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Josephson qubits

Josephson qubits. P. Bertet. SPEC, CEA Saclay (France ), Quantronics group. Outline. Lecture 1: Basics of superconducting qubits. Lecture 2: Qubit readout and circuit quantum electrodynamics. Readout by a linear resonator Nonlinear resonators for high-fidelity readout

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Josephson qubits

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  1. Josephson qubits P. Bertet SPEC, CEA Saclay (France), Quantronics group

  2. Outline Lecture 1: Basics of superconductingqubits Lecture 2: Qubit readout and circuit quantum electrodynamics • Readout by a linear resonator • Nonlinear resonators for high-fidelity readout • Resonant qubit-resonator coupling: • quantum state engineering and tomography Lecture 3: 2-qubitgates and quantum processor architectures

  3. Fabrication techniques Al/Al2O3/Al junctions O2 small junctions e-beam lithography 1) e-beam patterning 2) development 3) first evaporation 4) oxidation 5) second evap. 6) lift-off 7) electrical test PMMA PMMA-MAA SiO2 small junctions Multi angle shadow evaporation I.3) Decoherence

  4. gate 160 x160 nm QUANTRONIUM (Saclay group) I.3) Decoherence

  5. FLUX-QUBIT (Delft group) I.3) Decoherence

  6. TRANSMON QUBIT (Saclay group) 40mm I.3) Decoherence 2mm

  7. a a a + + + b b b The ideal qubit readout relax. ? 1 0 1 1 1 1 0 0 p=|b|2 1 a|0>+b|1> tmeas << T1 ? 1 0 ? 1 0 p=|a|2 0 0 0 0 0 0 0 Quantum Non Demolishing (QND) Hi-Fi BUT ….HOW ??? SURPRISING DIFFICULT AND INTERESTING QUESTION FOR SUPERCONDUCTING QUBITS II.1) Linearresonator

  8. The readout problem 1) Readout should be FAST : ) for high fidelity ( Ideally, 2) ReadoutshouldbeNON-INVASIVE Unwanted transition caused by readout process errors (but full dephasing can’t be avoided !!!) 3) ReadoutshouldbeCOMPLETELY OFF during quantum state preparation (avoid backaction) II.1) Linearresonator

  9. Readout by a linear resonator 1D CPWresonator Superconducting artificial atom R. Schoelkopf, 2004 A. Blais et al., Phys. Rev.A 69, 062320 (2004) A. Walraffet al., Nature 431, 162 (2004) I. Chiorescu et al., Nature 431, 159 (2004) Modern readout methods by coupling to a resonator (CIRCUIT QUANTUM ELECTRODYNAMICS) II.1) Linearresonator

  10. Physical realization L=3.2cm, fn=n 1.8GHz 3mm Coupling capacitor Cc 50mm 10mm 20mm Typical lateral dimensions : 10mm - 1-dimensional mode - Very confined : - Large voltage quantum fluctuations - Quality factor easily tuned by designing Cc II.1) Linearresonator

  11. CPB coupled to a CPW resonator A. Blais et al., PRA 69, 062320 (2004) Cg Vext 2-level approximation + RotatingWave Approximation Jaynes-Cummings Hamiltonian II.1) Linearresonator

  12. Strongcouplingregimewithsuperconductingqubits GEOMETRICALdependence of g Easilytuned by circuit design Can be made very large ! (Typically : 0 – 200MHz) Strongcoupling condition naturallyfulfilled withsuperconducting circuits (Q=100 enough for strongcoupling !!) II.1) Linearresonator

  13. The Jaynes-Cummings model |e,3> d |g,3> |e,2> d couples only level doublets |e,1> |g,2> |g,n+1> , |e,n> |g,1> |e,0> Exact diagonalization possible |g,0> |g,n+1> , |e,n> Restriction of HJ-C to Note : |g,0> state is left unchanged by HJ-C with Eg,0=-d/2 II.1) Linearresonator

