QCCQI 2008
Quantum/Classical Control in Quantum Information
QUROPE WORKSHOP QUANTUM/CLASSICAL CONTROL IN QUANTUM INFORMATION:
THEORY AND EXPERIMENTS
13-20, 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.
Quantum-Optical Control of Micromechanical Systems
Markus Aspelmeyer
Institute for Quantum Optics and Quantum Information (IQOQI)
Boltzmanngasse 3
A-1090 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
high-finesse 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
Schrödinger's cat paradox, and I will present a scheme for an
atom-mechanics
interface
that
promises
a
feasible
hybrid
architecture for quantum information processing.
Continously Monitoring the Quantum Oscillations of an
Electrical Circuit
P. Bertet (1), A. Palacios-Laloy (1), F. Mallet (1), F.
Nguyen (1),
A. Korotkov (2), D. Vion (1), D. Esteve (1)
(1) Quantronics Group, SPEC, CEA Saclay, 91191 Gif-sur-Yvette
CEDEX, FRANCE
(2) Department of Electrical Engineering, University of California
Riverside, California 92521-0204
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 on-chip 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 Cooper-Pair 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 spin-orbit coupling. In this talk, the
challenges and some theoretical solutions for electron 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 long-distance
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
fault-tolerance
threshold for realistic conditions.
Taming and controlling the non-equilibrium: 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 many-body 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
non-equilibrium.
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 matrix-product states
The final part of the talk will
be concerned with numerical work on the strongly interacting
case, using t-DMRG, 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.
Single-atom – single-photon interaction
Jürgen 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 single-photon source. The results range from the
observation of line shifts and mechanical effects of single
back-reflected
fluorescence
photons,
over
indistinguishability of photons from independent atoms, to
the study of heralded single-photon absorption. A possible
future perspective of the latter is the realisation of
photon-to-atom entanglement transfer.
Deterministic quantum interface between non-classical light and
room
temperature atomic ensembles
Thomas Fernholz
QUANTOP, Niels Bohr Institute, University of Copenhagen,
Copenhagen, Denmark
N.A.
Controlling errors in superconducting qubits
Göran Johansson
MC2, Chalmers University of Technology
The error rate is the main roadblock On the path towards
superconducting multi-qubit 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 error-proof 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 of
thermal decoherence
G. Kurizki , G. Gordon , N. Erez and N.Bar-Gill
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
thermally-induced decoherence in quantum systems ranging from
atomic qubits through entangled qubit pairs to macroscopic
quantum superpositions in BEC. This control relies on the
breakdown of the Markov and rotating-wave approximations as
per
the
universal
principles
laid
out
in
our
recent publications .
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 unravelling-techniques of
master equations allows to infer time-dependent 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, Harvard-Smithsonian Center for Astrophysics,
Cambridge, MA 02138, USA.
Techniques for cooling and manipulating motional states of a
nano-mechanical resonator are nowadays actively explored,
motivated by ideas from quantum information science, testing
quantum mechanics for macroscopic objects and potential
applications in nano-scale 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
nano-mechanical 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
Jaynes-Cummings 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 non-classical 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
Jean-Michel Raimond
Laboratoire Kastler Brossel
Département de physique de l'Ecole Normale Supérieure
24 rue Lhomond, 75005 Paris
Using long-lived circular Rydberg atoms as sensitive probes of
a quantum field trapped in a high-quality 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 non-classical Fock and `Schrödinger
cat' states exhibiting Wigner functions with striking nongaussian features and negative values. We observe in real time
the decoherence of a Schrödinger cat, through the progressive
decay of the quantum interference features in its Wigner
function.
This
quantum
state
reconstruction
opens
fascinating
perspectives for detailed non-classical state studies and
investigations of decoherence processes.
A real-time synchronization feedback for single-atom
frequency standards
Pierre Rouchon
Mines ParisTech
Centre Automatique et Systemes,
60, bd. Saint-Michel, 75272 Paris Cedex 06, France,
pierre.rouchon@ensmp.fr
Simple feedback loops, inspired from extremum-seeking, are
proposed to lock a probe-frequency to
the transition
frequency of a single quantum system following
quantum
Monte-Carlo trajectories. A 3-level 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 system-transition one and
its standard deviation can be made arbitrarily small. Closedloop simulations illustrate robustness versus jump-detection
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 06-3-13957.
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 (open-loop) 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 bang-bang control schemes to improve
information
transfer
in
spin
chains
to
a
critical,
comparative
analysis
of
time-domain
optimal
control
algorithms
and
alternatives
such
as
frequency
domain
optimization, we're
currently working on.
Time-permitting 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 Östereichischen Universitäten, TU-Wien
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 many-body systems
quantum can reveal the non-local correlations and entanglement of
underlying many-body 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 Schulte-Herbrüggen
Technical University Munich, Department of Chemistry
D-85747 Garching-Munich, 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 cutting-edge high-speed
parallel cluster HLRB-II (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 multi-qubit interaction modules with up to 10
qubits. We show how to assemble these CISC modules in a
scalable way for large-scale quantum computation (~100
qubits). Extending the restricted instruction set (RISC) of
universal gates by optimised complex multi-qubit instruction
sets thus paves the way to fight decoherence in realistic
settings. - We also discuss the relation between time-optimal
and relaxation optimised controls and in view of quantum CISC
compilation with error-protected 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.
Long-time 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
Bloch-Redfield approximation.
For macroscopic (charge and flux) qubits we find exponential
suppression of long-time non-Markovian 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, non-exponential in time
relaxation. The phenomenon is explained by many body effects
that add non-linear terms to the Bloch-Redfield equation.
Open-loop 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 resource-intensive 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 non-trivial 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 error-corrected
gates for universal quantum computation,'' submitted (2008).
Experimental inhibition of decoherence on flying qubits
via bang-bang 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 “bang-bang”
protection technique already employed for nuclear spins and
nuclear-quadrupole 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
CH-8093 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 on-chip
cavity and a qubit [2,3]. We also investigate the resonant
and non-resonant 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
read-out [5], also allow us to explore quantum geometric
phases and their use for information processing [6].
[1]
[2]
[3]
[4]
[5]
[6]
A.
A.
J.
J.
A.
P.
Blais et al., Phys. Rev. A 69, 062320 (2004)
Wallraff et al., Nature (London) 431, 162 (2004)
Fink et al., Nature (London) in print (2008)
Majer et al., Nature (London) 449, 443 (2007)
Wallraff et al., Phys. Rev. Lett. 95, 060501 (2005)
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 high-dimensional
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, Universität 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 fault-tolerant
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 many-body state.
Here, we report on the first demonstration of coupling
internal and motional states of trapped atomic ions using
radio-frequency instead of laser radiation [2]. This is
prerequisite for implementing multi-qubit 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 ion-trap based quantum computing and simulations where
only rf or microwave radiation, instead of laser light, is
employed for coherent manipulation.
Also, single-qubit 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 multi-qubit
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 fault-tolerant 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. Schmidt-Kaler 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 [quant-ph].
[3] F. Mintert and C. Wunderlich, Phys. Rev. Lett. 87, 257904
(2001); 91, 029902(E) (2003); c. Wunderlich, in Laser Physics at
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