Kenneth Brown, Georgia Tech

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1 Kenneth Brown, Georgia Tech

2 Choice of Bits 100 BC 1949 AD 1949 AD 1822 (1991) AD 2013 AD

3 Hearing Aid Images from

4 Choices of Qubits Waterloo Bristol Wisconsin NMR Photons Neutral Atoms Quantum Dots Harvard Sandia/GT Atomic Ions Yale Superconducting Qubits

5 Quantum computer requirements Quantum bits or qubits Carriers of quantum information One qubit gates Manipulate single qubits Two qubit gates Conditional operations Measurement Scalability Connecting many qubits

6 Ion Trap Quantum Computers Qubits Internal states One qubit gates Lasers/ Microwaves Two qubit gates Lasers / Microwaves + Coulomb repulsion Measurement Fluorescence Scalability Segmented Ion Traps Photonic Interconnects D. Kielpinksi, C. Monroe, D.Wineland Nature 417, 709 (2002) C. Monroe et al. Phys. Rev. A 89, (2014)

7 Ion Trap Articles to Start Scaling the ion trap quantum processor Monroe and Kim, Science 339, 1164 (2013) Entangling states of trapped atomic ions Blatt and Wineland, Nature 453, 1008 (2008) Quantum computing with trapped ions Häffner, Roos, and Blatt arxiv: Experimental issues in coherent quantum-state manipulation of trapped atomic ions Wineland et al quant-ph/

Wineland and NIST Ion Storage Nobel Prize 2012 Laser cooled ions: 1978 State prep: 1980 State measurement: 1986 Coulomb crystals: 1987 Ground state cooling: 1989 Ion-phonon entanglement:1995 Two ion

8 Wineland and NIST Ion Storage Nobel Prize 2012 Laser cooled ions: 1978 State prep: 1980 State measurement: 1986 Coulomb crystals: 1987 Ground state cooling: 1989 Ion-phonon entanglement:1995 Two ion entanglement:1998 Four ion entanglement: 2000 Decoherence free subspace: 2001 Shuttling architecture: 2002 Geometric phase gate: 2003 Classical error code: 2004 Surface electrode traps: 2005 Two-qubit microwave gate: 2011 Fast ion transport: 2012 Much more..

9 7 qubit quantum error correction code Nigg et al. Science (2014) Blatt, Innsbruck

10 Quantum Simulation / Emulation Nature Commun. (2011) Monroe, Maryland

Ion Trap Quantum Computers Qubits Internal states One qubit gates Lasers/ Microwaves Two qubit gates Lasers / Microwaves + Coulomb repulsion Measurement

11 Ion Trap Quantum Computers Qubits Internal states One qubit gates Lasers/ Microwaves Two qubit gates Lasers / Microwaves + Coulomb repulsion Measurement Fluorescence Scalability Segmented Ion Traps Photonic Interconnects D. Kielpinksi, C. Monroe, D.Wineland Nature 417, 709 (2002) C. Monroe et al. Phys. Rev. A 89, (2014)

Laser-cooled ions P 1/2 Ca + 397 nm 866 nm S 1/2 D 3/2 P 1/2 Yb+ [3/2] 1/2 935 nm 370 nm D 3/2 S 1/2

12 Laser-cooled ions P 1/2 Ca nm 866 nm S 1/2 D 3/2 P 1/2 Yb+ [3/2] 1/2 935 nm 370 nm D 3/2 S 1/2 Continually scatter 10 7 photons/sec Easy to measure Ions crystallize and become localized 20 m 40 Ca + 50 m 172 Yb +

13 Internal States ħ Optical Qubit Quadrupole transition (400 THz) Excited state lifetime ~ 1s Magnetic field sensitivity ~B Zeeman Qubit Electron spin Microwave transition ( MHz) Magnetic field sensitivity ~B Hyperfine qubit Nuclear spin (10 GHz) Magnetic field sensitivity ~B 2

14 Measurement (electron shelving) Optical qubit Hyperfine qubit P 1/2 1 D 5/2 S 1/ state decays in 1 s Cycling transition scatters 1 photon every 10 ns 0 0 Off-resonant scattering 0

15 Determine the State Simple Method Turn on detection laser Count photons Set threshold

16 Determine the State Better Method Turn on detection laser Measure two photons and note their arrival time Based on arrival times make a decision Photons must arrive before some threshold time or the ion is declared dark Myerson et al. PRL 100, (2008)

17 Control by resonant excitation 1 ħ 0 ħ ħ l 0 Two-level system interacting with an oscillating field H=1/2 [ - 0 Z exp[-i( l t+ )] + H.c. )]

