Decoherence of a qubit during free evolution during

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

DECOHERENCE DURING FREE EVOLUTION qubit relaxation dephasing DEPHASING noise

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

hn 01(GHz) energy (k. BK) 2) protected from dephasing d/2 p Ng Ng EJ=0. 86 k. BK EC=0. 68 k. BK readout + environment weaker dephasing at optimal point

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

Qubit control: Rabi precession switching probability (%) c Y Effective field X nµw rotation w. Rabi = a. URF Rabi oscillations

Readout fidelity ? 40% contrast (only)

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

Decoherence sources in the quantronium circuit d Ng drive d n. A Ng minimum relaxation due to d no dephasing no current n 01(GHz) optimal point Ng=1/2 , d=0 d/2 p Ng

Decoherence in the Quantronium d a + b environment Pure dephasing Relaxation P 0 if balanced junction ! not necessarily exponential

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

Relaxation of the Quantronium p t P 0 T 1=0. 5µs T 1: 0. 3 -2 ms

Ramsey interferences w. Rabi w =w 01 -w. RF p/2 pulse w. Rabi Free evolution (rotation also) p/2 pulse Ramsey interferences reveal decoherence of free evolution during the delay Projection Z readout

Characterizing dephasing: 1) decay of Ramsey fringes best ones: Dt n. RF = 16409. 50 MHz Fit Dn = 19. 84 MHz T 2 = 500 +/- 50 ns

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

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

n 01(GHz) Coherence time d/2 p Nc 0. 028 away from optimal point

Characterizing dephasing: 2 a) phase detuning pulses p/2 X Dt 1 p/2 X Dt 2

Characterizing decoherence: 3) resonance linewidth

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

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

Echo decay away from optimal point

Comparison exp vs model noise spectral densities Sd Gaussian model SNg 1/w w 4 MHz Conclusion: decay times ok, not time dependence w 0. 5 MHz non gaussian character of noise ? ? See G. Ithier et al. : Decoherence in a quantum bit Superconducting circuit, preprint

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

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

Determination of T*1 : Spin locking p/2 X a. Y p/2 X

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

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

decoherence in the rotating frame ? lab frame: Z Ramsey decay: Y T 2=300 ns X rotating frame: Z I 1*> *> I 0 drive Conclusion: more robust qubit encoding in the rotating frame T 2*=480 ns

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

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

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

Phase oscillations in a state dependent anharmonic potential (I. Siddiqi et al. , PRL 93, 207002 (2004)) Drive Qubit control port d I 0 g C Ui V Ur Vg Output LC oscillator GUr OSCILLATION AMPLITUDE The Josephson Bifurcation Amplifier : latching 180° -180° 1. 5 MICROWAVE DRIVE AMPLITUDE Frequency (GHz)

Microwave readout setup Micro. Wave Generator V RFin LO demodulator S 300 K M G=40 d. B Pulsing I Q TN=2. 5 K G=40 d. B -20 d. B 4 K -20 d. B -30 d. B LP 3. 3 GHz 600 m. K -30 d. B 4 k. W 1 k. W 20 m. K HP LP Directionnal 1. 3 GHz 2 GHz coupler Sample from Yale 50 W

frequency: 1. 4 GHz Rabi oscillations Readout contrast? 5 ns 100 ns Bifurcation probability tin>150 ns P Pulse duration (ns) Microwave power (d. Bm, top) Readout : 50% contrast (Yale: 60%) (best dc switching: 60%)

QND readout ? no pulse OR p pulse on qubit Readout 1 Readout 2 analysis yields for a single readout: Answer 1 Answer 0 partially QND (Yale & Saclay)

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

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

Yale quantronium sample 2 mm

Qubit in ground state

Quantum Non-Demolition Fraction Readout 1 (R 1) pulse 5 ns 100 ns 20 ns 125 ns Readout 2 (R 2) 20 ns 30 ns Ps(R 2/R 1) 13. 3% Ps(R 1 R 2 ) 3. 3% 28. 0% 19. 1% 31. 1% Ps(R 1) Ps(R 2) no pulse 17. 6% pulse 61. 3% T 1=1. 3 s QND Frac. 18. 8%