QUANTUM COHERENCE OF JOSEPHSON RADIO-FREQUENCY CIRCUITS OUTLINE

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1 INTERNATIONAL SCHOOL OF PHYSICS "ENRICO FERMI" QUANTUM COHERENCE IN SOLID STATE SYSTEMS QUANTUM COHERENCE OF JOSEPHSON RADIO-FREQUENCY CIRCUITS Michel Devoret, Applied Physics, Yale University, USA and Collège de France, Paris OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit BREAK 6. Coherence of Josephson circuits 7. Quantum bus concept 1

2 OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit 6. Coherence of Josephson circuits 7. Quantum bus concept IMPLEMENTATIONS OF A SINGLE, MANIPULABLE, QUANTUM-MECHANICALLY COHERENT SYSTEM micro PHOTON NUCLEAR SPIN ION ATOM MOLECULE ATOMIC-SIZE DEFECT IN CRYSTAL QUANTUM DOT coupling with env t. MACRO JOSEPHSON RF CIRCUIT (Leggett, '80) 2

CLASSICAL RADIO-FREQUENCY CIRCUITS Communications Hergé,

Army Photo WHAT IS A RADIO-FREQUENCY CIRCUIT?

element loop branch np V np I np node p TWO COLLECTIVE

DIPOLE ELEMENT AT EVERY INSTANT: Voltage across the

3 CLASSICAL RADIO-FREQUENCY CIRCUITS Communications Hergé, Moulinsart 1940's : MHz 2000's : GHz Computation Sony US Army Photo WHAT IS A RADIO-FREQUENCY CIRCUIT? A RF CIRCUIT IS A NETWORK OF ELECTRICAL ELEMENTS node n element loop branch np V np I np node p TWO COLLECTIVE DYNAMICAL VARIABLES CHARACTERIZE THE STATE OF EACH DIPOLE ELEMENT AT EVERY INSTANT: Voltage across the element: Current through the element: () Vnp t = E d n I t = j dσ np p () n p 3

4 CONSTITUTIVE RELATIONS EACH ELEMENT IS TAKEN FROM A FINITE SET OF ELEMENT TYPES EACH ELEMENT TYPE IS CHARACTERIZED BY A RELATION BETWEEN VOLTAGE AND CURRENT LINEAR NON-LINEAR inductance: V = L di/dt diode: I=G(V) capacitance: resistance: I = C dv/dt V = R I transistor: s g d I ds = G(I gs,v ds, ) V ds I gs = 0 QUANTUM INFORMATION ECONOMY suppose a function f j { 0,1023} k = f ( j) { 0,1023} Classically, need bit registers (10,000 bits) to store information about this function and to work on it. Quantum-mechanically, a 20-qubit register can suffice! Ψ = 1 2 N /2 N 2 1 j= 0 ( ) j f j 10 q-bits 10 q-bits Function encoded in a single quantum state of small register! (but a highly entangled one) 4

5 QUESTION: CAN WE BUILD A COMPLETE SET OF QUANTUM INFORMATION PROCESSING PRIMITIVES OUT OF SIMPLE CIRCUITS THAT WE WOULD CONNECT TO PERFORM ANY DESIRED FUNCTION? QUANTUM OPTICS QUANTUM RF CIRCUITS FIBERS, BEAMS BEAM-SPLITTERS MIRRORS LASERS PHOTODETECTORS ATOMS ~ TRANSM. LINES, WIRES COUPLERS CAPACITORS GENERATORS AMPLIFIERS JOSEPHSON JUNCTIONS DRAWBACKS OF CIRCUITS: ADVANTAGES OF CIRCUITS: ARTIFICIAL ATOMS PRONE TO VARIATIONS - PARALLEL FABRICATION METHODS - LEGO BLOCK CONSTRUCTION OF HAMILTONIAN - ARBITRARILY LARGE ATOM-FIELD COUPLING 5

6 OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit 6. Coherence of Josephson circuits 7. Quantum bus concept A CIRCUIT BEHAVING QUANTUM-MECHANICALLY AT THE LEVEL OF CURRENTS AND VOLTAGES? SIMPLEST EXAMPLE: SUPERCONDUCTING LC OSCILLATOR CIRCUIT d ~ 0.5 mm 6