19 Control by resonant excitation 1 ħ 0 ħ ħ l 0 Two-level system interacting with an oscillating field H=1/2 [ - 0 Z exp[-i( l t+ )] + H.c. )] Switch to the interaction picture l 0 H I =1/2 [ Z + cos( )X-sin( )Y)]

20 Control errors Errors in Power fluctuations Pointing instability Polarization oscillations Errors in l 0 Frequency instability of laser Fluctuating magnetic fields Errors in ħ 0 ħ ħ l Experimental time relative to local oscillator 1 0

21 Internal States Optical vs Hyperfine Qubit Benhelm et al., Phys. Rev. A 79, (2009) For hyperfine qubits driven by Raman beams, leakage errors and qubit state errors are intrinsically the same order of magnitude. At present errors are due to technical noise and leakage errors are not a major contributor to the error.

22 Single qubit gates are really good Error =10-6 Harty et al. Phys. Rev. Lett. 113, (2014) Oxford

23 Two qubit gates Goal: Ion-Ion entanglement Ion Phonon Entanglement Cirac-Zoller (PRL 1995) Sorensen-Molmer (PRL 1999) Ion Photon Entanglement Follows atom ensemble-photon entanglement Can be used in quantum network schemes e.g. DLCZ (Nature 2001) Direct Ion-Ion Entanglement Electron dipole electron dipole interaction Ozeri group: Kotler et al. Nature (2014)

24 Ion position Two-level system interacting with an oscillating field with spatial dependence H=1/2 [ - 0 Z exp[-i( l t-kx+ )] + H.c. )]

27 Zeeman Spectroscopy 397 nm 866 nm 729 nm

28 Zeeman Spectroscopy

29 Normal Modes of Two Ions Axial modes M 1 /M 2 Axial frequency of M 1 M. Drewsen et al. PRL (2004).

30 Two Calcium Ions S 1/2 -D 5/2 Measure peaks by electron shelving technique

31 Sideband Cooling P 3/2 m = -3/2 n -1 e 854 nm n n -1 D 5/2 m = -5/2 g S 1/2 m = -1/2 n n nm Cooling detected by sideband asymmetry RSB=k<n> BSB=k<n+1>

32 Load, cool, pump, cool, measure

33 Ground state cooling <n>=0.06 <n>=0.09 Axial motion of ion cooled from 1 mk to <20 K. in-phase: <n>=0.09 and out-of-phase: <n>=0.06 R.Rugango et al. New J. Phys., 17, (2015) One mode: G. Poulsen, Aarhus University PhD Thesis (2011). MgH + : Y. Wan et al. Phys. Rev. A 91, (2015)

34 Quantum Bus b red sideband on b red sideband on b b red sideband on b red sideband on b b b

35 Quantum Logic Gates Cirac-Zoller Requires ground state cooling Excites a phonon Mølmer-Sørensen Does not require ground state cooling Virtually excites phonons Geometric phase gate, etc. Generates phases by creating closed loops in the phase space of the external degrees of freedom whose sign depends on the internal states

36 Mølmer-Sørensen n b ( ) n b n b n+1 b n b n-1 b n+1 b n b n-1 b n b Detuned from red sideband on ion 1: Nothing excited Detuned from blue sideband on ion 2: Two-photon excitation Two paths cancel the error

37 Can apply to many ions Application of the bichromatic lasers to multiple ions can yield many entangled states. For the correct time, equivalent to doing a CZ gate between all ions at once T. Monz et al. Phys. Rev. Lett. 106, (2011)

38 7 qubit quantum error correction code Nigg et al. Science (2014) Blatt, Innsbruck

39 Geometric phase gate Consider a state-dependent optical force Tuned near a stretch mode, only the ions pushed in opposite directions will move. A phase is acquired equivalent to the area. Leibfried et al. Nature 422, 412 (2003)

40 QHO part 2

41 State dependent displacement

42 Mølmer-Sørensen

43 More than one mode Kim et al. Nature 465, 590 (2010) 2 ion: Friedenauer et al. Nature Phys. 4, 757 (2008)

44 Many ions, many modes 200 ions Britton et al. Nature 484, 489 (2012)

45 Photon generated entanglement Olmschenk et al. Science (2009)

46 How it works

48 Junctions and interaction zones D. Kielpinksi, C. Monroe, D. Wineland Nature 417, 709 (2002) N. Nickerson, J. Fitzsimons, S. Benjamin Phys. Rev. X 4, (2014)

ground RF RF RF DC ground ground Stability condition V rf / (r

50 Ion Trap Ions are trapped in an oscillating quadrupole field Ion stability is based on charge to mass ratio DC ground ground RF RF RF DC ground ground Stability condition V rf / (r 02 rf2 )] <1 J. Chiaverini et al., Quant. Inf. and Comp. 4, 419 (2005)

