Quantum computing with trapped ions Hartmut H ffner Institute for Quantum Optics and Quantum Information Innsbruck Austria Basics of ion trap quantum computing Measuring a density matrix Quantum gates Deutsch Algorithm FWF SFB SCALA QGATES Industrie Tirol IQI GmbH Berkeley Nov 25th 2008 Which technology 000 001 010 011 Quantum processor 100 011 110 011 Cavity QED NMR Superconducting qubits Quantum dots Trapped ions A Ekert Which technology 000 001 010 011 Quantum processor 100 011 110 011 Cavity QED NMR Superconducting qubits Quantum dots Trapped ions A Ekert Why trapped ions Good things about ion traps Ions are excellent quantum memories single qubit coherence times 10 minutes have been demonstrated Boulder 1991 Ions can be controlled very well Many ideas to scale ion traps Bad things about ion traps Slow 1 MHz Technically demanding The hardware P1 2 D5 2 Qubit S1 2 Innsbruck quantum processor Trapped ions form the quantum register Trap electrodes DiVincenzo criteria Scalable physical system well characterized qubits Ability to initialize the state of the qubits Long relevant coherence times much longer than gate operation time Universal set of quantum gates Qubit specific measurement capability Experimental procedure P1 2 1 Initialization in a pure quantum state D5 2 1s SS1 21 2 40 Ca Experimental procedure P1 2 1 Initialization in a pure quantum state D5 2 Doppler cooling SS1 21 2 1s Sideband cooling 40 Ca Experimental procedure P1 2 D5 2 Quantum state manipulation S1 2 1 Initialization in a pure quantum state 2 Quantum state manipulation on S1 2 D5 2 transition Experimental procedure P1 2 D5 2 1s Quantum state Doppler Fluorescence manipulationdetectionSideband cooling cooling 40 Ca SS1 21 2 1 Initialization in a pure quantum state 2 Quantum state manipulation on S1 2 D5 2 transition 3 Quantum state measurement by fluorescence detection Experimental procedure P1 2 D5 2 1s Quantum state Doppler Fluorescence manipulationdetectionSideband cooling cooling 40 Ca SS1 21 2 Two ions Spatially resolved detection with CCD camera 1 Initialization in a pure quantum state 2 Quantum state manipulation on S1 2 D5 2 transition 3 Quantum state measurement by fluorescence detection 5 m 50 experiments s Repeat experiments 100 200 times Rabi oscillations D state population P1 2 D5 2 S1 2 Rabi oscillations D state population P1 2 D5 2 S1 2 Rabi oscillations D state population P1 2 D5 2 S1 2 The phase t e The phase The phase Addressing single qubits coherent manipulation of qubits Paul trap 0 8 0 7 0 6 Excitation electrooptic deflector 0 5 0 4 0 3 0 2 0 1 0 10 dichroic beamsplitter Fluorescence detection CCD 8 6 4 2 0 2 4 6 8 10 Deflector Voltage V inter ion distance 4 m addressing waist 2 m 0 1 intensity on neighbouring ions Decoherence mechanisms Memory errors Bit flips Dephasing Operationial errors technical imperfections Dephasing of qubits Ramsey Experiment 2 Ramsey Time 15 9 ms 2 Zeeman shift Realized time scales 10 6 s 10 s 5 10 4 s 10 s 3 10 2 s 10 1 s 100 s 101 s 102 s 103 s Single qubit gates Two qubit gates Geometric phase gates Two qubit gates Cirac Zoller approach Single qubit coherence magnetic field sensitive Coherence of the motion Long lived qubits Raman transitions Excited state Ground state qubit Long lived qubits Raman transitions Excited state Ground state Long lived qubits Level scheme of 9Be From C Langer et al PRL 95 060502 2005 NIST Long lived qubits From C Langer et al PRL 95 060502 2005 NIST Realized time scales 10 6 s 10 s 5 10 4 s 10 s 3 10 2 s 10 1 s Single qubit gates Two qubit gates Geometric phase gates Two qubit gates Cirac Zoller approach Single qubit coherence magnetic field sensitive Coherence of the motion 100 s 101 s Single qubit coherence magnetic field insensitive 102 s 103 s Single qubit coherence magnetic field insensitive RF drive Having the qubits interact The common motion acts as the quantum bus Having the qubits interact The common motion acts as the quantum bus 50 m Ion motion harmonic trap Ion motion harmonic trap 2 level atom joint energy levels Coherent manipulation carrier carrier and sideband Rabi oscillations with Rabi frequencies Lamb Dicke parameter Introduction to quantum information Entangled states Teleportation Scaling of ion trap quantum computers Wiring up trapped ions Generation of Bell states Generation of Bell states 2 Generation of Bell states Generation of Bell states Generation of Bell states Bell states with atoms 9Be NIST fidelity 97 40Ca Oxford 83 111Cd Ann Arbor 79 25Mg Munich 40Ca Innsbruck 99 Analysis of Bell states Fluorescence detection with CCD camera Coherent superposition or incoherent mixture What is the relative phase of the superposition Measurement of the density matrix SS SD DS DD SDSS DDDS Measuring a density matrix A measurement yields the z component of the Bloch vector Diagonal of the density matrix Measuring a density matrix A measurement yields the z component of the Bloch vector Diagonal of the density matrix Rotation around the x or the y axis prior to the measurement yields the phase information of the qubit Measuring a density matrix A measurement yields the z component of the Bloch vector Diagonal of the density matrix Rotation around the x or the y axis prior to the measurement yields the phase information of the qubit coherences of the density matrix Decoherence properties of qubits SS SD DS DD SS SD DS DD DD DS SD SS SS SD DS DD DD DS DD DS SD SS SD SS A real thought experiment Measurement of the center ion Bell state survives Roos et al Science 304 1478 2004 Generalized Bell states Generalized Bell states Genuine 8 particle entanglement 656100 measurements 10 h measurement time H ffner et al Nature 438 643 2005 Quantum gates Having the qubits interact allows the realization of a universal quantum computer control target Having the qubits interact allows the realization of a universal quantum computer control target Most popular gates Cirac Zoller gate Schmidt Kaler et al Nature 422 408 2003 Geometric phase gate Leibfried et al Nature 422 412 2003 M lmer S rensen gate Sackett et al Nature 404 256 2000 A controlled NOT operation Target bit Control bit Target A controlled NOT operation Ion 1 Vibration Ion 2 Control qubit SWAP SWAP 1 Target qubit A controlled NOT operation Ion 1 Vibration Control qubit SWAP SWAP 1 Target qubit Ion 2 Pulse sequence Ion 1 Ion 2 Laser frequency Pulse length Optical phase Composite phase gate 2 rotation 1 2 3 4 Action on S 1 D 2 2 4 3 1 Single ion composite phase gate 0 0
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