SUPERCONDUCTING QUBITS

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

4 – 20 GHz

0 ATOM/CAVITY

Tunable f, f

LIGHT SOURCE

M. Hatridge et al., B.R. Johnson et al., Phys. Rev. B 83 (2011) Nature Physics 6 (2010) DETECTOR HOMODYNE COUNTING 4-8 GHz LINEAR CAVITIES

3D Waveguide

Q ~ 106-109…

2D Planar

Q ~ 105-106… THE NON-DISSIPATIVE JOSEPHSON JUNCTION OSCILLATOR

Quantized Levels

 : phase difference I0 ~ nA

S I S

Non-linear Oscillator

II()sin() 0 d I0 >mA Vt( )( )  2e dt

UI( ) cos( ) 2e 0 THE DAWN OF COHERENCE

T1, T2 ~ 1 ns Al / AlOx / Al T1, T2 ~ 100 ms Al / AlOx / Al

Observation of High Coherence in Josephson Junction Qubits Measured in a Three- Dimensional Circuit QED Architecture SUPERCONDUCTING TRANSMON QUBIT

LJ ~ 13 nH C ~ 70 fF

• Tunable qubit frequency

• w01 ~ 5-8 GHz

• T , T ~ 100s ms J. Koch et al., Physical Review A 76, 042319 (2007) 1 2 Josephson tunnel junctions

500 nm 1 Cavity 0 Transmission

Frequency EXPERIMENTAL SETUP T = 4K

(~25 added photons) OUTPUT

INPUT DRIVE

T = 0.02 K SYSTEM NOISE TEMPERATURE

system noise w/o paramp = 7K PARAMETRIC AMPLIFICATION

LJ ~ 0.1 nH C ~ 10000 fF

2

0 W ( / 2 )

U I0 e

M. J. Hatridge et al., Phys. Rev. B 83, 134501 (2011) Tunnel SQUID Al Lumped LC junction Resonator 4-8 GHz Coupled to 50 W Q = 26 4mm Nb ground plane Flux line Capacitor

Capacitor

100 mm 4th GENERATION CRYOPACKAGE

• Aluminum superconducting shield

• Removable CPW launch

• Magnet for tuning frequency

• Copper cover • (prevents any coupling to box mode)

• Thermalizing strap

OUTLINE

• WEAK MEASUREMENT

• SINGLE QUBIT EXPERIMENTS – Individual Quantum Trajectories – Distribution of Quantum Trajectories

• TWO QUBIT MEASUREMENTS – Remote Entanglement WEAK MEASUREMENT PHASE SENSITIVE PHASE SENSITIVE HOMODYNE MEASUREMENT QUBIT STATEQUBIT ENCODEDIN PHASESHIFT I { reflectedsignal

Q {

1 I

0 Q MEASUREMENT: COUPLE TO E-M FIELD OF CAVITY (Jaynes-Cummings)

1 0 ∝ 푛 VARY MEASUREMENT STRENGTH Cavity USING DISPERSIVE SHIFT & Transmission PHOTON NUMBER

NEED TO DETECT ~ SINGLE

MICROWAVE PHOTONS in T1 ~ ms Frequency STRONG vs. WEAK MEASUREMENT

Weak

휏 CONTROL 푛

Strong READOUT/TOMOGRAPHY MEASUREMENT STRENGTH

1 0 Δ푉2 S=0.32 푆 = 휎2

64휏휒2푛 휂 푆 = S=3.2 휅 푛

t: measurement time c: dispersive shift : photon number S=7.0 푛 DV k: cavity decay rate h: detector efficiency 2s 휂 = 0.49 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 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). BACKACTION OF SINGLE QUADRATURE MEASUREMENT

Cavity Output q=0 After Amplification q=0 I I

pump • Obtain qubit state Q Q information • Tip Bloch vector

Cavity Output q=p/2 After Amplification q=p/2 I I

• Obtain cavity photon pump number information Q Q • Rotate Bloch vector INDIVIDUAL TRAJECTORIES

z

0

y 1 휏 x 푉푚 휏 = 푉 푡 푑푡 휏 0 1

• Prepare state along +x • Continuous weak measurement • Integrated readout is trajectory BAYESIAN UPDATE

