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Paolo Silvestrini

Macroscopic Quantum Coherence and Quantum Computing. Paolo Silvestrini. MQC group in Naples. Valentina Corato Carmine Granata Sara Rombetto Berardo Ruggiero Maurizio Russo Roberto Russo. Seconda Università di Napoli -Dip. di Ingegneria dell’Informazione

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Paolo Silvestrini

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  1. Macroscopic Quantum Coherence and Quantum Computing Paolo Silvestrini MQC group in Naples Valentina Corato Carmine Granata Sara Rombetto Berardo Ruggiero Maurizio Russo Roberto Russo Seconda Università di Napoli -Dip. di Ingegneria dell’Informazione CNR - Istituto di Cibernetica “Eduardo Caianiello”

  2. Back to basics… Fundamental carrier of information: the bit Possible bit states: “0” “1” or Fundamental carrier of quantum information: the qubit Possible qubit states: any superposition described by the wavefunction

  3. Z Y X qbit

  4. 1H 13C Quantum computationwith chloroform NMR Cl Cl Cl Deutsch algorithm demonstrated.

  5. Five Criteria for physical implementation of a quantum computer • Well defined extendible qubit array -stable memory • Preparable in the “000…” state • Long decoherence time (>104 operation time) • Universal set of gate operations • Single-quantum measurements D. P. DiVincenzo, in Mesoscopic Electron Transport, eds. Sohn, Kowenhoven, Schoen (Kluwer 1997), p. 657, cond-mat/9612126; “The Physical Implementation of Quantum Computation,” quant-ph/0002077.

  6. Liquid-state NMR NMR spin lattices Linear ion-trap spectroscopy Neutral-atom optical lattices Cavity QED + atoms Linear optics with single photons Nitrogen vacancies in diamond Electrons on liquid He Josephson devices “charge” qubits “flux” qubits “phase” qubits Spin spectroscopies, impurities in semiconductors Coupled quantum dots Qubits: spin,charge,excitons Physical systems actively consideredfor quantum computer implementation

  7. P(t) R1<R2< R3 Dissipation effects (Chakravarty and Leggett PRL 1984, Grabert and Weiss PRL 1984) Long decoherence time Low dissipation Low T

  8. Superconducting Josephson qubits Chalmers NEC Schoelkopf et al, Yale TUDelft quantronium Y ( N ) >> N 2 1 charge-phase N NIST 2 N ~ 1 flux charge phase NEW: « atom in cavity » :

  9. JJ IN 50 m I( A) 0 -50 Stato Josephson -4 -2 2 4 0 V(mV) U Stato resistivo  Tilt Washboard Potential R Idc C

  10. 50 m I( A) 0 -50 -4 -2 2 4 0 V(mV)

  11. x rf SQUID   U = x x f rf-SQUID • Quantizzazione del flussoide • Effetto Josephson

  12. I b i a s Ip Is rf SQUID dc SQUID    V o u t LP Li Iecc excitation coil flux transformer x  rf-SQUID •Simmetry of potential   rf SQUID xdc •Hight of the barrier Flux transformer •Coupling to the readout dc-SQUID Stacked JJ Controls:

  13. flux transformer dc-SQUID rf-SQUID modulation and feedback coils Josephson junction 350 mm excitation coil rf-SQUID flux transformer 50 mm

  14. I I |L> |R> Rf-SQUID Potential + - A. J. Leggett, Prog. Theor. Phys.69, 80 (1980)

  15. Quantum picture Potential barrier Potential Wjk Gj Tunnel rate Quantizied Energy levels

  16. Quantum Tunneling Thermal Activation U U F F

  17. Measurements of Macroscopic Quantum Tunneling out of the Zero-Voltage of a Current-Biased Josephson Junction M. H. Devoret, J. M. Martinis, and J. Clarke, PRL 55, 1543 (1985)

  18. data 1 -1 10 -1 -1 t t / TR -2 10 2 3 4 10 10 10 Q P. Silvestrini, R. Cristiano, S. Pagano, O. Liengme, and K. E. Gray, “Effect of dissipation on Thermal Activation in an underdamped Josephson Junction: First evidence of a Transition between Different Damping Regimes” PRL 60, 844 (1988)

  19. 1,4 D I exp 1,2 D I teo 1,0 0,8 0 4 8 12 n Observation of Energy Level Quantization in Underdamped Josephson Junctions above the Classical-Quantum Regime Crossover Temperature R>20K P.Silvestrini, V.G. Palmieri, B. Ruggiero, and M. Russo, Phys. Rev. Lett. 79, 3046 (1997)

  20. Observation of Resonant Tunneling between Macroscopically Distinct Quantum Levels R. Rouse, S. Han, and J. E. Lukens, PRL 75, 1614 (1995) Resonant macroscopic quantum tunneling in SQUID systems P.Silvestrini, B.Ruggiero, and Y.Ovchinnikov; PRB 54, 3046 (1996)

  21. Tℓ U 

  22. Quantum superposition of distinct macroscopic states Jonathan R. Friedman, Vijay Patel, W. Chen, S. K. Tolpygo & J. E. Lukens NATURE | VOL 406 | 6 JULY 2000

  23. Coherent control ofmacroscopic quantum statesin a single-Cooper-pair box Y. Nakamura, Yu. A. Pashkin& J. S. Tsai NATURE |VOL 398 | 29 APRIL 1999 Manipulating the Quantum State of an Electrical Circuit D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina,D. Esteve, M. H. Devoret SCIENCE VOL 296 3 MAY 2002 dec=0.5 s