  14. The Jaynes-Cummings model |e,3> d |g,3> |e,2> d couples only level doublets |e,1> |g,2> |g,n+1> , |e,n> |g,1> |e,0> Exact diagonalization possible |g,0> Coupled states II.1) Linearresonator

  15. The Jaynes-Cummings model II.1) Linearresonator

  16. The Jaynes-Cummings model II.1) Linearresonator

  17. Two interesting limits RESONANTREGIME (d=0) II.1) Linearresonator

  18. Two interesting limits RESONANTREGIME (d=0) DISPERSIVEREGIME (|d|>>g) DISPERSIVEREGIME (|d|>>g) II.1) Linearresonator

  19. Two interesting limits QUANTUMSTATEENGINEERING QUBIT STATEREADOUT QUBIT STATEREADOUT RESONANTREGIME (d=0) DISPERSIVEREGIME (|d|>>g) DISPERSIVEREGIME (|d|>>g) II.1) Linearresonator

  20. The Jaynes-Cummings model : dispersive interaction with the dispersive coupling constant 2) Light shift of the qubit transition in the presence of n photons Field in the resonator causes qubitfrequency shift and decoherence 1) Qubit state-dependentshift of the cavityfrequency Cavitycan probe the qubit state non-destructively II.1) Linearresonator

  21. Dispersive readout of a transmon: principle |0> or |1> ?? II.1) Linearresonator

  22. Dispersive readout of a transmon: principle |0> or |1> ?? w=wc II.1) Linearresonator

  23. Dispersive readout of a transmon: principle |a1> |0> or |1> ?? |a0> w=wc II.1) Linearresonator

  24. Dispersive readout of a transmon: principle |a1> |0> or |1> ?? |a0> w=wc p |0> |1> -p wd/wc II.1) Linearresonator

  25. Dispersive readout of a transmon: principle |a1> |0> or |1> ?? |a0> L.O w=wc or ??? p |0> |1> -p wd/wc II.1) Linearresonator

  26. Q=700 80mm Typicalimplementation (Saclay) (f0=6.5GHz) 5 mm (optical+e-beam lithography) 40mm 2mm II.1) Linearresonator

  27. Typicalsetup (Saclay) MW meas 50MHz 20dB A(t)‏ Fast Digitizer I MW drive (t)‏ LO Q COIL Vc G=56dB 300K dB G=40dB 20dB TN=2.5K 50 4K DC-8 GHz 30dB 600mK 1.4-20 GHz 4-8 GHz 18mK 20dB 50 II.1) Linearresonator

  28. 2008 Observation of the vacuum Rabi splittingwithelectrical circuits (courtesy of S. Girvin) Signature for strong coupling: Placing a single resonant atom inside the cavity leads to splitting of transmission peak vacuum Rabi splitting atom off-resonance observed in: cavity QED R.J. Thompson et al., PRL 68, 1132 (1992) I. Schuster et al. Nature Physics 4, 382-385 (2008) circuit QED A. Wallraff et al., Nature 431, 162 (2004) quantum dot systems J.P. Reithmaier et al., Nature 432, 197 (2004) T. Yoshie et al., Nature 432, 200 (2004) on resonance II.1) Linearresonator A. Wallraff et al., Nature 431, 162 (2004)

  29. Qubit spectroscopywith dispersive readout MW drv Pump TLS Probe resonator phase MW meas   /c II.1) Linearresonator

  30. n01 n12 nc Typicalspectroscopy of a transmon + cavity circuit II.1) Linearresonator

  31. Rabi oscillations measuredwith dispersive readout Δt Variable-length drive MW drv x 10000  Ensemble averaging Projectivemeasurement MW meas T2R=316 ns Y X II.1) Linearresonator

  32. Dispersive readout : the signal-to-noise issue |a1> |0> or |1> ?? |a0> Ideal amplifier L.O w=wc or ??? p |0> |1> -p wd/wc II.1) Linearresonator

  33. Dispersive readout : the signal-to-noise issue |a1> |0> or |1> ?? Real amplifier TN=5K L.O |a0> w=wc or ??? No discrimination in 1 shot p |0> |1> -p wd/wc II.1) Linearresonator

