1. 1 0 Fluctuating environment -during free evolution -during driven evolution A -meter AC drive Decoherence of Josephson Qubits : G. Ithier et al.: Decoherence in a quantum bit superconducting circuit, PRB 2005 TheQuantronium 1µm box qp trap dcgatedcgate µw readoutjunction TowardsQND readout

2. DECOHERENCE DURING FREE EVOLUTION dephasing qubit relaxation noise DEPHASING

3.  Decoherence sources in the quantronium circuit 01 (GHz) NgNg  optimal point N g =1/2,  =0 no dephasing no current NgNg  nA N g drive minimum relaxation due to 

4.  Decoherence in the Quantronium a b + environment Relaxation if balanced junctions ! Pure dephasing P0P0 not necessarily exponential

5. Model for dephasing: charge and phase noise   N g ou  Spectral density (linear coupling)

6. Relaxation of the Quantronium t  P0P0 T 1 =0.5µs T 1 : 0.3-2  s

7. Free evolution coherence time T 2 : Ramsey interferences readout Free evolution (rotation also)   01  RF  Rabi  /2 pulse Projection Z Ramsey interferences reveal decoherence of free evolution during the delay

8. RF  = 16409.50 MHz Fit  = 19.84 MHz T  = 500 +/- 50 ns tt Characterizing dephasing: 1) decay of Ramsey fringes best ones:

9. typical sample Fit with the linked cluster expansion: static approximation for noise during each pulse sequence ( Makhlin Shnirman, Paladino, Falci)

10. Comparing envelope fits “static” approximation ( Makhlin Shnirman, Paladino, Falci) gaussian noise 500 ns Simple exponential

11. N g =1/2 NgNg   =0 Delay between  /2 pulses (ns) Coherence away from optimal point Ng=Ng=  P 0 : N g =1/2  =0 Ramsey oscillations time 100 ns best coherence at optimal point

12. Characterizing dephasing: 2) phase detuning pulses  /2 X t1t1 t2t2 At optimal point

13. Characterizing dephasing: 2) charge detuning pulses  /2 X

14. Characterizing decoherence: 3) resonance linewidth

15. 5) Probing the dynamics: spin echo experiments  /2 

17. Direct mapping of echo amplitude  /2   low frequency noise

18. Echo decay away from optimal point

19. Gaussian model SS  1/  4MHz S Ng  1/  0.5MHz Comparison exp vs model noise spectral densities

20. Closer look at charge and phase spectral densities: [S(  )] [  ] (Hz)  NgNg 1/f [  ] (Hz) Phase noiseCharge noise Cut-off at.5 MHz !!  Ng Partly external

21. Decoherence in phase Qubits (at UCSB)

22. Increasing I (arb. Units)  (GHz) p 1 =0 :blue p 1 =1 : red  10  21 II Level-crossings with two level systems Martinis et al (2003) spectroscopy  (GHz) p1p1 Coupling to other degrees of freedom 2 level systems couple to qubit! Oxyde? Tunnel junction? Relation to charge noise?

23. Decoherence and Materials Im{  }/Re{  } =  = 1/Q 1/2 [V] future a- Dielectric loss in x-overs Where’s the problem? TLS in tunnel barrier Two Level States (TLS) New design Theory: Martin et al Yu & UCSB group xtal Al 2 O 3 a-Al 2 O 3

24. Spectroscopy Bias current I (au) saturate IpIp IwIw meas. Microwave frequency (GHz)  10 ( I ) 26 few TLS resonances P 1 = grayscale T1 still short : 100-150 ns

25. New Qubit design 60  m SiN x capacitor (loss of SiN x limits T 1 )

26. P 1 (probability) Rabi 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 050100150200250300350400 t [ns] P |1> t Rabi (ns) Rabi oscillations

27. New junction technology ? II: Epitaxial Materials Al 2 O 3 (substrate) Al 2 O 3 Re Al LEED: Bias current I  wave freq. (GHz) Spectroscopy: epi-Re/Al 2 O 3 qubit ~30x fewer TLS defects! (NIST)

28. DECOHERENCE IN FLUX QUBITS At NEC

29. Relaxation: T 1 measurement initialization to ground state is always better than 90%  relaxation dominant  classical noise is not important at qubit frequency  ~ 4ns delay readout pulse

30. T 1 vs f  ~ 4ns delay readout pulse ??

31.  1 vs  E: Comparison of two samples sample3 sample5 Random high-frequency peaks. Broad low-frequency structure and high-frequency floor.

32.  1 vs  E (sample3) assuming flux noise positive and negative side coincide

33. Dephasing: T 2Ramsey, T 2echo measurement (sample5)   ~ 4ns t/2 readout pulse  ~2ns t/2   ~2ns t correspond to detuning readout pulse Ramsey interference spin echo

34. T2 vs f, vs Ib (sample5) f=f * I b =I b * Notice: fitted with exponential decay

35. T 1 and T 2echo at I b =I b *, f=f * (sample5) T1=545  16ns Pure dephasing from high frequency noise (>MHz) is negligible Echo decay time is limited by relaxation

36. Echo at I b =I b *, f  f * assuming 1/f flux noise do not fit does not fit

37. Exp+GaussExp Ramsey Extract flux noise

38. Ramsey signal I b =0 I b =-0.2 I b =-0.4 Also exponential decay (more or less…)

39. Estimation of I b noise amplitude Increase |I b -I b * |  Introduce I b noise coupling relaxation: dephasing: assuming ohmic noise (cf. Yu. Makhlin PRL92, 178301 (2004)) For T=0.1K, modeled environment: From the fitting:

40. 1 0 Fluctuating environment -during free evolution -during driven evolution -at readout A -meter AC drive Decoherence of a qubit:

41. Bloch-Redfield description Free Decoherence: driven evolution versus free evolution Driven at  Rabi

42. : Spin locking  /2 X aYaY Determination of T * 1

43. Decay of Rabi oscillations with Rabi frequency Determination of T * 2 :

44. T* 2 ~ 480 ns Decay of Rabi oscillations with frequency

45. decoherence in the rotating frame ? Z X Y lab frame: T2=300ns Ramsey decay: rotating frame: Z I1 * > I0 * > drive T2*=480 ns Conclusion: more robust qubit encoding in the rotating frame, but limited use.