7 A CIRCUIT BEHAVING QUANTUM-MECHANICALLY AT THE LEVEL OF CURRENTS AND VOLTAGES? SIMPLEST EXAMPLE: SUPERCONDUCTING LC OSCILLATOR CIRCUIT d ~ 0.5 mm MICROFABRICATION L ~ 3nH, C ~ 1pF, ω r /2π ~ 5GHz d << λ: LUMPED ELEMENT REGIME A CIRCUIT BEHAVING QUANTUM-MECHANICALLY AT THE LEVEL OF CURRENTS AND VOLTAGES? SIMPLEST EXAMPLE: SUPERCONDUCTING LC OSCILLATOR CIRCUIT d ~ 0.5 mm MICROFABRICATION L ~ 3nH, C ~ 1pF, ω r /2π ~ 5GHz d << λ: LUMPED ELEMENT REGIME SUPERCONDUCTIVITY ONLY ONE COLLECTIVE VARIABLE INCOMPRESSIBLE ELECTRONIC FLUID SLOSHES BETWEEN PLATES. NO INTERNAL DEGREES OF FREEDOM. 7

8 DEGREE OF FREEDOM IN ATOM vs CIRCUIT: SEMI-CLASSICAL DESCRIPTION Rydberg atom Superconducting LC oscillator L C DEGREE OF FREEDOM IN ATOM vs CIRCUIT: SEMI-CLASSICAL DESCRIPTION Rydberg atom Superconducting LC oscillator L C 2 Possible correspondences: charge dynamics velocity of electron current through inductor force on electron voltage across capacitor field dynamics velocity of electron voltage across capacitor force on electron current through inductor 8

9 DEGREE OF FREEDOM IN ATOM vs CIRCUIT Rydberg atom semiclassical picture Superconducting LC oscillator L φ C 2 Possible correspondences: charge dynamics velocity of electron current through inductor force on electron voltage across capacitor field dynamics velocity of electron voltage across capacitor force on electron current through inductor FLUX AND CHARGE IN LC OSCILLATOR φ electrical world I +Q V -Q φ = LI -I Q = CV M mechanical world f X k 1 X X = eq k f P = MV position variable: φ X-X eq momentum variable: Q P gener alized force : Ι f gener alized velocity: V V gener alized mass : C M gener alized spring const ant : 1/L k 9

10 HAMILTONIAN FORMALISM electrical world mechanical world φ I +Q -Q V M f X k H charge on capacitor ( φ, Q) conjugate variables time-integral of voltage on capacitor ( φ φ ) 2 eq 2 Q = + 2C 2L momentum of mass (, ) H X P conjugate variables position of mass w/r wall ( ) 2 2 P k X X eq = + 2M 2 HAMILTON'S EQUATION OF MOTION electrical world mechanical world φ I +Q -Q V M f X k H Q φ = = Q C H δφ Q = = φ L ω = r 1 LC H P X = = P M H P = = kδ X X ω = r k M 10

11 FROM CLASSICAL TO QUANTUM PHYSICS: CORRESPONDENCE PRINCIPLE X Xˆ P Pˆ (, ) Hˆ ( Xˆ, Pˆ) H X P AB AB = { A, B} Aˆ, Bˆ / i PB X P P X Poisson bracket {, } 1 ˆ, ˆ X P = X P = i PB position operator momentum operator hamiltonian operator commutator position and momentum operators do not commute FLUX AND CHARGE DO NOT COMMUTE φ I +Q -Q V For every branch in the circuit: ˆ φ, Qˆ = i We have obtained this result thru correspondance principle after having recognized flux and charge as canonical conjugate coordinates. "Cannot quantize the equations of the stock market!" A.J. Leggett We can also obtain this result from quantum field theory thru the commutation relations of the electric and magnetic field. Tedious. 11

12 LC CIRCUIT AS QUANTUM HARMONIC OSCILLATOR E φ +Q -Q hω r ( aˆ aˆ ) Hˆ = ω 1 r + 2 ˆ φ Qˆ ˆ φ Qˆ ˆ ; ˆ φ Q φ Q a= + i a = i φ = r Q r = r r r r 2 ω L r 2 ω C r 0 φ annihilation and creation operators SUPPRESSION OF THERMAL EXCITATION OF LC CIRCUIT φ E I hω r φ Can place the circuit in its ground state ω r kt 5 GHz 10mK B 12

13 φ WAVEFUNCTIONS OF LC CIRCUIT E I hω r In every energy eigenstate, (photon state) current flows in opposite directions simultaneously! Ψ(φ) Ψ 1 2φ r 0 Ψ 0 φ φ EFFECT OF DAMPING E φ important: as little dissipation as possible φ dissipation broadens energy levels i 1 En = ωr n see Q more Q = RCω later r 13

14 ALL TRANSITIONS ARE DEGENERATE φ E hω r φ CANNOT STEER THE SYSTEM TO AN ARBITRARY STATE IF PERFECTLY LINEAR NEED NON-LINEARITY TO FULLY REVEAL QUANTUM MECHANICS Potential energy Position coordinate 14

