
SCIENTIFIC PROGRAMS AND ACTIVITIES 

January 27, 2015  
Quantum Information and Quantum Control Conference

Robert Alicki, University of Gdansk
Is quantum error correction feasible?
It is rather generally accepted that without, at least in principle,
effective quantum error correction schemes quantum computers cannot
overpower classical ones and provide merely another very interesting
example of hybrid digitalanalog computing machines which do not violate
ChurchTuring thesis. The main aim of this talk is to discuss critically
the existing schemes of error correction schemes and the threshold results
for the faulttolerant quantum computation. The recent progress in formulating
and proving nogo theorem for mantaining unknown quantum state in the
presence of noise and its relevance for the quantum error correction
schemes will be presented also.
Thomas Baumert, Universitaet Kassel
Quantum control in intense phase shaped laser fields
Joint work with M. Wollenhaupt, A. Assion, A. Präkelt, D. Liese,
C. Sarpe. The ability to selectively steer quantum systems from
an initial state i> to any desired final state f> with the help
of suitably shaped light fields opens up undreamedof prospects for
applications in physics, chemistry, biology and engineering ranging
from quantum computation to the control of complex chemical reactions.
It turns out that the manipulation of the interferences of matter waves
is the key ingredient of quantum control. In the weak field regime,
i.e. when perturbation theory is operative, a couple of methods have
been devised and are well understood [1] [2]. In addition, strong field
control schemes such as the rapid adiabatic passage (RAP) and the stimulated
Raman adiabatic passage (STIRAP) with all their extensions have been
demonstrated to achieve population transfer with 100 % efficiency and
remarkable robustness (see also [1] [2]). A theoretical method to obtain
laser pulses which effectively excite a preselected target state is
provided by the optimal control theory (OCT) [3]. The experimentalist's
analogue to OCT, the socalled optimal control experiments (OCE) makes
use of the combination of pulse shaping techniques with adaptive feedback
learning loops (see [4] for theory and [5] [6] for selected experimental
realizations). This technique allows to optimize virtually any conceivable
observable with enormous success. However, especially in strong field
cases the underlying physical mechanism cannot be inferred from the
electrical fields obtained by this procedure.
Our approach is based on the investigation of specific control objectives
studied on simple well defined model systems using well characterized
femtosecond laser pulses in order to elucidate possible physical mechanisms
of quantum control especially in strong fields. To that end we combine
time resolved photoelectron spectroscopy, femtosecond pumpprobe and
pulse shaping techniques together with atomic / molecular beam techniques.
In a first experiment we demonstrate that the coherence properties of
femtosecond laser pulses can be transferred to electron wave packets
in the continuum. The coherence properties of the electron wave packet
are studied in an interference experiment where we use a sequence of
two time delayed laser pulses to ionize potassium atoms [7].
In a second experiment on potassium atoms we investigate strong field
quantum control with shaped femtosecond laser pulses where the manipulation
of the quantum mechanical phase with intense phase modulated pulses
leaves a fingerprint in the measured photoelectron spectra [8]. Pulse
sequences, chirped pulses and sinusoidally phase modulated pulses as
well as "closed loop" adaptive pulse shaping are employed
to elucidate a robust physical mechanism of adaptive strong field control
based on the selective population of dressed states.
[1] S. A. Rice and M. Zhao, Optical control of molecular dynamics (Wiley,
New York, 2000).
[2] M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular
Processes (John Wiley & Sons, Hoboken, New Jersey, ed. 1, 2003).
[3] A. Peirce, M. Dahleh, H. Rabitz, Phys.Rev.A 37, 49504964 (1988).
[4] R. S. Judson and H. Rabitz, Phys.Rev.Lett. 68, 15001503 (1992).
[5] A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried,
M. Strehle, G. Gerber, Science 282, 919923 (1998).
[6] T. Brixner, G. Krampert, T. Pfeifer, R. Selle, G. Gerber, M. Wollenhaupt,
O. Graefe, Ch. Horn, D. Liese, T. Baumert, Phys.Rev.Lett. 92, 20830112083014
(2004).
