Paolo Silvestrini

Paolo SilvestriniMacroscopic Quantum Coherence and Quantum ComputingSeconda Universit di Napoli -Dip. di Ingegneria dellInformazione CNR - Istituto di Cibernetica Eduardo CaianielloMQC group in NaplesValentina CoratoCarmine Granata Sara RombettoBerardo Ruggiero Maurizio RussoRoberto Russo

Back to basicsFundamental carrier of information: the bitPossible qubit states: any superposition describedby the wavefunction01orFundamental carrier of quantum information: the qubitPossible bit states:

Quantum computationwith chloroform NMRDeutsch algorithmdemonstrated.ClClCl

Five Criteria for physical implementation of a quantum computerWell defined extendible qubit array -stable memoryPreparable in the 000 stateLong decoherence time (>104 operation time)Universal set of gate operationsSingle-quantum measurementsD. 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.

Physical systems actively consideredfor quantum computer implementationLiquid-state NMRNMR spin latticesLinear ion-trap spectroscopyNeutral-atom optical latticesCavity QED + atomsLinear optics with single photonsNitrogen vacancies in diamondElectrons on liquid He Josephson devicescharge qubitsflux qubitsphase qubitsSpin spectroscopies, impurities in semiconductorsCoupled quantum dotsQubits: spin,charge,excitons

Dissipation effects (Chakravarty and Leggett PRL 1984, Grabert and Weiss PRL 1984)Long decoherence time Low dissipation Low T

Superconducting Josephson qubits NEW: atom in cavity :

fluxphasecharge

Tilt Washboard Potential RCIdc

-50050I(mA)-4-2024V(mV)

rf-SQUID Quantizzazione del flussoide Effetto Josephson

Controls:

A. J. Leggett, Prog. Theor. Phys. 69, 80 (1980)

Quantizied Energy levelsTunnel ratePotentialPotential barrierWjkGjQuantum picture

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 RegimesPRL 60, 844 (1988)

Observation of Energy Level Quantization in Underdamped Josephson Junctions above the Classical-Quantum Regime Crossover TemperatureP.Silvestrini, V.G. Palmieri, B. Ruggiero, and M. Russo, Phys. Rev. Lett. 79, 3046 (1997)R>20K

Quantum superposition of distinct macroscopic statesJonathan R. Friedman, Vijay Patel, W. Chen, S. K. Tolpygo & J. E. LukensNATURE | VOL 406 | 6 JULY 2000

Coherent Quantum Dynamics of a Superconducting Flux QubitI. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, J. E. Mooijdec =20 nsScience 299, 1869 (2003)

Quantum oscillations in two coupled charge qubitsYu. A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D. V. Averin & J. S. TsaiNATURE |VOL 421 | 20 FEBRUARY 2003dec =2.5 nsdec =0.6 ns

Coupling a flux qubit and a harmonic oscillatorRelaxation-limited dephasingat the optimal pointDynamics of a flux-qubit coupled to a harmonic oscillator (P. Bertet)

Coupling phase qubits

Quantronium:-arbitrary robust operations-decoherence fought: echoes, mwave driving-new readout developed at Yale SPIN-LOCKINGRabi

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

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

The theoretical model (II)

There are localized states even for the free Hamiltonian: the ground state decays exponentially along the fingersG. Giusiano, F. P. Mancini, P. Sodano, A. Trombettoni, Int. J. Mod. Phys. B 18, 691 (2004)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 temperatureHamiltonian Solutions for a comb graph

Chip designThe realized arrays have 4mmx4mm and 5mmx5mm junctions8 different chips with different current density were fabricated and testedThe Backbone (BB) and its reference (RBB) have 72JJ while finger (CF) and its reference (RCF) have 80JJ

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

Experimental Results on BackboneBackbone shows a critical current higher than the reference one in particoular at T=1.2KThe gap voltage is the sum of the number of junctions (72JJs)

Experimental Results on FingersThe CFA shows an increased disuniformity at T=1.2K

Further testBBArray before cuttingBBArray After cuttingreduced to a Linear array

Experimetal Results on Backbone Voltage is normalized to the number of junctions

Effect of noise and disuniformityCalculated current switchingsEffect of temperature

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

Fit at all temperature BBA 4x4m2BBA present a larger disuniformity at T < 5K

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

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

Summary

We have observed a critical current enhancement along the backbone of a comb-shaped Josephson Junction arrayWe have inferred from data its temperature dependenceAt the same time we observed along the finger a critical current reduction away from the backboneThe whole effect is related to the inhomogenous topology (connectivity)

No tunable coupling needed (\sigma_x \sigma_x).Not so easy to generate the bias pulses with required S:N-- similar requirements to the single qubit biasing.Bus couplingThere is a better controlled phase gate using couplings to the 02 and 11 states

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Paolo Silvestrini