1. Coherence and decoherence in Josephson junction qubits Yasunobu Nakamura, Fumiki Yoshihara, Khalil Harrabi Antti Niskanen, JawShen Tsai NEC Fundamental and Environmental Research Labs. RIKEN Frontier Research System CREST-JST Decoherence of qubit, bias dependence Tunable coupling scheme based on parametric coupling using quantum inductance

2. Josephson junction qubits smalllarge Josephson energy = confinement potential charging energy = kinetic energy  quantized states typical qubit energy typical experimental temperature Flux qubitCharge qubitPhase qubit Energy

3. Examples of Josephson junction qubits 2  m charge qubit/NECflux qubit/Delft charge qubit (quantronium)/Saclay phase qubit/NIST/UCSB ~100  m

4. SQUID readout of flux qubit 0 switch I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij, Science 299, 1869 (2003) Ib pulse ~30 ns rise/fall time time ~1  s ~20 ns To hold voltage state after switching 01 qubit +underdamped SQUID qubit SQUID w/o  -pulse w/  -pulse

5. Coherent control of flux qubit resonant microwave pulse visibility~79.5% Rabi oscillations

6. Study of decoherence environment interaction qubit = Characterization of environment tunable

7. Possible decoherence sources phonons? photons? magnetic-field noise? charge fluctuations? paramagnetic/nuclear spins? trapped vortices? charge/Josephson-energy fluctuations? quasiparticle tunneling? environment circuit modes?

8. Flux qubit: Hamiltonian and energy levels J.E. Mooij et al. Science 285, 1036 (1999) f/f* f*=0.5

9. Sensitivity to noises relaxation dephasing transverse coupling longitudinal coupling

10. Energy relaxation relaxation and excitation for weak perturbation: Fermi’s golden rule qubit energy  E variable relaxation  S(+  ) and excitation  S(-  )  quantum spectrum analyzer ex. Johnson noise in ohmic resistor R spontaneous emission absorption zero-point fluctuation of environment

11. T 1 measurement initialization to ground state is better than 90%  relaxation dominant  classical noise is not important at qubit frequency ~ 5GHz  ~ 4ns delay readout pulse

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

13.  1 vs  E assuming flux noise (not assured) Data from both sides of spectroscopy coincide Positions of peaks are not reproduced in different samples Peaks correspond to anticrossings in spectroscopy

14.  1 vs  E: Comparison of two samples sample3 sample5 Random high-frequency peaks. Broad low-frequency structure and high-frequency floor.

15. Dephasing free evolution of the qubit phase dephasing for Gaussian fluctuations sensitivity of qubit energy to the fluctuation of external parameter information of S(  ) at low frequencies

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

17. Optimal point to minimize dephasing IbIb f two bias parameters –External flux: f =  ex /  0 –SQUID bias current I b f  E (GHz) IbIb G. Burkard et at. PRB 71, 134504 (2005)

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

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

20.  2Ramsey,  2echo vs f cf. 7±3x10 -6 [  0 ] for 2500-160000  m 2 F.C.Wellstood et al. APL50, 772 (1987) ~1x10 -4 [  0 ] for 5.6  m 2 G.Ithier et al. PRB 72, 134519 (2005) Red lines: fit For for 3.17  m 2

21. Optimal point to minimize dephasing f  E (GHz) IbIb IbIb f two bias parameters –External flux: f =  ex /  0 –SQUID bias current I b

22. T 1, T 2Ramsey, T 2echo vs I b can be obtained experimentally at I b =I b * at |I b -I b * |=large

23. Echo at f=f*, I b  I b * at I b =I b * at |I b -I b * |=large exponential fitGaussian fit -echo does not work -exponential decay  white noise (cutoff>100MHz)

24. Sammary T 1, T 2 measurement in flux qubit, T 1,T 2 ~1  s dependence on flux bias and SQUID-current bias condition  characterization of environment Optimal point f=f*, I b =I b * T 1 limited echo decay Pure dephasing due to low freq. noise We do not understand yet -T 1 vs flux bias -dephasing at optimal point -origin of 1/f noise f  f*, I b =I b * 1/f flux noise dominant f=f*, I b  I b * ‘white’ I b noise dominant

25. Optimal point and quantum inductance At optimal point –Dephasing is minimal –Persistent current is zero Inductive coupling ~  x  x ; effective only for  1  2 Current readout should be done elsewhere –Quantum inductance is finite Depend on flux bias  tunable parametric coupling Depend on qubit state  nondemolition inductance readout  current  inductance

26. Tunable coupling between flux qubits Use nonlinear quantum inductance of high-frequency qubit3 as transformer loop Drive the nonlinear inductance at |  1 -  2 | and parametrically induce effective coupling between qubit1 and qubit2 Effective coupling; can be zero at dc At the optimal point for qubit1 and qubit2

27. Tunable coupling between flux qubits Advantages –Qubits are always biased at optimal point –Coupling is proportional to MW amplitude; can be effectively switched off –Induced coupling term also has protection against flux noise Simulated time evolution vs. control MW pulse width Double-CNOT within tens of ns A.O. Niskanen et al., cond-mat/0512238 |10  |01  |10  |01 

28. Simple demonstration of tunable coupling between flux qubits Three qubits and a readout SQUID Easy to distinguish |00  and |11  (not |01  and |10  ) qubit1qubit2 qubit3 |1-2||1-2| 11 |00   |10    |10  +  |01    |00  +  |11  readout tt  Psw tt |00  |11  A.O. Niskanen et al., cond-mat/0512238

29. Future Single qubit control Tunable coupling Nondemolition readout Long coherence time