  34. Dispersive readout : the signal-to-noise issue QUANTUM- LIMITEDAMPLIFIER ?? |a1> |0> or |1> ?? |a0> Real amplifier TN=5K L.O w=wc or in one single-shot ?? p |0> |1> -p wd/wc II.1) Linearresonator

  35. How to build an amplifier with minimal noise ??? Nonlinearresonator pump signal in l/4 l/4 signal out Junction causes Kerr non-linearity Resonatorcanbehave as parametric amplifier K. Lehnert group M. Devoret group I. Siddiqi group II.2) Nonlinearresonator

  36. A nonlinearresonator as quantum-limited amplifier max M. J. Hatridge, R. Vijay, D. H. Slichter, J. Clarke and I. Siddiqi, Phys. Rev. B 83, 134501 (2011) II.2) Nonlinearresonator (courtesy I. Siddiqi)

  37. A nonlinearresonator as quantum-limited amplifier Small signal Saturated (courtesy I. Siddiqi) II.2) Nonlinearresonator

  38. Signal-to-noise enhancement by a paramp M. Castellanos-Beltran, K. Lehnert, APL (2007) (quantum limiton how good an amplifier canbe : Caves theorem) Actuallyreached in severalexperiments : quantum limitedmeasurement II.2) Nonlinearresonator

  39. Qubit and amplifier at 30 mK OUTPUT INPUT DRIVE (courtesy I. Siddiqi) II.2) Nonlinearresonator

  40. Individual measurement traces readout off readout on R. Vijay, D.H. Slichter, and I. Siddiqi, PRL 106, 110502 (2011) (courtesy I. Siddiqi) II.2) Nonlinearresonator

  41. Bivalued histograms Single-shot discrimination of qubit state (courtesy I. Siddiqi) II.2) Nonlinearresonator

  42. Otherstrategy : sample-and-hold detector integratedwithqubit pump Nonlinearresonator used as threshold detector l/4 l/4 II.2) Nonlinearresonator

  43. Otherstrategy : sample-and-hold detector integratedwithqubit Kerr-nonlinearresonator l/4 l/4 pump H Pd /Pc = 0.2 0.5 1.0 1.8 L - BISTABILITY FOR II.2) Nonlinearresonator

  44. The Cavity Josephson Bifurcation Amplifier (CJBA) M. Devoret group, Yale JBA: I. Siddiqi et al., PRL (2004) CJBA: M. Metcalfe et al, PRB (2007) MW drive : Pd(t) , wd Non linear resonator jin jout H Pd Pd Hstate Bistable region L Switchingfrom L to H : BIFURCATION wd L state Stochasticprocessgoverned by thermal or quantum noise. M.I. Dykman and M.A. Krivoglaz, JETP 77, 60 (1979) M.I. Dykman and V.N. Smelyanskiy, JETP 67, 1769 (1988) wc II.2) Nonlinearresonator

  45. The Cavity Josephson Bifurcation Amplifier (CJBA) M. Devoret group, Yale JBA: I. Siddiqi et al., PRL (2004) CJBA: M. Metcalfe et al, PRB (2007) MW drive : Pd(t) , wd Non linear resonator jin jout H Pd Pd Hstate Bistable region L wd L state wc II.2) Nonlinearresonator

  46. Readout of transmonwith CJBA MW drive : Pd(t) , wd Non linear resonator jin jout qubit in|0> or|1> Pd Pd Hstate |1> wd L state |0> wc|1> wc|0> SINGLE-SHOT QUBIT READOUT II.2) Nonlinearresonator

  47. 400ns 250ns h12 h01 Rabi oscillations visibility tp,12 Dt Pswitch (%) TRabi=500ns Mallet et al., Nature Physics (2009) Dt(µs) Single-shot93% contrastRabi oscillations Seealso A. Lupascu et al., Nature Phys. (2007) II.2) Nonlinearresonator

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