46. NIST Chalmers NEC TU Delft CONCLUSIONS: Framework for understanding decoherence large decoherence: Coherence times up to 500 ns Microscopic decoherence sources ?? Decoherence can be fought QND readout achievable quantum computing applications presently beyond reach

47. The work on YALE SPEC I. SIDDIQI F. PIERRE E. BOAKNIN L. FRUNZIO R. VIJAY C. RIGETTI M. METCALFE M. DEVORET G. ITHIER E. COLLIN N. BOULANT D. VION P. ORFILA P. SENAT P. JOYEZ P. MEESON D. ESTEVE Karlsruhe Landau Roma A. SHNIRMAN G. SCHOEN Y. MAKHLIN F. CHIARELLO 1 0 Fluctuating environment A -meter theQuantronium 1µm box qp trap dcgatedcgate µw readoutjunction Appl. Physics SQUBIT

48. Thanks to NEC / Japan 2004

49. Towards QND readout ‘at’ optimal point flux qubit :charge qubit : SQUID inductance quantum capacitance Chalmers, Helsinki charge-phase qubit : readout junction inductance Quantum capacitance C/C J 0 1 TU DelftYale, Saclay 00 11

50. PULSE IN PULSE OUT  U “RF” pulse   dynamics in anharmonic potential more complex, but: -better fidelity ? -no reset: possibly QND  switching dc pulse simple, but: -fidelity 40% -qubit reset : NOT QND  U rf readout (M. Devoret, Yale) dc versus ac readout in the quantronium

51. M. Devoret team at Yale I. Siddiqi et al., (2004) µW Pulse IN QuBit control  00 11 OUT Towards non destructive readout at optimal point with an AC drive UJUJ optimal P 1 0 Similar dispersive methods developed for other qubits

52. M. Devoret team at Yale I. Siddiqi et al., (2004) µW Pulse IN QuBit control  00 11 OUT UJUJ optimal P 1 0 180° -180°  amplitude µW drive amplitude µW phase  State dependent bifurcation The Josephson Bifurcation Amplifier Enhanced

53. 300 K Quantronium from Yale Quantronium + JBA SETUP 4 K 0.6 K 30 mK 1.3-2 GHz M S -20dB -30dB Q 50  T N =2.5K G=40dB I LO demodulator bifurcation NO bifurcation

54.  45-50% Rabi oscillations with the JBA Contrast : 50% 100ns 125ns JBA pulse (Saclay exprt)

55. 100ns 125ns 5ns 20ns 40ns  JBA readout 10ns gate 100ns 0 1 0 1 0 1 0 1  partially QND 1 0 34% 100% 66% 0% 1 0 25% 9% 30% 36% 1 0 17% 83% 1 0 0% Notice: relaxation again partly avoidable by tuning the qubit Quantum Non Demolition ? read twice AB & correlations Note: results for flux-qubit now available

56. Dispersive readout of the flux qubit A. Lupascu et al. TU DELFT

57. Activation rates for different detuning values F = 775 MHz F res =822 MHz I ac,bifurcation 2 slope=u dyn /(kT) Thy: M. Dykman

58. Activation rates for different detuning values

59. Optimal qubit manipulation and readout 87%

60. Rabi oscillations with optimal settings Dt = length of MW pulse

61. Ramsey oscillations with optimal settings Rabi oscillation Ramsey:  ge -  mw = 69 MHz Ramsey frequency vs detuning Relatively strong low frequency fluctuations visible in the drift of the Ramsey frequency. QND data : analysis in progress

62. Depts. of Applied Physics & Physics Yale University expt. Andreas Wallraff David Schuster Luigi Frunzio Experiments in Cavity QED with Superconducting Circuits Rob Schoelkopf Funding: And discussions w/ J. Zmuidzinas & M. Devoret theory Steve Girvin Alexandre Blais Ren-Shou Huang Packard Foundation Keck Foundation Merci to D. Esteve & co. for assistance!

63. A Circuit Analog for Cavity QED 2g = vacuum Rabi freq.  = cavity decay rate  = “transverse” decay rate L = ~ 2.5 cm Cooper-pair box “atom” 10  m 10 GHz in out transmission line “cavity” Blais, Huang, Wallraff, Girvin & RS, cond-mat/0402216; to appear in PRA

64. Cavity QED with a Cooper pair box: first dispersive readout R. Schoelkopf, A. Wallraff, S. Girvin et al., Yale (2004) Dispersive readout with out of resonance photons

65. Dressed Artificial Atom: Resonant Case ? T 2g T 1 “vacuum Rabi splitting”

66. Rabi Oscillations of Qubit P rf = 0 dB P rf = +6 dB P rf = 18 dB

67. Coherence time measurements with 2 pulse Ramsey sequence