P(V|) P(V|) P

V

Event: P P(V) A = Avalanche S = Snow > 10 feet

Likelihood: Prob. snow Prior: Historic chance V accompanied avalanche of an avalanche

푃 푆 퐴 푃(퐴) 푃 퐴 푆 = 푃(푆) P(V|) P() Posterior: Chance of an Prob. of Snow P(  V) = avalanche given snow P(V) WEAK MEASUREMENT OF THE QUBIT STATE

S=0.32

• Initial state along +X • Measure Z (phase quadrature)

푍 WANT 휎푍 |푉푚 ≝ 푍 푍 TO 휎푋 |푉푚 ≝ 푋 EVALUATE: 푍 TOMOGRAPHIC 휎푌 |푉푚 ≝ 푌 PROCEDURE: 푉 푆 푍푍 = tanh( 푚 ) BAYES 2Δ푉 RULE: 푍 2 −훾휏 푋 = 1 − 휎푍 푒 2 ∗ 훾 = 8휒 푛 1 − 휂 /휅 + 1/푇2 WEAK MEASUREMENT OF THE PHOTON NUMBER

푛 =0.46

휙 WANT 휎푍 |푉푚 ≝ 푍 TO 휙 휎푋 |푉푚 ≝ 푋 EVALUATE: 휙 푛 =0.46 휎푌 |푉푚 ≝ 푌

푆푉푚 BAYES 푋휙 = cos( )푒−훾휏 RULE: 2Δ푉 푆푉 푌휙 = sin( 푚 )푒−훾휏 2Δ푉 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) DISTRIBUTION OF QUANTUM TRAJECTORIES MEASUREMENT INDUCED DYNAMICS ONLY

Initial State along +x

Integration time t needed to resolve state: 1.25 ms MEASUREMENT w. POSTSELECTION

Initial State along +x Final State at z = -0.85

Can Identify Most Likely Path

Predict with Theory? EXTREMIZING THE QUANTUM ACTION

Classical Example: Kramer’s Escape L • Consider paths to saddle point L • Establish canonical phase space (p,q) • Define action S • Calculate most favorable path, etc…

Quantum Case for Pre/Post-Selected Trajectories: A. Chantasri, J. Dressel, A.N. Jordan, PRA 2013

• Consider paths connecting quantum state

qI qF • Double quantum state space ( canonical) • Express joint probability of measurement & trajectories as path integral • Calculate statistical distributions • Minimize action • Treat case of measurement backaction  ODE for equation of motion with control pulses W (Schrödinger dynamics) MEASUREMENT w. POSTSECLECTION: THEORY

Z

Initial State along +x Final State at z = -0.85

EOM for Optimized Path

X No Driving (W=0) −훾푡 푟 푡 푥 푡 = 푒 sech( 휏) r: detector output 푟 푡 max likelihood 푧 푡 = tanh( 휏) QUANTUM TRAJECTORIES WITH RABI DRIVING 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” DISTRIBUTION OF RABI TRAJECTORIES

Excellent agreement with ODE solutions CAN WE ENTANGLE TWO REMOTE SUPERCONDUCTING QUBITS via MEASUREMENT ?

“TRACKING ENTANGLEMENT GENERATION BETWEEN TWO SPATIALLY SEPARATED SUPERCONDUCTING QUBITS”

N. Roch et al., PRL 112, 170501, 2014 TWO DISTANT QUBITS

JOINT DISPERSIVE MEASUREMENT

I

Q

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

I

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

I

Q JOINT DISPERSIVE MEASUREMENT

I

Q WEAK CONTINUOUS MEASUREMENT

No classical OR quantum observer can discriminate eigenstates; system is perturbed, but not projected, by measurement.

Hatridge et al., Science 2013 MEASUREMENT HISTOGRAMS MEASUREMENT INDUCED ENTANGLEMENT TRAJECTORIES

Ensemble measurements:

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 PULSE SEQUENCE & ANALYSIS QUANTUM BAYESIAN UPDATE BAYESIAN TRAJECTORY RECONSTRUCTION BAYESIAN TRAJECTORY RECONSTRUCTION CONDITIONAL TOMOGRAPHY MAPPING 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 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