51 51 Movie: GTRI

53 Junctions and interaction zones D.Kielpinksi, C.Monroe, D.Wineland Nature 417, 709 (2002) N. Nickerson, J. Fitzsimons, S. Benjamin Phys. Rev. X 4, (2014)

54 Surface Electrode Trap Electrodes are printed onto a surface using layers of metal and SiO 2 GTRI X Trap K.Wright et al. New J. Phys (2013) Images courtesy of Quantum Information Systems group at GTRI. quantum.gatech.edu

55 Surface Electrode Trap Sandia Y Trap Sandia Y Trap Grahame Vittorini and Gang Shu Trap fabricated by Sandia National Labs Microsystems Center. Trap details: D. Moehring et al. New J.Phys. 13, (2011)

56 Surface noise Distance (micrometers) Spectral density x trap frequency

100, 013001 (2012) Distance (micrometers) + Labaziewicz et al.

57 Solutions: Freeze or Clean Spectral density x trap frequency Cleaning Cooling Hite et al. Phys. Rev. Lett. 100, (2012) Distance (micrometers) + Labaziewicz et al. Phys. Rev. Lett. 100, (2008) x Labaziewicz et al. Phys. Rev. Lett. 101, (2008)

58 Sideband Measurement P 3/2 854 nm P 1/2 D 5/2 866 nm 397 nm 729 nm D 3/2 S 1/2 Simple temperature measurement RSB=k<n> BSB=k<n+1> Transition linewidth < trap frequency G.Vittorini et al. Rev. Sci. Inst. 84, (2013)

59 Linear motion /7 /5 Round trip: m Fast transport: NIST, Mainz

60 Heating through junction Sampling rate = 700 khz Sampling rate = 350 khz G. Shu, G.Vittorini, et al. Phys. Rev. A 89, (2014)

61 Mirror Trap (with GTRI) J.T. Merrill, Curtis Volin, et al., New J. Phys. 13, (2011)

62 Mirror Trap 1.9 x improvement in light collection

63 171 Yb + Hyperfine Qubit (w/gtri) C. Shappert, J.T. Merrill, et al., New J. Phys. 15, (2013) Collaboration with GTRI

64 171 Yb + Hyperfine Qubit 171 Yb + F=1 M F =-1 M F =+1 M F = GHz ~5% variation F=0 M F =0 Fraction population in F=1

65 Broadband pulse sequences Variation across trap Fractional error We can increase uniformity over the length of the trap using multi-pulse sequences

66 Correcting for the 5% variation C. Shappert, J.T. Merrill, et al., New J. Phys. 15, (2013)

67 Two-qubit microwave gates Magnetic field gradient required to compensate for weak electric field gradient of microwaves. At NIST accomplished by oscillating magnetic field gradient. Ospelkaus et al. Nature 2011 Warring et al. PRA (2013)

68 Two-qubit microwave gates Magnetic field gradient required to compensate for weak electric field gradient of microwaves. Static magnetic field gradient also works. Sussex Wunderlich, U. Siegen Hensinger, U. Sussex

69 Components Trap development community: NIST, MIT, Mainz, Berkeley, Oxford, Sussex, Osaka, Griffiths, Innsbruck, Lincoln Lab, GTRI, Sandia, Honeywell,.

70 Ion Traps with Photons Computational Qubit Photon-Coupled C. Monroe et al. Phys. Rev. A 89, (2014)

71 PhD students Dr. Craig Clark Dr. James Goeders Dr. True Merrill Dr. Grahame Vittorini Dr. Yu Tomita Dr. Ncamiso Khanyile Dr. Chingiz Kabytayev Mauricio Gutierrez Rene Rugango Colin Trout Smitha Janardan Aaron Calvin Harrison Ansley Postdocs Dr. Gang Shu Dr. Kisra Egodapitiya Cold Molecular Ions Ion Trap Quantum Computing Quantum Control and Error Correction Funding IARPA/ARO MQCO ARO MURI ARO Physics NSF PIF NSF AMOP AvHumboldt

Different ion-qubit choises. - One electron in the valence shell; Alkali like 2 S 1/2 ground state.

Different ion-qubit choises. - One electron in the valence shell; Alkali like 2 S 1/2 ground state. Different ion-qubit choises - One electron in the valence shell; Alkali like 2 S 1/2 ground state. Electronic levels Structure n 2 P 3/2 n 2 P n 2 P 1/2 w/o D Be + Mg + Zn + Cd + 313 nm 280 nm 206 nm 226