SUPERCONDUCTING QUBITS

Transcription

1 SUPERCONDUCTING QUBITS Theory Collaborators Prof. A. Blais (UdS) Prof. A. Clerk (McGill) Prof. L. Friedland (HUJI) Prof. A.N. Korotkov (UCR) Prof. S.M. Girvin (Yale) Prof. L. Glazman (Yale) Prof. A. Jordan (UR) Dr. M. Sarovar (Sandia) Prof. B. Whaley (UCB) IRFAN SIDDIQI Quantum Nanoelectronics Laboratory Department of Physics, UC Berkeley

2 MICROWAVE OPTICS & SUPERCONDUCTING ARTIFICAL ATOMS GHz ATOM/CAVITY 0 Tunable f, f LIGHT SOURCE DETECTOR M. Hatridge et al., Phys. Rev. B 83 (2011) HOMODYNE B.R. Johnson et al., Nature Physics 6 (2010) COUNTING

3 4-8 GHz LINEAR CAVITIES 3D Waveguide Q ~ D Planar Q ~

4 THE NON-DISSIPATIVE JOSEPHSON JUNCTION OSCILLATOR Quantized Levels : phase difference I 0 ~ na S I S I( ) I0 sin( ) d Vt ( ) ( ) 2e dt U( ) I0 cos( ) 2e I 0 >ma Non-linear Oscillator

5 THE DAWN OF COHERENCE T 1, T 2 ~ 1 ns Al / AlOx / Al T 1, T 2 ~ 100 ms Al / AlOx / Al Observation of High Coherence in Josephson Junction Qubits Measured in a Three- Dimensional Circuit QED Architecture

6 SUPERCONDUCTING TRANSMON QUBIT L J ~ 13 nh C ~ 70 ff Tunable qubit frequency w 01 ~ 5-8 GHz J. Koch et al., Physical Review A 76, (2007) T 1, T 2 ~ 100s ms

7 Josephson tunnel junctions 500 nm

8 Cavity Transmission 1 0 Frequency

9 T = 4K EXPERIMENTAL SETUP (~25 added photons) OUTPUT INPUT DRIVE T = 0.02 K

10 SYSTEM NOISE TEMPERATURE system noise w/o paramp = 7K

11 PARAMETRIC AMPLIFICATION L J ~ 0.1 nh C ~ ff U ( I 0 / 2 e ) 2 0 W M. J. Hatridge et al., Phys. Rev. B 83, (2011)

12 Flux line Tunnel junction SQUID 4mm Capacitor Al Lumped LC Resonator 4-8 GHz Coupled to 50 W Q = 26 Nb ground plane Capacitor 100 mm

13 4 th GENERATION CRYOPACKAGE Aluminum superconducting shield Removable CPW launch Magnet for tuning frequency Copper cover (prevents any coupling to box mode) Thermalizing strap

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15 OUTLINE WEAK MEASUREMENT SINGLE QUBIT EXPERIMENTS Individual Quantum Trajectories Distribution of Quantum Trajectories TWO QUBIT MEASUREMENTS Remote Entanglement

16 WEAK MEASUREMENT

17 { { QUBIT STATE ENCODED IN PHASE SHIFT 1 0 reflected signal I I Q Q PHASE SENSITIVE HOMODYNE MEASUREMENT

18 MEASUREMENT: COUPLE TO E-M FIELD OF CAVITY (Jaynes-Cummings) Cavity Transmission 1 0 n VARY MEASUREMENT STRENGTH USING DISPERSIVE SHIFT & PHOTON NUMBER Frequency NEED TO DETECT ~ SINGLE MICROWAVE PHOTONS in T 1 ~ ms

19 STRONG vs. WEAK MEASUREMENT Weak τ CONTROL n Strong READOUT/TOMOGRAPHY

20 MEASUREMENT STRENGTH S = ΔV2 σ 2 S= S = 64τχ2 nη κ n S=3.2 t: measurement time c: dispersive shift n : photon number k: cavity decay rate h: detector efficiency η = 0.49 S=7.0 DV 2s

21 WHAT DO YOU DO WITH THIS WEAK MEASUREMENT SIGNAL? 1 Control Signal for Feedback (eg. Stabilized Rab Osc.) Construct Trajectories 0 Feed it to Another Qubit to Generate Entanglement

22 CAN WE TRACK A PURE STATE ON THE SURFACE OF THE BLOCH SPHERE? OBSERVING SINGLE QUANTUM TRAJECTORIES OF A SUPERCONDUCTING QUBIT K. Murch et al., Nature 502, 211 (2013).

23 BACKACTION OF SINGLE QUADRATURE MEASUREMENT Cavity Output q=0 I After Amplification q=0 I Q pump Q Obtain qubit state information Tip Bloch vector Cavity Output q=p/2 I After Amplification q=p/2 I Q pump Q Obtain cavity photon number information Rotate Bloch vector

24 INDIVIDUAL TRAJECTORIES z y x 1 V m τ = 1 τ 0 τv t dt Prepare state along +x Continuous weak measurement Integrated readout is trajectory

25 BAYESIAN UPDATE P P(V ) P(V ) V Event: A = Avalanche S = Snow > 10 feet P P(V) Likelihood: Prob. snow accompanied avalanche Prior: Historic chance of an avalanche V P A S = Posterior: Chance of an avalanche given snow P S A P(A) P(S) Prob. of Snow P( V) = P(V ) P( ) P(V)