[7] M. Wollenhaupt, A. Assion, D. Liese, C. SarpeTudoran, T. Baumert,
S. Zamith, M. A. Bouchene, B. Girard, A. Flettner, U. Weichmann, G.
Gerber, Phys.Rev.Lett. 89, 17300111730014 (2002).
[8] M. Wollenhaupt, A. Assion, O. Bazhan, Ch. Horn, C. SarpeTudoran,
M. Winter, T. Baumert, Phys.Rev.A 68, 01540110154014 (2003).
Charles H. Bennett, IBM
Back Communication and Forward Capacities of Quantum Channels
Long ago Shannon showed that classical back communication cannot increase
a classical channel's forward capacity. For quantum channels the situation
is more complicated. It is known that classical back communication can
increase quantum capacity, but no example was known where it increased
a quantum channel's classical capacity. Granting a widely held additivity
conjecture, we have found channels where this occurs. These channels
may be thought of as having a "data" input and output, as
well as a control input that partly influences, and a control output
that partly reveals, which of a set of unitary evolutions the data undergoes
en route from input to output. The channel is designed so that the data's
evolution can be exactly inferred by a classically coordinated processing
of the control output, and a reference system entangled with the control
input, but not from either of these resources alone. The same family
of channels can be used to demonstrate various other capacity inequalities.
Joint work with Igor Devetak, Peter Shor, and John Smolin. quantph/0406086.
Gilles Brassard, Université de
Montréal
A Quarter of Century of Quantum Cryptography
For ages, mathematicians have searched for a system that would allow
two people to exchange messages in absolute secrecy. Around the middle
of last century, Shannon proved that this dream is possible if and only
if the legitimate participants share a random secret key as long as
the message they wish to transmit. But Shannon's theorem did not take
account of the quantum world in which we live. When information is appropriately
encoded as quantum states, any attempt from an eavesdropper to access
it yields partial information at best and entails a probability of spoiling
it irreversibly. This unavoidable disturbance can be detected by the
legitimate users. This phenomenon can be exploited to implement a cryptographic
system that is unconditionally secure even against an eavesdropper with
unlimited computing power and technology, with no need for a long shared
secret key. Sophisticated prototypes have been built in several countries,
over tens of kilometres of ordinary optical fibre as well as lineofsight
optical paths. Satellitebased implementations are being contemplated.
In this talk, I shall provide a historical perspective on quantum cryptography, which goes back 35, 25 or 20 years in the past, depending on where you start counting. I shall also discuss the present and the future of the field.
No prior knowledge of quantum cryptography will be assumed.
Philip H. Bucksbaum, FOCUS Center and
Department of Physics, University of Michigan
Control Analysis based on Learning Feedback Experiments
Feedback learning algorithms are widely used to control ultrafast optical
pulse shapes. A new problem in the study of quantum control of manybody
systems is how to use the solutions found by these algorithms to learn
about the system quantum dynamics. We are developing techniques to analyze
the principal controls that are discovered by a genetic learning algorithm
during its search. I will discuss how this technique can be used to
reveal the number and character of the degrees of freedom responsible
for control, and may aid in the construction of an effective Hamiltonian
for the dynamics.
Richard Cleve, University of Calgary
Consequences and Limits of Nonlocal Strategies
We investigate connections between (a) the nonlocal effects that can
occur when entangled quantum information is shared between two parties
and (b) certain
notions of "proof systems" that arise in computational complexity
theory. One way to think about Bell inequalities is to imagine that
two "provers" are trying
to convince a "verifier" that a certain mathematical object
exists. In a classical twoprover interactive proof system, the verifier
becomes convinced
only when the object exists. If prior entanglement between the provers
is introduced into the model then such systems can become invalid, and
the
expressive power of the underlying model can, in some respects, become
weaker.