  24. Coherent Temporal Oscillations improvement of Macroscopic Quantum States in a Josephson Junction Yang Yu, Siyuan Han, Xi Chu, Shih-I Chu, Zhen Wang SCIENCE 296, 889 (2002) dec=5 s Rabi oscillations in a large Josephson-junction qubit John M. Martinis, S. Nam, J. Aumentado, andC. Urbina Phys. Rev. Lett 89, 117401 (2002) dec=10 ns

  25. Coherent Quantum Dynamics of a Superconducting Flux Qubit I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, J. E. Mooij dec=20 ns Science 299, 1869 (2003)

  26. Quantum oscillations in twocoupled charge qubits Yu. A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura,D. V. Averin & J. S. Tsai dec=2.5 ns dec=0.6 ns NATURE |VOL 421 | 20 FEBRUARY 2003

  27. Dynamics of a flux-qubit coupled to a harmonic oscillator(P. Bertet) Coupling a flux qubit and a harmonic oscillator Relaxation-limited dephasing at the optimal point

  28. Coupling phase qubits Ib I* U U g g

  29. Quantronium: -arbitrary robust operations -decoherence fought: echoes, mwave driving -new readout developed at Yale combined X&Y rotations Corpse composite pulse SPIN-LOCKING Rabi

  30. BIFURCATION AMPLIFICATION • Bifurcation amplifier: sensitive to any input variable coupled to I0 • minimal back-action • - no on-chip dissipation • - efficiently thermalize load • - backaction narrow band

  31. Demonstration of conditional gate operation using superconducting charge qubit T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura, & J. S. Tsai

  32. Superconducting Adiabatic Quantum Device NP-Hard Problems: i=ij ……….. ……….. …. …. …. ….

  33. Josephson Networks L. B. Ioffe and M. V. Feigel'man, Phys. Rev. B66, 224503 (2002) B. Douçot., M. V. Feigel'man and L. B. Ioffe, Phys. Rev. Lett. 90, 107003 (2003) Bose-Einstein Condensation in Inhomogeneous Josephson Junctions Arrays R. Burioni, D. Cassi, I. Meccoli, M. Rasetti, S. Regina, P. Sodano, A. Vezzani, Europhys.Lett.52, 251, (2000).R. Burioni, D. Cassi, M. Rasetti, P. Sodano, A. Vezzani, J.Phys.B., 34, 4697, (2001). 

  34. fingers t is a positive hopping parameter Axy,x'y' is the adiacency matrix 1 If xy-x'y' is a link 0 otherwise Axy,x'y' = Backbone Eigenvalue equation The theoretical model (II)

  35. Hamiltonian Solutions for a comb graph There are localized states even for the free Hamiltonian: the ground state decays exponentially along the fingers • Topology induces new phases at finite temperature for bosons on graphs • The experimental signature of the Bose Einstein condensation is given by the inhomogeneity of Josephson critical currents below the BEC critical temperature • G. Giusiano, F. P. Mancini, P. Sodano, A. Trombettoni, Int. J. Mod. Phys. B 18, 691(2004)

  36. b) a) JJ RCF CF BB 50mm 1mm RBB Chip design The realized arrays have4mmx4mm and 5mmx5mm junctions 8 different chips with different current density were fabricated and tested The Backbone (BB) and its reference (RBB) have 72JJ while finger (CF) and its reference (RCF) have 80JJ

  37. I- I+ V+ V- I- I+ V+ V- Measurement Junctions are connected in series and incresing the bias current the switch to the gap branch of each junction is well visible. We can count the number of junctions in the array

  38. I+ V+ I+ V+ V- I- V- I- Measurement Junctions are connected in series and incresing the bias current the switch to the gap branch of each junction is well visible. We can count the number of junctions in the array

  39. I I I I V V V V I I I I V V V V Experimental Results on Backbone The gap voltage is the sum of the number of junctions (72JJs) Backbone shows a critical current higher than the reference one in particoular at T=1.2K

  40. V I V I V I V I Experimental Results on Fingers The CFA shows an increased disuniformity at T=1.2K

  41. JJ 50mm 50mm Further test BBArray After cutting reduced to a Linear array BBArray before cutting

  42. I I I I I I V V V V V V RBA BBA After cut BBA Experimetal Results on Backbone Voltage is normalized to the number of junctions

  43. Effect of a Ic disuniformity Effect of noise and disuniformity Calculated current switchings Effect of temperature

  44. Fit of data 1.2K - 4.2K The only free parameter to fit IV curve is the mean Ic: the sigma is 4% in 4x4 BBACUT and 3% in BBACUT 5x5arrays

  45. Fit at all temperature BBA 4x4m2 BBA present a larger disuniformity at T < 5K

  46. Critical Current Temperature Behaviour Critical Current is measured and normalized to the 64 JJ switching on a total number of 72JJs

  47. Critical Current Temperature Behaviour Critical Current is measured and normalized to the 50 JJ switching on a total number of 55 JJs

  48. Sample Junction area (μm2) Number of Junctions Mean Ic (μA) Sigma (%Ic) Ic BBA / Ic BBACUT BBA3 4x4 72 18 4 1.17 BBA4 5x5 72 24 3 1.13 BBA5 5x5 72 25 3 1.11 BBA6 5x5 55 26 3 1.04 BBA6a 4x4 72 17 4 1.07

  49. We have observed a critical current enhancement along the backbone of a comb-shaped Josephson Junction array We have inferred from data its temperature dependence At the same time we observed along the finger a critical current reduction away from the backbone The whole effect is related to the inhomogenous topology (connectivity) Summary

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