Which technology? Quantum processor. Cavity QED NMR. Superconducting qubits Quantum dots. Trapped atoms/ions. A. Ekert

Transcription

1 Which technology? Quantum processor Cavity QED NMR Superconducting qubits Quantum dots Trapped atoms/ions A. Ekert

2 Which technology? Quantum processor Cavity QED NMR Superconducting qubits Quantum dots Trapped atoms/ions A. Ekert

3 Ion trap quantum computing Trapped ions form the quantum register Trap electrodes

4 Ca+-level scheme P1/2 D5/2 qubit S1/2

5 Di Vincenzo criteria 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

6 Experimental procedure P P1/2 1/2 D D5/2 5/2 =1s SS1/21/2 40 Ca Initialization Initialization in in aa pure pure quantum quantum state state

7 Experimental procedure P1/2 D5/2 Quantum state manipulation S1/ Initialization Initialization in in aa pure pure quantum quantum state state 2.2.Quantum Quantumstate statemanipulation manipulationon on SS1/21/2 DD5/25/2transition transition

8 Experimental procedure P P1/2 1/2 D D5/2 5/2 =1s Fluorescence detection 40 SS1/21/2 Ca+ 1. Initialization in a pure quantum state 2. Quantum state manipulation on S1/2 D5/2 transition 3. Quantum state measurement by fluorescence detection

9 Experimental procedure P P1/2 1/2 D D5/2 5/2 =1s Fluorescence detection 40 SS1/21/2 Two ions: Spatially resolved detection with CCD camera Ca+ 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 µm 50 experiments / s Repeat experiments times

10 Rabi oscillations D-state population P1/2 D5/2 S1/2

11 Rabi oscillations D-state population P1/2 D5/2 S1/2

12 Rabi oscillations D-state population P1/2 D5/2 S1/2

13 The phase iωt +e = =

14 The phase iωt +e = =

15 The phase...

16 The phase...

17 Addressing single qubits coherent manipulation of qubits Paul trap Excitation electrooptic deflector Dichroitic beamsplitter Fluorescence detection CCD Deflector Voltage (V) inter ion distance: ~ 4 µm - addressing waist: ~ 2 µm < 0.1% intensity on neighbouring ions

18 Having the qubits interact The common motion acts as the quantum bus. 50 µm

19 Ion motion harmonic trap

20 Ion motion harmonic trap 2-level-atom joint energy levels

21 Ion motion carrier carrier and sideband Rabi oscillations with Rabi frequencies Lamb-Dicke parameter

22 Generation of Bell states

23 Generation of Bell states

24 /2 Generation of Bell states

25 Generation of Bell states

26 Generation of Bell states Bell Bellstates stateswith withatoms atoms Be Be+:: NIST NIST(fidelity: (fidelity:97 97%) %) Ca Ca+:: Oxford Oxford(99.6 (99.6%) %) Cd Cd+::Ann AnnArbor Arbor(79%) (79%) Yb: Yb:Maryland Maryland(96%) (96%) Mg Mg+::Munich Munich(97%) (97%) Ca Ca+:: Innsbruck Innsbruck(99.3%) (99.3%)

27 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

28 Measuring a density matrix A measurement yields the z-component of the Bloch vector => Diagonal of the density matrix

29 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.

30 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

31 Bell states SS SD DS DD SS SD DS DD DD DS SD SS SS SD DS DD DD DS DD DS SD SS SD SS

32 Generalized Bell states

33 Generalized Bell states Genuine 8-particle entanglement measurements ~ 10 h measurement time Häffner et al., Nature 438, 643 (2005)

34 Universal set of quantum gates

35 Having the qubits interact...allows the realization of a universal quantum computer! control control target target

36 Having the qubits interact...allows the realization of a universal quantum computer! control control target 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)). - Mølmer-Sørensen gate (Sackett et al., Nature 404, 256 (2000)).

37 Mølmer-Sørensen gate creates entangled states Raman transitions between Interaction of two ions via common motion. n=1 n=0

38 Mølmer-Sørensen gate creates entangled states Raman transitions between Interaction of two ions via common motion.

39 Mølmer-Sørensen gate creates entangled states Raman transitions between Interaction of two ions via common motion.

40 Entangling ions entangled? J. Benhelm et al., Nature Physics 4, 463 (2008) Theory: C. Roos, NJP 10, (2008)

41 Entangling ions entangled measure entanglement via parity oscillations gate duration 51 s average fidelity: 99.3 (2) %

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43 Achieved times scales for ion trap QIP 10-5 s 10-4 s Operations 10-6 s 10-3 s Fast universal gate Single qubit gates, fidelities Universal gate, fidelity Initialization / Read-out, fidelity 10-2 s 10-1 s 101 s 102 s 103 s Coherence 100 s Single qubit coherence of magnetic field sensitive states Decoherence-free subspace / magnetic field insensitive Well-choosen qubit