This is joint work with Peter Hoyer, Ben Toner, and John Watrous.
David DiVincenzo, IBM Research
Control and decoherence in Josephson junction qubits
Josephson junction qubits are unique in that they are specified entirely
as electrical circuits. I will review the general theoretical procedure
for turning the description of the circuit into a Hamiltonian. This
Hamiltonian can be separated into a system part, an environment part,
and a coupling part. I will review what controls are available in the
system part, how we estimate the decoherence from the coupling and bath
parts, and how this theory has been applied to a variety of fluxbased
Josephson qubits in the laboratory.
Mark Dykman, Michigan State University
Localizing excitations in a quantum computer with perpetually coupled
qubits
Joint work with L. Santos and M. Shapiro. Strong manyexcitation localization
is studied in a chain of perpetually coupled qubits, which describes
many proposed models of a quantum computer. In these models, the transition
frequencies of the qubits can be individually controlled. We propose
a sequence of the qubit transition frequencies, that eliminates resonant
excitation transfer between both nearest and remote neighbors. It leads
to strong onsite singleexcitation localization. It also leads to a
large lifetime of strongly localized manyexcitation states. This lifetime
exceeds the reciprocal frequency of interqubit excitation hopping by
six orders of magnitude for a comparatively narrow bandwidth of the
qubit transition frequencies. The proposed frequency sequence is robust
with respect to small errors. This makes quantum computing with timeindependent
qubit coupling viable.
Mark Eriksson, University of Wisconsin
Silicon/SiliconGermanium for Quantum Computation
Silicon/SiliconGermanium quantum wells have many properties that
make them interesting candidates for spinbased quantum computation.
I will review recent progress in achieving low noise quantum dots and
Coulomb blockade in strained silicon/silicongermanium quantum wells.
I will also discuss recent advances in topgating silicon quantum dots.
An important spin decoherence mechanism in quantum wells in any material
is the fluctuating effective magnetic field that arises due to scattering
and the Rashba effect. I will provide an overview of this effect and
discuss recent measurements on six different quantum wells revealing
a wide range in Rashba parameters. Finally, silicon differs from many
other quantum well materials in that its conduction band has a sixfold
valley degeneracy in its bulk state. This sixfold degeneracy is lifted
by both strain and confinement in silicon quantum wells. I will present
a simple and direct spectroscopic measurement of the key splitting,
the valley splitting, over a wide magnetic field range.
Daniel Gottesman, Perimeter Institute
High Fidelity to Low Weight
In order to establish a property in cryptography, generally we have
to do some test, and rarely is this test completely reliable. As a trivial
example, we might wish to test that a state is 0>, but we do so
on a large ensemble of such states, and only sample a small fraction
of them. Even if the state passes the test, we cannot be sure that all
the states are 0>; indeed, an adversary could include a small number
of 1> states with a fairly small chance of being caught. In general,
the state that passes the test will thus not be an all0> state,
but rather a state with high fidelity to the subspace of lowweight
states, which are mostly 0>, but with a few 1>s. In quantum
cryptography, we could in general have an entangled state with this
property. I will discuss a lemma about such "high fidelity to low
weight" states, bounding their distribution in a complementary
basis. I have so far used this lemma twice in security proofs, and I
will describe the more recent such application, to quantum key distribution
with imperfect apparatus.
Ronnie Kosloff, The Hebrew University
of Jerusalem
Quantum molecular computing: Optimal control theory for unitary transformations
The dynamics of a quantum system driven by an external field is well
described by a unitary transformation generated by a time dependent
Hamiltonian. The general quantum compiler is the inverse problem of
finding the field that generates a specific unitary transformation.
We study this problem within the context of a quantum model composed
of a large Hilbert space where only a small fraction serves to store
quantum information. Specifically we study the inversion of a Fourier
transform using as registers the vibrational levels of the $X^1\Sigma^+_g$
electronic state of Na$_2$. Ramanlike transitions through the $A^1\Sigma^+_u$
electronic state induce the transitions. Using optimal control theory
light fields are found that are able to implement the Fourier transform
within a picosecond time scale. Such fields can be obtained by pulseshaping
techniques of a femtosecond pulse. The implementation of the $Q$ qubit
Fourier transform in the Na$_2$ molecule was carried out for up to 5
qubits.
