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Vorlesung Quantum Computing SS 08 1 Quantum Computing Physik der Quanten-Informationsverarbeitung C. Meyer, C.M. Schneider Vorlesung SS 08.

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Presentation on theme: "Vorlesung Quantum Computing SS 08 1 Quantum Computing Physik der Quanten-Informationsverarbeitung C. Meyer, C.M. Schneider Vorlesung SS 08."— Presentation transcript:

1 Vorlesung Quantum Computing SS 08 1 Quantum Computing Physik der Quanten-Informationsverarbeitung C. Meyer, C.M. Schneider Vorlesung SS 08

2 Vorlesung Quantum Computing SS 08 2 Heise-online: 14.02.2007 12:49 > VorigeNächste Erster Quantenprozessor der Welt vorgestellt Das kanadische Start-up D-Wave Systems hat in Kalifornien einen Quantenprozessor mit 16 Qubits vorgestellt. Die Qubits werden von je einer kreisförmigen supraleitenden Stromschleife aus dem Metall Niob dargestellt. Die Betriebstemperatur des Prozessors beträgt 5 Millikelvin, 0,005 Grad über dem absoluten Nullpunkt. "Unser Durchbruch in der Quantentechnologie ist ein wichtiger Fortschritt bei der Lösung wirtschaftlicher und wissenschaftlicher Probleme, die bislang nur schwer in den Griff zu bekommen waren", erklärte D- Wave-Systems CEO Herb Martin.D-Wave SystemsQubits in the media 14.02.2007 12:49

3 Vorlesung Quantum Computing SS 08 3 plan… 1.introduction 2.quantum mechanical background 3.basic operations/superposition/entanglement 4.quantum computing with ion traps 5.Deutsch-Josza algorithm and its implementation 6.NMR quantum computing 7.Shor algorithm and its implementation (15 = 5x3) 8.magnetic resonance QC in solid state 9.quantum dots for quantum computing 10.first experiments 11.superconducting qubits 12.quantum error correction 13.invitation to Research Centre J ü lich

4 Vorlesung Quantum Computing SS 08 4 technology of computation 2-state (binary) logic: 0 and 1 state is defined by a switch: open & closed logic operations: array of switches (gates) mechanical switches (Zuse Z1) electromechanical relays (Zuse Z3) Rebuilt 1960 by K. Zuse Deutsches Museum München Built Techniques Frequency Speed Format Weight Tasks Processor: 600 relays Memory: 1400 relays Multiplication 22-bit digits floating point Technical calculations, chess

5 Vorlesung Quantum Computing SS 08 5 ENIAC Electronic Numerical Integrator And Computer 17468 vacuum tubes weight 20 t, power consumption 150 kW 1946

6 Vorlesung Quantum Computing SS 08 6 Moores law

7 Vorlesung Quantum Computing SS 08 7 birth of microelectronics 1947 invention of transistor 1958 invention of integrated circuit (TI) 1971 first microprocessor (4004)

8 Vorlesung Quantum Computing SS 08 8 microprocessors 4-bit8-bit32-bit64-bit Intel 4004 1971 Intel 8080 1974 2000 2005 1985 16-bit increase power of microprocessors by bus bit width and clock frequency

9 Vorlesung Quantum Computing SS 08 9 microprocessor design http://www.offis.de/ Embedded Hardware- / Software-Systems Dr. Jens Appell

10 Vorlesung Quantum Computing SS 08 10 breaking the barrier? minimum size of chip components (nm) source: quantum effects in silicon technology barrier silicon year proteins, macro-molecules size of viruses and DNA semiconductor industry exponential extrapolation

11 Vorlesung Quantum Computing SS 08 11 computational power we want to increase our capability of solving problems speed accuracy complexity increase what is a complex problem? Is there a subset of {2,3,15,14,7,10} which adds up to 0? Easy: verify that sum{-2,-3,15,-10} = 0 Difficult: identify this subset Similar problem: find prime factors of 1601

12 Vorlesung Quantum Computing SS 08 12 fundamental approach Question: Is there a general method or process by which one could decide whether a mathematical proposition could be proved? Answer: No! On computable numbers, with an application to the Entscheidungsproblem Proceedings of the London Mathematical Society, Series 2, Vol.42 (1936 - 37) pages 230 to 265 online available: http://web.comlab.ox.ac.uk/oucl/research/areas/ieg/e-library/sources/tp2-ie.pdf Turing Machine what is a computer and what kind of problems can it solve?