44 The DiVincenczo criteria for quantum computing 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

45 The DiVincenczo criteria for quantum computing I. Scalable physical system, well characterized qubits II. Ability to initialize the state of the qubits with sufficient fidelity III. Long relevant coherence times, much longer than gate operation time IV. Universal set of quantum gates with sufficient fidelity V. Qubit-specific measurement capability with sufficient fidelity need to beat the fault-tolerant threshold

46 Quantum error correction Repeatable quantum error correction: P. Schindler et al, Science 332, 1059 (2011)

47 Consequences for QEC P. Schindler et al, Science (2011)

48 Quantum error correction Threshold for quantum computing: 99.99% fidelity / operation Status of ion-trap QIP: - Initialization / Read-out: 99.5% 99.99% - Single qubit gates: 99% % - Universal gate: 99.9% Repeatable quantum error correction: P. Schindler et al, Science 332, 1059 (2011)

49 The DiVincenczo criteria for quantum computing I. Scalable physical system, well characterized qubits II. Ability to initialize the state of the qubits with sufficient fidelity III. Long relevant coherence times, much longer than gate operation time IV. Universal set of quantum gates with sufficient fidelity V. Qubit-specific measurement capability with sufficient fidelity

50 The DiVincenczo criteria for quantum computing I. Scalable physical system, well characterized qubits II. Ability to initialize the state of the qubits with sufficient fidelity III. Long relevant coherence times, much longer than gate operation time IV. Universal set of quantum gates with sufficient fidelity V. Qubit-specific measurement capability with sufficient fidelity

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52 Scaling of ion trap quantum computers Kielpinski, Monroe, Wineland Cirac, Zoller, Kimble, Mabuchi Zoller, Tian, Blatt

53 Scaling of ion trap quantum computers Kielpinski, Monroe, Wineland

54 Scaling of ion trap quantum computers D. Leibfried, D. Wineland et al., NIST

55 Scaling of ion trap quantum computers D. Leibfried, D. Wineland et al., NIST

56 Segmented ion traps as scalable trap architecture (ideas pioneered by D. Wineland, NIST) Segmented trap electrode allow to transport ions and to split ion strings State of the art: Transport of ions Splitting of two-ion crystal 1 mm within 50 µs tseparation 200 µs no motional heating small heating n 1 Architecture for a large-scale ion-trap quantum computer, D. Kielpinski et al, Nature 417, 709 (2002) Transport of quantum states, M. Rowe et al, quant-ph/

57 Scaling of ion trap quantum computers D. Leibfried

58 Scaling of ion trap quantum computers

59 Scaling of ion trap quantum computers

60 Scaling of ion trap quantum computers

61 Scaling of ion trap quantum computers Architecture for a large-scale ion-trap quantum computer, D. Kielpinski et al., Nature 417, 709 (2002).

62 Coherent transport through a junction NIST: Blakestad, et al., High fidelity transport of trapped-ion qubits through an X-junction trap array, arxiv: v1

63 Surface traps V8 5 V3 V1 V2 VR F sin(ωr Ft) V1 V9 V10 V4 V11 V5 V12 V6 V13 V7 V14 0 V Current VR F parameters: 0V VR F Ion height 220 μm ΩRF 2 15 MHz VRF 100 V VDC < 10 V ωh MHz ωv MHz ωa khz 0V

64 Surface traps NIST: Amini, et al., Scalable ion traps for quantum information processing. arxiv: v1

65 Surface traps Need to split and merge ion strings fast for multi-qubit gates. Wineland (1998) NIST: Amini, et al., Scalable ion traps for quantum information processing. arxiv: v1

66 Entangling ions

67 Motional decoherence d~100 m

68 Motional decoherence

69 Motional decoherence From: Labaziewicz et al., PR 100, (2008

70 Excessive heating in ion traps Scaled electric field noise SE ( (V/m)2 ) From: Expected Johnson noise Fault tolerant Ion electrode distance ( m)

71 What is causing the anomalous heating? - fluctuating patch potentials, ad-atom diffusion (Wineland 1998) - independently fluctuating dipoles (Daniilidis 2010) - fluctuating strength of dipoles (Safavi-Naini 2011) - all of the above and probably something else

72 Copper on Aluminum trap 20 nm Cu 1 m Al

73 Monitoring the cleaning

74 Scaled electric field noise SE ( (V/m)2 ) Excessive heating in ion traps Hite et al. UC Berkeley Required for fault tolerancy Ion electrode distance ( m)

75 More material: Review on "Quantum computing with trapped ions", H. Häffner, C. F. Roos, R. Blatt, Physics Reports 469, 155 (2008), Most recent progress: NIST, Boulder Innsbruck University of Maryland:

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