The classical computation effort for implementing the quantum compiler
was found to scale exponentially with the number of levels. This estimate
was based on Krotov's method for optimal control theory solving the
inversion required to obtain the algorithm with a given fidelity. The
resources required are related to the number of controlled interference
pathways $K$ used to construct the evolution. For low intensity $K$
scales linearly with the product of lightfield bandwidth and pulse
duration. But $K$ increases exponentially with the pulse intensity.
This means that only a moderate increase in intensity is required with
increase
in the number of qubits. The possibility of teaching the molecule to
compute via an experimentally implemented feedback algorithm is explored.\\
Jose P. Palao and Ronnie Kosloff,
Phys. Rev. Lett., {\bf 89},\hspace{0.25em}188501 (2002).\\
Jose P. Palao and Ronnie Kosloff,
Phys. Rev. A, {\bf 68},\hspace{0.25em}062308 (2003).
Manny Knill, NIST
Postselected Quantum Computation
Postselected quantum computation is quantum computation that succeeds
and gives the correct answer with probability 0<p<1. For each
instance of the computation, whether it succeeded is known. Postselected
quantum computation can be implemented faulttolerantly with high depolarizing
error probabilities per gate (well above 1%). The techniques that achieve
this can be modified for faulttolerant conditional preparation of states
that can be used in standard faulttolerant quantum computation. Heuristics
and direct simulation indicate that with these techniques, it is possible,
at least in principle, to realize scalable quantum computers with depolarizing
error probabilities per gate well above 1%.
Gershon Kurizki, The Weizmann Institute
of Science
A Unified Approach to Dynamical Control of Decoherence
Joint work with A.Kofman , S.Pellegrin and D. Petrosyan. We present
our progress towards the development of a comprehensive strategy for
the prevention or suppression of decoherence and decay in entangled
multipartite systems coupled to arbitrary reservoirs or sources of fluctuations.
This strategy employs dynamical perturbations of the system by coherent
electromagnetic fields . The perturbations are tailored to the spectra
of the couplings between the system
and its environment , based on a universal master equation developed
by us for arbitrarily driven multidimensional systems undergoing non
Markovian relaxation. Dynamically induced cooperative multipartite effects
are used to suppress the decoherence more effectively , but strictly
individual relaxation of the different particles to their respective
environments can be dynamically suppressed as well. Surprisingly , nonadiabatic
periodic modulation of the energy levels may outperform adiabatic manipulations
in suppressing decoherence and maintaining high fidelity of quantum
logic.
Raymond Laflamme, University of Waterloo
Experimental quantum error correction
In the past few years, there has been a flurry of activity in the area
of experimental quantum information processing. Many technologies have
demonstrated control of a few qubits by characterising noise and implementing
various protocols and algorithms. One of the main obstacle for scaling
up is the fragility of quantum information. Fortunately quantum error
correction has been discovered. I will give a brief review of the importance
of quantum error correction and of various experiments which have implemented
some of its elements. I will discuss NMR experiments which have implemented
two qubit error detecting code and quantum error correcting codes correcting
for phase and full one bit error. I will also describe the encoding
of information in a noiseless subsystems which protects against collective
rotation. Then I will show how these noiseless subsystems can be useful
to protect states used for quantum cryptography. I will also discuss
quantum error correction using ion traps and photonic technologies.
I will put an emphasis on what are we and what can we learn by implementing
the protocols. I will conclude by pointing the task that lies ahead
to implement robust quantum information processing.
Daniel Lidar, University of Toronto
Hybrid quantum error prevention, reduction, and correction methods
Various methods have been designed to overcome decoherence and noise
in quantum information processing tasks. Wellknown examples are quantum
error correcting codes, dynamical decoupling, and decoherencefree subspaces/subsystems.