13 Vorlesung Quantum Computing SS 08 13 Turing machine head Consists of a stripe and a head ə 0 0 0 1 1100000 Stripe consists of symbols 0, 1, blank, ə b,f Head can be in states, e.g. b and f Symbols determine the action of the head: - Writing/Erasing of symbol - Direction of reading - change of state

14 Vorlesung Quantum Computing SS 08 14 boolean algebra and logic gates classical (irreversible) computing gate in out 1-bit logic gates: identity x NOT x 01 10 x Id 00 11 NOT xNOT x

15 Vorlesung Quantum Computing SS 08 15 boolean algebra and logic gates 2-bit logic gates: y x OR y 0 1 0 1 0 0 1 1 x 0 1 1 1 y x AND y 0 1 0 1 0 0 1 1 x 0 0 0 1 x y x OR y x y x AND y

16 Vorlesung Quantum Computing SS 08 16 Turing Machine 01ə bR,bR,fP1,L,bR,b fE,R,fR,fL,b ə 0 0 0 1 1100000 head b b b f f b f f f b 1 f b 1 b 1 b b f table of states what happens, depends on the states of the head ə 0 0 0 1 1100000 head f f f b f 56 + 7 = 63

17 Vorlesung Quantum Computing SS 08 17 complexity classes Deterministic Turing Machine (DTM) models all classical computers therefore called universal Probabilistic Turing Machine (PTM): actions are carried out with certain probability P: problems that can be solved with a DTM in polynomial time ZPP: problems that can be solved with a PTM with zero probability of error in polynomial time. NP: problems that can be solved with a NDTM in polynomial time. Non-Deterministic Turing Machine (NDTM): multiple computation paths (computation tree)

18 Vorlesung Quantum Computing SS 08 18 traveling salesman problem the traveling salesman problem is NP-complete What is the shortest route between a given number of cities? scales exponentially with number of cities for a DTM Can a physical implementation be found that provides a better solution? Experiment

19 Vorlesung Quantum Computing SS 08 19 physical system designed for problem soap bubbles can (theoretically) be used to solve some optimization problems in NP-complete soap bubbles NDTMquantum computer NDTM [Feynman1982]....certain quantum mechanical effects cannot be simulated efficiently on a classical computer. This observation led to speculation that perhaps computation in general could be done more efficiently if it made use of these quantum effects. R. P. Feynman, Int. J. Theor. Phys. 21, 467(1982); Found. Phys. 16, 507(1986)

20 Vorlesung Quantum Computing SS 08 20 Quantum Turing Machine Read, write, and shift operations are accomplished by quantum interactions Tape and head exist each in a quantum state symbols 0 or 1 are replaced by qubits, which can hold a quantum superposition of | 0 and | 1 The quantum Turing machine can encode many inputs to a problem simultaneously, and then it can perform calculations on all the inputs at the same time. This is called quantum parallelism. David Deutsch, Proceedings of the Royal Society of London A 400 (1985), 97

21 Vorlesung Quantum Computing SS 08 21 quantum bits conventional bit on 3.2 - 5.5 V 1 off -0.5 - 0.8 V 0 quantum mechanical bit (qubit) | 0 | 1 1 0 ( ( 0 1 ( ( a 1 | 0 + a 2 | 1 = a1a1 a2a2 () superposition:

22 Vorlesung Quantum Computing SS 08 22 quantum parallelism a 1 F |00> + a 2 F |01> + a 3 F |10> + a 4 F |11> a 1 |00> + a 2 |01> + a 3 |10> + a 4 |11> input b 1 |00> + b 2 |01> + b 3 |10> + b 4 |11> = output F

23 Vorlesung Quantum Computing SS 08 23 quantum computing calculationpreparationread-out time classical bit 1 ON 3.2 – 5.5 V 0 OFF -0.5 – 0.8 V exponentially faster for Fourier transformation (Shor algorithm) quantum-bit (qubit) 0 1 a 1 0 + a 2 1 = a1a1 a2a2 HH -1 U |A| time decoherence

24 Vorlesung Quantum Computing SS 08 24 important algorithms database search N data sets e.g. find no. in phonebook (60 million data sets) 30 million steps 7746 steps 89 steps10 19 steps taskalgorithm classical computer quantum computer prime factor decomposition e.g. 128 bit decoding

25 Vorlesung Quantum Computing SS 08 25 trapped ions C. Monroe, D.Wineland, et al. Nature 2000 R. Blatt group (Innsbruck) '97 - '00 C. Monroe group, Michigan 06

26 Vorlesung Quantum Computing SS 08 26 spin resonance 7 mm

27 Vorlesung Quantum Computing SS 08 27 quantum dots J. R. Petta et al., Science 2005 F. Koppens et al., Nature 2006

28 Vorlesung Quantum Computing SS 08 28 superconductor electronics Y. Nakamura et al., Nature 1999 I. Chiorescu et al., Science 2003

29 Vorlesung Quantum Computing SS 08 29 implementations atoms or ions in traps electronic states of atoms/ions vibrational modes spintronic electron spins in quantum dots exchange interaction superconductor electronics Cooper pairs or flux Josephson coupling spin resonance (NMR, ESR) spins in molecules or solid state matrix hyperfine, exchange, or magnetic dipolar interaction

30 Vorlesung Quantum Computing SS 08 30 from classic to quantum we live in Hilbert Space H the state of our world is |


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