal control theory and a comparison with composite pulses reveals the great robustness of the former. Low error rates are an essential requirement for scalable faulttolerant quantum computing. Thus, a versatile tool to achieve this goad with trapped ions is implemented.
[1] For instance, J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995); F. SchmidtKaler et al., Nature 422, 408 (2003); D. Leibfried et al., Nature 422, 412 (2003); K.A. Birckman et al., Phys. Rev. A 72, 050306(R) (2005); J. P. Home et al., New Journal of Physics 8, 188 (2006).
[2] M. Johanning et al. arXiv:0801.0078v1 [quantph].
[3] F. Mintert and C. Wunderlich, Phys. Rev. Lett. 87, 257904 (2001); 91, 029902(E) (2003); c. Wunderlich, in Laser Physics at the Limit (Springer, Heidelberg, 2002), p. 261; D. McHugh and J. Twamley, Phys. Rev. A 71, 012315 (2005).
[4] N. Timotey et al., Phys. Rev. A 77, 052334 (2008).
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