Each method has its limited set of advantages and realm of applicability.
It is advantageous to consider a combination of these various methods
in order to optimize their performance and compatibility with experimental
constraints. This talk will survey our recent progress along these lines.
It appears that hybrid methods are particularly wellsuited to spinbased
solidstate quantum computing proposals, as well as to trapped ions.
Time permitting, these applications will be discussed as well.
Norbert Lütkenhaus, University
of Erlangen
Quantum Correlations in Quantum Cryptography
Joint work with M. Curty (Erlangen), M. Lewenstein (Hannover). In
basic quantum communication protocols one party creates quantum states
and uses a quantum channel to transmit it to another party that performs
immediately some measurement on it. This means, we effectively create
correlated (classical) data between distant parties. In order to use
the power of quantum mechanics, these correlation must show effects
of quantum mechanics.
In the specific example of quantum key distribution one uses the correlations to distill a secret key in (classical) public discussion protocols e.g. via sifting, error correction and privacy amplification. We give a necessary condition for the success of any public discussion protocol: the observed correlations should allow to prove the presence of an internal, virtual state of entanglement in the distribution. This poses a first test whether any presented real quantum key distribution is indeed useful for the desired purpose. Moreover, a gap between the parameter regime of proven security of given realistic schemes and the regime of proven presence of vitual entanglement furthers the search for the optimal public discussion protocol.
Ari Mizel, Penn State University
Teleportation in ground state quantum computation
Ground state quantum computation is an alternative to the usual timedependent
approach to quantum computation. This alternative (which possesses some
noteworthy similarities to existing digital computer architectures)
presents its own challenges and advantages. We review ground state computation
and show how it can be improved using teleportation methods.
Herschel Rabitz, Princeton University
The Landscape for Controlling Quantum Phenomena
Controlling quantum phenomena includes applications ranging from
steering about a dynamic observable through the creation a particular
unitary transformation for quantum information science applications.
Regardless of the application, the desired objective is a functional
of the input control field. In the case of quantum state preparation,
mounting simulations and laboratory evidence suggest that attaining
good yields is surprisingly easy even in cases where hundreds of control
variables are being searched over. The reason for this behavior is shown
to lie in a kinematic analysis of controlled quantum phenomena. The
control landscape is defined as the desired output as a functional of
the control field, or alternatively, as a function of a complete set
of discrete variables. The control landscapes are shown to have particularly
simple structure for the cases of state or unitary transformation preparation.
The topology of the landscapes will be discussed in relation to the
ease of finding effective controls and robustness to control fluctuations.
Stuart A. Rice, The University of Chicago
Variations on Adiabatic Passage in Optical Control of Molecular Processes
A number of variations on adiabatic passage for the realization
of efficient and selective population transfer in both the gas and liquid
phases will be discussed. The advantageous use of decaying quantum states
and/or the influence of continuous measurements during the population
transfer will be stressed.
Aephraim M. Steinberg, University of
Toronto
Shedding a Bit of Information on Light: Measurement and Manipulation
of Quantum States
Over the past decade, a revolution has begun in the way we think
about physics, putting information at the centre of quantum mechanics.
In this talk, I will describe some recent experiments with nonclassical
states of photons and of trapped atoms, showing how information can
be stored in quantum systems and how it can be extracted. In particular,
quantum state and process tomography will be used to show how quantum
devices can be characterized, a necessary step for quantum computation
and error correction. The problem of unambiguous discrimination between
nonorthogonal quantum states will also be presented, showing that nonunitary
transformations can enable us to achieve things which would be impossible
with only unitary operations. We will also demonstrate the application
of such operations to the generation of novel 3photon entangled states,
previously experimentally unattainable. If time permitted, some more
controversial topics such as "interactionfree" measurement,
"weak" measurement, and Hardy's "retrodiction" paradox
would also be touched upon.
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