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ICT Information Day Vladimír Bužek

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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

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QGATES & CONQUEST

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TRAPPED IONS (IN QED CAVITY)

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NEUTRAL ATOMS IN CAVITIES

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ATOMS & PHOTONS

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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.

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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

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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

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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. ?

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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

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

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Physical approximation of non-physical maps Nonlinear polarization rotation

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Reconstruction of Wigner functions of Fock States in Cavities – ENS experiment 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, (2002)] MaxEnt scheme – up to 5 orders more reliable than pattern-function or inverse Radon schemes, requires just 3 distributions for rotated quadratures,

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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. At the output of the homogenizer all qubits are in a vicinity of the state. Theorem 1: Q-H is a contractive map that can be realized only by a partial- swap operation 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.

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Continuous version of discrete dynamical semigroup Simulation of the discrete process of collision-like interaction between a system qubit nad reservoir Lindblad master equation continuous interpolation of the discrete process – one can determine from the “first” principle decay time and decoherence

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III. Quantum Random Walks “Quantization” of classical discrete random walks (Markov) Direction of the next step depends on |d> Quadratic/exponential improvement in mixing/hitting properties Implementation by means of optical multiports which “flip” the coin. Multidimensional QRW: Quantum coin: flipped at every step

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Quantum Random Walks Recurrent probability: Coins (legend): Classical: Grover: Fourier: Analytic solution of recurrent probability: where:

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IV. Universal quantum entangler No-go theorem: Best possible CP approximation – optimal UQE

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V. Programmable Quantum Processors Quantum control of dynamics, e.g. C-NOT Quantum information distributors control via input states of two ancillas (prorgam), e.g assymetric cloners or Universal NOT gate (specific processor) NO-GO Theorem (Nielsen & Chuang) – Universal quantum processors implementing arbitrary program encoded in program registers and applied to data registers do not exist Probabilistic quantum processors - measurement of program register realizes arbitrary map on data register Deterministic processors – realize specific classes maps t c data program measurement data program

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“universal” processor projective yes/no measurement probability of success: Universal Probabilistic Processor -Quantum processor U dp -Data register r d, dim H d = D -Quantum programs U k = program register r p, dim H p = Nielsen & Chuang: -N programs Þ N orthogonal states -Universal quantum processors do not Hillery-Ziman-Buzek: -Probabilistic implementation -{U k } operator basis, -program state Example: Data register = qudit, program register = 2 qudits Error-correting schemes - U(1) programmable rotations

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VI. Ising Model Linear chain of qubits in a magnetic field the cyclic condition Interaction energy level shifts Interaction Q entanglement In the interacting Universe factorized states are more exotic than entangled states

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(N=2n+1)-qubit Ising X-state Level crossing 2 n degeneracy such that at additionalalso at at;this means degeneracy X-state sum over all states with even number of (u is even) is the shortest distance between

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Super Entanglement Bounds on shared entanglement Ising model provides miraculously entangled states

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