ICT Information Day

1
ICT Information Day
26.02.2009

• Vladimír Bužek

2
Projects

• QUBITS
• Quantum gates for information processing (QGATES)
  
• Quantum applications (QAP) 10MEURO
• EQUIP
• Entanglement in distributed systems (QUPRODIS)
• Hibrid Information processors (HIP)
• QUEST
• Controlled quantum coherence and entanglement in
  systems of trapped particles (CONQUEST)
  coordination 2.5 MEURO
• QUIPROCONE
• QUROPE
• ERA-Pilot QIST
• Quantum technologies (INTAS) coordination

3
QGATES CONQUEST
4
TRAPPED IONS (IN QED CAVITY)
5
NEUTRAL ATOMS IN CAVITIES
6
ATOMS PHOTONS
7
NOBEL PRIZE 2005
Prof. Ted Hänsch Prof. Ted Hänsch received the
Nobel prize for his contribution to laser
spectroscopy, and in particular the frequency
comb technique. The frequency comb cleverly uses
pulsed lasers to realize frequency "ruler", which
allows one to measure optical frequencies with
extreme precision. For the first time, the
frequency (that is, the colour) of light emitted
by atoms and ions can now be directly measured in
terms of the fundamental SI unit of frequency,
which is realized in atomic clocks.
Applications range from the measurement of
fundamental constants all the way to
higher-bandwidth optical fibre communications. In
particular, the frequency comb opens the door for
use of trapped atoms and ions (the object studied
in CONQUEST) as a clockwork in optical clocks,
which are expected to be more than 100 times more
precise than the best clocks existing today. The
fundamental property of light waves which enables
the frequency comb is its coherence - the same
property which is now being studied in CONQUEST
for matter waves.
8
Príncipe de Asturias de Investigación Científica
2006
Prof. Ignacio Cirac The Prince of Asturias
Foundation was formed in 1980 in the City of
Oviedo, the capital of the Principality of
Asturias, in a ceremony presided over by His
Royal Highness the Prince of Asturias, Heir to
the Throne of Spain, accompanied by his parents,
King Juan Carlos I and Queen Sofía. The Prince of
Asturias Awards symbolize the main objectives of
the Foundation to contribute to upholding and
promoting all those scientific, cultural and
humanistic values that form the heritage of
humanity. One goal of reasearch of Prof. Cirac
is to propose and analyze experiments that aim at
observing and discovering interesting quantum
phenomena in atomic systems. Under certain
conditions e.g. atomic gases can take on exotic
properties once they reach very low temperatures.
Another focus is to investigate, how atomic
systems can be controlled and manipulated at the
quantum level using lasers. Professor Cirac is
also leading in the development of a theory of
Quantum Information which will be the basis of
several applications in the world of
communication and computation once microscopic
systems can be completely controlled at the
quantum level. The concepts developed in the
field of Quantum Optics and Quantum Information
are also applied to other fields, in particular
to Condensed Matter Physics
9
CONTENT
I. Reconstruction of quantum channels from
incomplete data - from non-physical to
physical maps via Max-Likelihood -
reconstruction of photon states in the
cavity-QED II. De-coherence in information
processing - q-decoherence from first
principles III. Quantum random walks -
QRW on a hypercube scattering model IV.
Universal Quantum Machines - universal
quantum entangler V. Programmable
processors - realization of POVMs via
programmable devices - general
theory VI. Graphs of entanglement, Ising model
QIT

10
I. Black box Problem

• How can we determine properties of unknown
  q-channel (black box with no memory)? We can use
  qubits as probes and from correlations between in
  and out states we can determine the map.

11
Maximum Likelihood

• ML works with finite sets of data, not with
  infinite ensembles
• In case of quantum operations, the related data
  are
• Input state specification
• Measurement direction
• Measurement outcome (binary)
• We build a functional
• The numerical task is to find the , for which
  this functional reaches the maximum (using the
  logarithm of functional)
• Trace-preservation is obtained automatically from
  the parameterization, CP has to be checked in the
  algorithm

12
Experimental Data

• Data from the group of Ch. Wunderlich were
  analyzed
• Depolarization channel was expected

13
Physical approximation of non-physical maps

• Nonlinear polarization rotation

14
Reconstruction of Wigner functions of Fock States
in Cavities ENS experiment

• MaxEnt scheme up to 5 orders more reliable than
  pattern-function or inverse Radon schemes,
  requires just 3 distributions for rotated
  quadratures,

The Wigner function of Fock states of cavity
fields from the experimental data obtained at
the ENS, Paris obtained from the measurement of a
parity operator P.Bertet et al., PRL. 89, 200402
(2002)
15
II. Decoherence due to Flow of q-Information

• Q-Homogenization is the process in which an open
  system interacts with a reservoir. The original
  state of the open system is transformed into the
  state of reservoir particles.

• Theorem 1 Q-H is a contractive map that can be
  realized only by a partial-swap operation

At the output of the homogenizer all qubits are
in a vicinity of the state .

• Theorem 2 Original information encoded in the
  state is transferred into correlations
  between the system and reservoir particles. This
  information can be recovered iff classical info
  about the order of interaction is know.

16
Continuous version of discrete dynamical semigroup

• Simulation of the discrete process of
  collision-like interaction between a system
  qubit nad 25 000 reservoir

• Lindblad master equation continuous interpolation
  of the discrete process one can determine from
  the first principle decay time and decoherence

17
III. Quantum Random Walks
18
Quantum Random Walks

• Recurrent probability
• Coins (legend)
• Classical
• Grover
• Fourier
• Analytic solution of recurrent probability
• where

19
IV. Universal quantum entangler

• No-go theorem
• Best possible CP approximation optimal UQE

20
V. Programmable Quantum Processors
t

• Quantum control of dynamics, e.g. C-NOT

c

• Quantum information distributors control via
  input states of two ancillas (prorgam), e.g
  assymetric cloners or Universal NOT gate
  (specific processor)

data
program

• NO-GO Theorem (Nielsen Chuang) Universal
  quantum processors implementing arbitrary program
  encoded in program registers and applied to data
  registers do not exist

data

• Probabilistic quantum processors - measurement of
  program register realizes arbitrary map on data
  register

measurement
program

• Deterministic processors realize specific
  classes maps

21
Universal Probabilistic Processor

• Quantum processor Udp
• Data register rd, dim Hd D
• Quantum programs Uk program register rp, dim
  Hp

• Nielsen Chuang
• N programs Þ N orthogonal states
• Universal quantum processors do not

• Hillery-Ziman-Buzek
• Probabilistic implementation
• Uk operator basis,
• program state

• Error-correting schemes
• - U(1) programmable rotations

22
VI. Ising Model

• Linear chain of qubits in a magnetic field

• Interaction energy level shifts
• Interaction Q entanglement
• In the interacting Universe factorized states are
  more exotic than entangled states

the cyclic condition
23
(N2n1)-qubit Ising X-state

• Level crossing

• X-state

24
Super Entanglement

• Bounds on shared entanglement
• Ising model provides miraculously entangled states

25

• www.quniverse.sk