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Quantum Computer with Trapped Ions

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Quantum Computer with Trapped Ions Quantum Information Processing with Trapped Ions Overview: Experimental implementation of quantum information processing with trapped ions 1. Implementation concepts of QIP with trapped ions 2. Quantum gate operations and entanglement with trapped ions 3. Advanced QIP procedures, scaling the ion-trap quantum computer Quantum Information Science with Trapped Ions 1 Handouts for lectures … are available from the organizers as pdf-files (ask Prof. Knoop, web-pages) Part 1: Implementation concepts of QIP with trapped ions Part 2: Quantum gate operations, entanglement etc. Part 3: Advanced QIP procedures, scaling… plus 3 review articles, covering basics and advanced features … are available from organizers (as pdf-files) Quantum dynamics of single trapped ions D. Leibfried, R. Blatt, C. Monroe, D. Wineland, Rev. Mod. Phys. 75, 281 (2003) Quantum computing with trapped ions H. Häffner, C. Roos, R. Blatt, Physics Reports 469, 155 (2008) Entangled states of trapped atomic ions Rainer Blatt and David Wineland, Nature 453, 1008 (2008) Quantum Information Processing Experimental Implementation with Trapped Ions Rainer Blatt Institute of Experimental Physics, University of Innsbruck, Institute of Quantum Optics and Quantum Information, Austrian Academy of Sciences 1. Implementation concepts and basic techniques generics of QIP, the ion trap quantum computer, spectroscopy, measurements, basic interactions and gate operations 1. Implementation concepts and basic techniqes 1.1 Generics of quantum information processing 1.2 Realization concepts 1.3 Ion trap quantum computer – the basics 1.4 Spectroscopy in ion traps 1.5 Addressing individual ions 1.6 Basic gate operations, composite pulses Why Quantum Information Processing ? applications in physics and mathematics factorization of large numbers (P. Shor, 1994) can be achieved much faster on a quantum computer than with a classical computer factorization of number with L digits: classical computer: ~exp(L1/3), quantum computer: ~ L2 fast database search (L. Grover, 1997) search data base with N entries: classical computer: O(N), quantum computer: O(N1/2) simulation of Schrödinger equations spectroscopy: quantum computer as atomic „state synthesizer“ D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996) quantum physics with „information guided eye“ Computation is a physical process input physical object set computation physical process shift output physical object read Classical Computer Quantum Computer - bits, registers - qubits, quantum registers - gates - quantum gates - classical processes (switches), - coherent processes dissipative - preparation and manipulation of entangled states The requirements for quantum information processing D. P. DiVincenzo, Quant. Inf. Comp. 1 (Special), 1 (2001) I. Scalable physical system, well characterized qubits II. Ability to initialize the state of the qubits III. Long relevant coherence times, much longer than gate operation time IV. “Universal” set of quantum gates V. Qubit-specific measurement capability VI. Ability to interconvert stationary and flying qubits VII. Ability to faithfully transmit flying qubits between specified locations The seven commandments for QIP !! Quantum bits and quantum registers classical bit: physical object in state 0 or 1 register: bit rows 0 1 1 . quantum bit (qubit): superposition of two orthogonal quantum states quantum register: L 2-level atoms, 2L quantum states 2L states correspond to numbers 0,....., 2L – 1 most general state of the register is the superposition (binary) (decimal) Universal Quantum Gates Operations with single qubit: (1-bit rotations) together universal ! Operations with two qubits: (2-bit rotations) CNOT – gate operation (controlled-NOT) analogous to XOR control bit target bit How a quantum computer works quantum processor input computation: sequence of quantum gates output Circuit quantum computer model: notation control qubit qubit target input computation: sequence of quantum gates output 1. Implementation concepts and basic techniqes 1.1 Generics of quantum information processing 1.2 Realization concepts 1.3 Ion trap quantum computer – the basics 1.4 Spectroscopy in ion traps 1.5 Addressing individual ions 1.6 Basic gate operations, composite pulses Which technology ? Quantum 000 Processor 100 001 011 010 110 011 011 Cavity QED NMR superconductors quantum dots trapped ions © A. Ekert Realization concepts Quantum Information Science and Technology Roadmaps: US – http://qist.lanl.gov/ EU – http://qist.ect.it/Reports/ Ion traps Neutral atoms in traps (opt. traps, opt. lattices, microtraps) Neutral atoms and cavity QED NMR (in liquids) Superconducting qubits (charge-, flux-qubits) Solid state concepts (spin systems, quantum dots, etc.) Optical qubits and LOQC (linear optics quantum computation) Quantum Systems Electrons on L-He surfaces Spectral hole burning that can be controlled and …and more manipulated the DV criteria translated to an implementer… I. Find two-level systems, II. that can be individually controlled III. that are stable and don’t decay while you work on them IV. that interact to allow for CNOT gate operation V. that can be efficiently measured or ~100% VI. Find a way to interconnect remote qubits VII. Make sure, your interconnection is good 1. Implementation concepts and basic techniqes 1.1 Generics of quantum information processing 1.2 Realization concepts 1.3 Ion trap quantum computer – the basics 1.4 Spectroscopy in ion traps 1.5 Addressing individual ions 1.6 Basic gate operations, composite pulses Meeting the DiVincenzo criteria with trapped ions criterion physical implementation technique scalable qubits internal atomic transitions linear traps (2-level-systems) (trap arrays) initialization laser cooling, optical pumping, state preparation laser pulses long coherence times narrow transitions coherence time (optical, microwave) ~ ms - min universal quantum gates single qubit operations, Rabi oscillations two-qubit operations Cirac-Zoller CNOT qubit measurement quantum jump detection individual ion fluorescence convert qubits to coupling of ions with high CQED, bad cavity limit T flying qubits finesse cavity E faithfully transmit coupling of cavities via fiber coupling pulse T flying qubits (photonic channel) sequences (CZKM) E Quantum computation with trapped ions J. I. Cirac P. Zoller other gate proposals (and more): • Cirac & Zoller • Mølmer & Sørensen, Milburn • Jonathan & Plenio & Knight • Geometric phases • Leibfried & Wineland Quantum computation with trapped ions control bit target bit other gate proposals (and more): • Cirac & Zoller • Mølmer & Sørensen, Milburn • Jonathan & Plenio & Knight • Geometric phases • Leibfried & Wineland Quantum bits (qubits) with trapped ions Storing and keeping quantum information requires long-lived atomic states: optical transition frequencies microwave transitions (forbidden transitions, (hyperfine transitions, intercombination lines) Zeeman transitions) S – D transitions in alkaline earths: alkaline earths: Ca+, Sr+, Ba+, Ra+, (Yb+, Hg+) etc. 9Be+, 25Mg+, 43Ca+, 87Sr+, 137Ba+, 111Cd+, 171Yb+ P3/2 P1/2 D5/2 TLS S1/2 TLS S1/2 Boulder 9Be+; Michigan 111Cd+; 40 + Innsbruck Ca Innsbruck 43Ca+, Oxford 43Ca+; Maryland 171Yb+; … many more Quantum Computer with Trapped Ions J. I. Cirac, P. Zoller; Phys. Rev. Lett. 74, 4091 (1995) L Ions in linear trap quantum bits, quantum register state vector of quantum computer - narrow optical transitions - groundstate Zeeman coherences 2-qubit quantum gate laser pulses entangle pairs of ions control bit target bit needs individual addressing, efficient single qubit operations small decoherence of internal and motional states quantum computer as series of gate operations (sequence of laser pulses) 1. Implementation concepts and basic techniqes 1.1 Generics of quantum information processing 1.2 Realization concepts 1.3 Ion trap quantum computer – the basics 1.4 Spectroscopy in ion traps 1.5 Addressing individual ions 1.6 Basic gate operations, composite pulses Ion trap experiment Linear Ion Trap Linear ion trap I. Waki et al., Phys. Rev. Lett. 68, 2007 (1992) M.G. Raizen et al., Phys. Rev. A 45, 6493 (1992) - up to about 30 ions (string) - ions separated by a few µm collective quantized motion - anisotropic oscillator: νz << νx, νy - ion motion coupled by Coulomb repulsion - eigenmodes (nearly) independent of the number of ions center of mass mode breathing mode Ion strings scale favorably.... Coulomb repulsion defines a length scale Mode frequencies are nearly independent of ion number A. Steane, Appl. Phys. B 64, 623 (1997) D. James, Appl. Phys. B 66, 181 (1998) Ion strings as quantum registers 1996 – 2006 1 - 10 qubits 2007 - 2012 32 qubits 40 70 Level scheme of Ca+ qubit on narrow S - D quadrupole transition P3/2 854 nm P1/2 866 nm D5/2 393 nm 397 nm D3/2 729 nm S1/2 Spectroscopy with quantized fluorescence (quantum jumps) P D absorption and emission cause fluorescence steps monitor spectroscopy (digital quantum jump signal) S histogram of absorption events S absorptions D laser detuning State detection by quantized fluorescence 8 D state occupied S state occupied 7 s t n 6 detection efficiency: e m e 5 r 99.85% u s a 4 e m 3 f o # e 2 g 1 0 0 20 40 60 80 100 120 counts per 9 ms Laser – ion interactions ...1 An ion trapped in a harmonic potential with frequency ω interacting with the travelling wave of a single mode laser tuned close to a transition that forms an effective two-level system, is described by the Hamiltonian k, ωl, φ: wavenumber, frequency and
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