15 OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit 6. Coherence of Josephson circuits 7. Quantum bus concept JOSEPHSON JUNCTION PROVIDES A NON-LINEAR INDUCTOR 1nm S I S superconductorinsulatorsuperconductor tunnel junction L J C j 15

16 JOSEPHSON JUNCTION PROVIDES A NON-LINEAR INDUCTOR 1nm S I S superconductorinsulatorsuperconductor tunnel junction L J C j Ι t ( ') φ = V t dt' JOSEPHSON JUNCTION PROVIDES A NON-LINEAR INDUCTOR 1nm S I S superconductorinsulatorsuperconductor tunnel junction L J C j Ι Ι Ι = φ / L J L J 2 φ0 φ0 = = E I J 0 t ( ') φ = V t dt' φ ( ) I = I sin φ / φ 0 0 φ 0 = 2e 16

17 COUPLING PARAMETERS OF THE JOSEPHSON JUNCTION "ATOM" REST OF CIRCUIT q ext I t φ = ˆ V ( t' ) dt' t Q ( ) = ˆ I t' dt' THE hamiltonian: (we mean it!) H j 1 ( ) 2 cos 2 eφ = Q qext EJ 2C j COUPLING PARAMETERS OF THE JOSEPHSON JUNCTION "ATOM" REST OF CIRCUIT q ext THE hamiltonian: (we mean it!) H j 1 ( ) 2 cos 2 eφ = Q qext EJ 2C j Comparable with lowest order model for hydrogen atom H 2 1 ea e 1 = pˆ 2m 4πε rˆ e

18 Two dimensionless variables: Hamiltonian becomes : TWO ENERGY SCALES H 2e ˆ φ ˆ ϕ = ˆ ˆ Q N = 2e j ˆ, ϕ Nˆ = i ( N N ) 2 ext = 8E cos ˆ C EJ ϕ 2 Coulomb charging energy for 1e Josephson energy E C 2 e = 2C j reduced offset charge q et x Next = 2e E J = valid for opaque barrier barrier transp cy 1 NT Δ 8 gap # cond ion channels LOW-LYING EXCITATIONS OF ISOLATED JUNCTION: CHARGE STATES + + +ne -ne 2Δ e tunneling CP tunneling E J n = N/2 = E C 18

19 MECHANICAL ANALOG OF JOSEPHSON COUPLING ENERGY rotating magnet angular velocity: 4E C N ext Ω= h compass needle ˆϕ needle angular momentum: Nh torque on needle due to magnet velocity of needle in magnet frame current through junction voltage across junction CHARGE STATES vs PHOTON STATES A 2 n N A 1 θ ϕ Hilbert spaces have different topologies 19

independent of DC value of N ext credit I. Siddiqi and F.

20 HARMONIC APPROXIMATION H j ( N N ) 2 ext = 8E cos ˆ C EJ ϕ 2 H jh, ( N N ) 2 2 ext ˆ ϕ = 8EC + EJ 2 2 Josephson plasma frequency ω = P 8 C E E J Spectrum independent of DC value of N ext credit I. Siddiqi and F.Pierre TUNNEL JUNCTIONS IN REAL LIFE credit L. Frunzio and D. Schuster E J ~ 50K ω p ~ 30-40GHz E J ~ 0.5K 100nm 20

21 OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit 6. Coherence of Josephson circuits 7. Quantum bus concept 3 TYPES OF BIASES charge flux current I 0 I 0 I 0 2C g C U 2C g L C Φ b C I b 21

22 EFFECTIVE POTENTIAL OF 3 BIAS SCHEMES charge bias flux bias phase bias ϕ 2eφ = 2π h CEA Saclay, Yale NEC, Chalmers, JPL,... 2eφ h TU Delft, NEC, NTT, MIT UC Berkeley, IBM, SUNY IPHT Jena... 2eφ h UC Berkeley, NIST, UCSB, U. Maryland, CRTBT Grenoble... EFFECTIVE POTENTIAL OF 3 BIAS SCHEMES charge bias flux bias -1 2eφ +1 phase bias h CEA Saclay, Yale NEC, Chalmers, JPL,... 2eφ h TU Delft, NEC, NTT, MIT UC Berkeley, IBM, SUNY IPHT Jena... 2eφ h UC Berkeley, NIST, UCSB, U. Maryland, CRTBT Grenoble... 22

23 U COOPER PAIR "BOX" Φ island U 2 control parameters C g U/2e and Φ/Φ 0 C g Φ Bouchiat et al. 97 Nakamura, Pashkin & Tsai 99 Vion et al ANHARMONICITY vs CHARGE SENSITIVITY Cooper pair box soluble in terms of Mathieu functions (A. Cottet, PhD thesis, Orsay, 2002) 23

ANHARMONICITY vs CHARGE SENSITIVITY IN THE LIMIT E C /E J << 1 ("TRANSMON") anharmonicity: ω12 ω01 EC 12 01 /2 8EJ ( ω + ω ) peak-to-peak charge modulation amplitude of level m: J. Koch et al.