26 WEAK MEASUREMENT OF THE QUBIT STATE S=0.32 Initial state along +X Measure Z (phase quadrature) WANT TO EVALUATE: BAYES RULE: σ Z V m Z Z σ X V m X Z σ Y V m Y Z Z Z = tanh( V ms 2ΔV ) X Z = 1 σ Z 2 e γτ γ = 8χ 2 n 1 η /κ + 1/T 2 TOMOGRAPHIC PROCEDURE:

27 WEAK MEASUREMENT OF THE PHOTON NUMBER n=0.46 WANT TO EVALUATE: σ Z V m Z φ σ X V m X φ σ Y V m Y φ n=0.46 BAYES RULE: X φ = cos( SV m 2ΔV )e γτ Y φ = sin( SV m 2ΔV )e γτ

28 REALTIME TRACKING Prepare qubit along X axis Evolve under measurement Use Bayes rule to update our guess of the qubit state (dots) Perform tomography for each time step (solid)

29 DISTRIBUTION OF QUANTUM TRAJECTORIES

30 MEASUREMENT INDUCED DYNAMICS ONLY Initial State along +x Integration time t needed to resolve state: 1.25 ms

31 MEASUREMENT w. POSTSELECTION Initial State along +x Final State at z = Can Identify Most Likely Path Predict with Theory?

32 EXTREMIZING THE QUANTUM ACTION Classical Example: Kramer s Escape Consider paths to saddle point L Establish canonical phase space (p,q) Define action S Calculate most favorable path, etc L Quantum Case for Pre/Post-Selected Trajectories: A. Chantasri, J. Dressel, A.N. Jordan, PRA 2013 Consider paths connecting quantum state q I q F Double quantum state space ( canonical) Express joint probability of measurement & trajectories as path integral Minimize action ODE for equation of motion Calculate statistical distributions Treat case of measurement backaction with control pulses W (Schrödinger dynamics)

33 MEASUREMENT w. POSTSECLECTION: THEORY Z Initial State along +x Final State at z = EOM for Optimized Path No Driving (W=0) X x t = e γt sech( rt τ ) z t = tanh( rt τ ) r: detector output max likelihood

34 QUANTUM TRAJECTORIES WITH RABI DRIVING

35 TRAJECTORIES w. RABI DRIVE: TOMOGRAPHY NO RABI DRIVE WITH RABI DRIVE Trajectories w. Rabi drive: two step update (master eqn. + Bayes) Individual trajectories show high purity

36 DISTRIBUTION OF RABI TRAJECTORIES Excellent agreement with ODE solutions

37 CAN WE ENTANGLE TWO REMOTE SUPERCONDUCTING QUBITS via MEASUREMENT? TRACKING ENTANGLEMENT GENERATION BETWEEN TWO SPATIALLY SEPARATED SUPERCONDUCTING QUBITS N. Roch et al., PRL 112, , 2014

38 TWO DISTANT QUBITS

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40 JOINT DISPERSIVE MEASUREMENT I Q Theory Proposal: Kerckhoff et al., Phys Rev A 2009

41 JOINT DISPERSIVE MEASUREMENT I 1 0 Q Theory Proposal: Kerckhoff et al., Phys Rev A 2009

42 JOINT DISPERSIVE MEASUREMENT I Q

43 JOINT DISPERSIVE MEASUREMENT I Q

44 WEAK CONTINUOUS MEASUREMENT No classical OR quantum observer can discriminate eigenstates; system is perturbed, but not projected, by measurement. Hatridge et al., Science 2013

45 MEASUREMENT HISTOGRAMS

46 MEASUREMENT INDUCED ENTANGLEMENT

47 Ensemble measurements: TRAJECTORIES Single experimental realization: (measurement back-action) Quantum trajectory reconstruction allows us to directly observe quantum state evolution under measurement Single Qubit Trajectories: Murch et al., Nature 2013 Weber et al., Nature 2014

48 PULSE SEQUENCE & ANALYSIS

49 QUANTUM BAYESIAN UPDATE

50 BAYESIAN TRAJECTORY RECONSTRUCTION

51 BAYESIAN TRAJECTORY RECONSTRUCTION

52 CONDITIONAL TOMOGRAPHY MAPPING

53 FUTURE DIRECTIONS IMPROVE DETECTION EFFICIENCY (ON-CHIP PARAMPS) TRAVELING WAVE AMPLFIERS (BW ~ 2 GHz) FEEDBACK STABILIZATION OF ENTANGLEMENT WEAK MEASUREMENT IN QUBIT CHAINS Adaptive State Estimation (cf. tomography) Weak Value Amplification of Errors/Couplings Information Flow / Equilibration / Perturbations

54 QNL Dr. Shay Hacohen-Gourgy Dr. David Toyli Natania Antler Andrew Eddins Chris Macklin Leigh Martin Vinay Ramasesh Mollie Schwartz Steven Weber Alumni Dr. Kater Murch (Wash U) Dr. Ofer Naaman (NGC) Dr. Nico Roch (CNRS) Dr. Andrew Schmidt (IBM) Dr. R. Vijay (TIFR) Michael Hatridge (Yale) Edward Henry Eli Levenson-Falk (Stanford) Zlatko Minev (Yale) Ravi Naik (U. Chicago) Anirudh Narla (Yale) Seita Onishi (UC Berkeley) Daniel Slichter (NIST) Yu-Dong Sun