Coherence and decoherence in Josephson junction qubits

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. Charge qubit Flux qubit Phase qubit Energy typical qubit energy typical experimental temperature Josephson junction qubits small large Josephson energy = confinement potential charging energy = kinetic energy  quantized states

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

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

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

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

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

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

9. Sensitivity to noises relaxation transverse coupling dephasing longitudinal coupling

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

11. T1 measurement p ~ 4ns p readout pulse delay initialization to ground state is better than 90%  relaxation dominant  classical noise is not important at qubit frequency ~ 5GHz

12. T1 vs f p ~ 4ns delay readout pulse

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

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

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

16. spin echo p/2~2ns p/2 p ~ 4ns readout pulse t/2 t/2 Dephasing: T2Ramsey, T2echo measurement correspond to detuning Ramsey interference (free induction decay) p/2~2ns p/2 readout pulse t

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

18. T1 and T2echo at f=f*, Ib=Ib* T1=54516ns Echo decay time is limited by relaxation Pure dephasing due to high frequency noise (>MHz) is negligible

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

20. Red lines: fit 2Ramsey, 2echo vs f For for 3.17 mm2 cf. 7±3x10-6 [F0] for 2500-160000 mm2 F.C.Wellstood et al. APL50, 772 (1987) ~1x10-4 [F0] for 5.6 mm2 G.Ithier et al. PRB 72, 134519 (2005)

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

22. T1, T2Ramsey, T2echo vs Ib can be obtained experimentally at Ib=Ib* at |Ib-Ib*|=large

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

24. Optimal point f=f*, Ib=Ib* T1 limited echo decay Pure dephasing due to low freq. noise Sammary • T1, T2 measurement in flux qubit, T1,T2~1s • dependence on flux bias and SQUID-current bias condition •  characterization of environment f=f*, IbIb* ‘white’ Ib noise dominant ff*, Ib=Ib* We do not understand yet -T1 vs flux bias -dephasing at optimal point -origin of 1/f noise 1/f flux noise dominant

25. 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 Optimal point and quantum inductance

26. 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 Tunable coupling between flux qubits At the optimal point for qubit1 and qubit2 Effective coupling; can be zero at dc

27. 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 Tunable coupling between flux qubits |10 |01 Simulated time evolution vs. control MW pulse width Double-CNOT within tens of ns |10 |01 A.O. Niskanen et al., cond-mat/0512238

28. Three qubits and a readout SQUID   1 t |1-2| |00  |10  |10+|01  |00+|11 readout |00 Psw |11 t Simple demonstration of tunable coupling between flux qubits qubit3 qubit1 qubit2 Easy to distinguish |00 and |11 (not|01 and |10) A.O. Niskanen et al., cond-mat/0512238

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