Fluctuating environment

1. Fluctuating environment 1 0 AC drive Decoherence of a qubit: -during free evolution -during driven evolution -at readout A -meter Daniel ESTEVE of Michel DEVORET SPEC YALE

2. qubit relaxation noise DECOHERENCE DURING FREE EVOLUTION dephasing DEPHASING

3. 2 knobs : U 2 energies: F Statedependent persistent currents i The quantronium: 1) a split Cooper pair box 1 d° of freedom

4. hn01 readout + environment weaker dephasing at optimal point 2) protected from dephasing energy (kBK) n01(GHz) d/2p d/2p Ng Ng EJ=0.86 kBK EC=0.68 kBK

5. Readout of persistent currents with dc switching 1: switching 1 0: no switching 0 discrimination 3) with a readout junction d/2p Ng

6. Qubit control: Rabi precession switching probability (%) Rabi oscillations c Y Effective field X nµw rotation wRabi = aURF

7. Readout fidelity ? 40% contrast (only)

8. Qubit manipulation   Z Y X arbitrary transformations adiabatic frequency pulses for Z rotations robust transformations Composite ‘  p  ’  CORPSE  : 60°X 300°-X 420 X° ‘  p  ’   CORPSE Single pulse

9. n01(GHz) optimal point Ng=1/2 , d=0 Ng drive d/2p d Ng no dephasing no current nA minimum relaxation due to d Ng Decoherence sources in the quantronium circuit d

10. a + environment Pure dephasing b not necessarily exponential Decoherence in the Quantronium d Relaxation P0 if balanced junction !

11. Model for dephasing: charge and phase noise d DNg ou Dd (linear coupling) Spectral density

12. p t Relaxation of the Quantronium P0 T1=0.5µs T1: 0.3-2 ms

13. wRabi wRabi w=w01-wRF Projection Z readout p/2 pulse p/2 pulse Free evolution (rotation also) Ramsey interferences Ramsey interferences reveal decoherence of free evolution during the delay

14. Characterizing dephasing: 1) decay of Ramsey fringes Dt Fit Dn = 19.84 MHz T2 = 500 +/- 50 ns best ones: nRF= 16409.50 MHz

15. typical sample Fit with the linked cluster expansion: static approximation ( Makhlin Shnirman, Paladino, Falci)

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

17. n01(GHz) d/2p Nc away from optimal point Coherence time 0.028 0.028 0.028

18. p/2X p/2X Characterizing dephasing: 2a) phase detuning pulses Dt1 p/2X p/2X Dt2

19. Characterizing decoherence: 3) resonance linewidth

20. p p/2 p/2 5) Probing the dynamics: spin echo experiments

21. p/2 p/2 p p/2 p/2 p/2 p/2 p Direct mapping of echo amplitude low frequency noise

22. Echo decay away from optimal point

23. Comparison exp vs model noise spectral densities Sd SNg Gaussian model 1/w 1/w w w 4MHz 0.5MHz non gaussian character of noise ?? Conclusion: decay times ok, not time dependence See G. Ithier et al.: Decoherence in a quantum bit Superconducting circuit circuit, preprint

24. d Ng Ng d [S(w)] 1/f 1/f [w] (Hz) [w] (Hz) Closer look at charge and phase spectral densities: Phase noise Charge noise Partly external Cut-off at .5 MHz

25. Driven at wRabi Decoherence: driven evolution versus free evolution Bloch-Redfield description Free See preprint on decoherence G. Ithier et al.

26. p/2X p/2X p/2X p/2X aY : Spin locking Determination of T*1

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

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

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

30. Fluctuating environment 1 0 Decoherence at readout: projection fidelity ? ideal QND readout: Readout: 1 Readout: 0 errors: wrong answer + projection error A -meter

31. U d Decoherence :dc versus rf readout dc readout V resets the qubit dc pulse  switching • simple, but: • rep rate limited by quasiparticles • qubit reset : NOT QND

32. U d Decoherence :dc versus rf readout PULSE IN rf readout (M. Devoret, Yale) PULSE OUT U d “RF” pulse dc pulse  switching  ddynamics in anharmonic potential • simple, but: • -fidelity 40% • qubit reset : NOT QND more complex, but: -better fidelity ? -no reset: possibly QND

33. Phase oscillations in a state dependent anharmonic potential Drive Ui I0 C g d V Ur Vg Output LC oscillator GUr 180° -180° 1.5 Frequency (GHz) (I. Siddiqi et al., PRL 93, 207002 (2004)) Qubit control port The Josephson Bifurcation Amplifier : latching OSCILLATION AMPLITUDE MICROWAVE DRIVE AMPLITUDE

34. Microwave readout setup MicroWave Generator RFin LO V demodulator 300 K S G=40dB M Pulsing I Q Vg TN=2.5K G=40dB -20dB 4 K -20dB LP 3.3GHz -30dB -30dB 600 mK 1 kW 4 kW 20 mK HP 1.3GHz LP 2GHz Directionnal coupler 50 W 50 W Sample from Yale

35. tin>150ns 100ns frequency: 1.4GHz Rabi oscillations 5ns Readout contrast? Bifurcation probability P Pulse duration (ns) Microwave power (dBm, top) (best dc switching: 60%) Readout : 50% contrast (Yale: 60%)

36. QND readout ? ppulse on qubit nopulse on qubit Readout 1 Readout 1 Readout 2 OR analysis yields for a single readout: Answer 1 Answer 0 Answer 1 Answer 1 Answer 0 Answer 0 partially QND (Yale & Saclay)

37. QND readout with an ac drive at optimal point ? flux qubit charge qubit quantronium SQUID inductance box capacitance JBA TU Delft, Helsinki (for SSET) Yale Saclay partially QND (in progress) Chalmers Readout fidelity & QND readout are (still) issues

38. Fluctuating environment 1 0 This work on : the Quantronium dc gate dc gate µw qp box trap A -meter readout junction 1µm SPEC Appl. Physics YALE I. SIDDIQI F. PIERRE E. BOAKNIN L. FRUNZIO G. ITHIER E. COLLIN P. ORFILA P. SENAT P. JOYEZ D. VION P. MEESON D. ESTEVE A. SHNIRMAN G. SCHOEN Y. MAKHLIN F. CHIARELLO R. VIJAY C. RIGETTI M. METCALFE M. DEVORET Karlsruhe Landau Roma remind: 10-4 error rate on qubit gates…, QND useful but not mandatory

39. Yale quantronium sample 2mm

40. Qubit in ground state

41. Quantum Non-Demolition Fraction  pulse Readout 1 (R1) Readout 2 (R2) 5ns 100ns 20ns 125ns 20ns 30ns Ps(R1) Ps(R2) Ps(R1R2) Ps(R2/R1) 17.6% 13.3% 3.3% 18.8% no  pulse  pulse 61.3% 28.0% 19.1% 31.1% T1=1.3 s QND Frac. 