24 ANHARMONICITY vs CHARGE SENSITIVITY IN THE LIMIT E C /E J << 1 ("TRANSMON") anharmonicity: ω12 ω01 EC /2 8EJ ( ω + ω ) peak-to-peak charge modulation amplitude of level m: J. Koch et al. 07 TRANSMON: SHUNT JUNCTION WITH CAPACITANCE 290 μm Courtesy of J. Schreier and R. Schoelkopf SPECTROSCOPY OF A COOPER PAIR BOX IN TRANSMON REGIME ω 12 J. Schreier et al. 07 ω 02 2 ω 12 ω 02 2 ω 01 ω 01 ω ω = Anharmonicity: MHz C Sufficient to control the junction as a two level system E Slide courtesy of J. Schreier and R. Schoelkopf T 1 > 2μs 24

25 ATOM IN SEMI-CLASSICAL REGIME: CIRCULAR RYDBERG ATOM 2r n old Bohr theory essentially exact! 2 meωr = n constraint Coulomb potential p+ ω n r n E = a n n (,, ) 2 Ψ n x yz 0 ωn n ± 1 = 3 d n n± 1 2 Ry = 2 n Ry 2 n ern = 2 valid when: ω ( E) 1 E TRANSMON AS ANALOG OF CIRCULAR RYDBERG ATOMS Josephson potential energy 2E J π Spectroscopic lines (high T): +π Junction phase ϕ ω ω ω ω 12ω 01 nn, + 1 n+ 1, n+ 2 nn, ω 25

26 TRANSMON AS ANALOG OF CIRCULAR RYDBERG ATOMS Josephson potential energy 2E J π +π Junction phase ϕ Spectroscopic lines (low T): ω OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit 6. Coherence of Josephson circuits 7. Quantum bus concept 26

27 THE READOUT PROBLEM QUBIT OFF ON READOUT or 1 THE READOUT PROBLEM QUBIT OFF ON READOUT QUBIT OFF ON READOUT 0 1 QUBIT OFF ON READOUT 0 1 WANT: 1) SWITCH WITH LARGE ON-OFF RATIO 2) FAITHFUL READOUT CIRCUIT 27

28 DIVERSITY OF CIRCUIT STRATEGIES SACLAY -- YALE (Quantronium) TU DELFT -- NEC -- NTT YALE (circuit-qed) NIST -- UCSB analogous to cavity QED expts by Haroche, Raimond, Brune et al. DISPERSIVE READOUT STRATEGY rf signal in ω ω 01 QUBIT CHIP 0 or 1 28

29 DISPERSIVE READOUT STRATEGY rf signal in rf signal out or QUBIT CHIP 0 or 1 QUBIT STATE ENCODED IN PHASE OF OUTGOING SIGNAL, NO ENERGY DISSIPATED ON-CHIP DISPERSIVE READOUT STRATEGY rf signal in rf signal out or 0 QUBIT CHIP or 1 Requirements: 1) low noise in detection 2) enough phase shift DO WITH ENOUGH PHOTONS TO GET 1 CLASSICAL BIT OF INFORMATION 29

30 DISPERSIVE READOUT STRATEGY rf signal in rf signal out or 0 QUBIT CHIP or 1 Requirements: 1) low noise in detection 2) enough phase shift DO WITH ENOUGH PHOTONS TO GET 1 CLASSICAL BIT OF INFORMATION PLACE QUBIT IN MICROWAVE CAVITY TO FILTER OUT IRRELEVANT PART OF SPECTRUM SUPERCONDUCTING MICROWAVE RESONATOR: ANALOG OF FABRY-PEROT CAVITY Al or Nb mirror = capacitors Si or Al2O3 length ~1cm, but photon propagation length ~ 10km! can get Q up to 10 6 ( in bulk: Q ~ ) COPLANAR WAVEGUIDE: 2D VERSION OF COAXIAL CABLE 30

31 SUPERCONDUCTING MICROWAVE RESONATOR: ANALOG OF FABRY-PEROT CAVITY Al or Nb RF GEN. ~ Si or Al2O3 length ~1cm, but photon propagation length ~ 10km! IN CHIP OUT can get Q up to 10 6 ( in bulk: Q ~ ) ADC SUPERCONDUCTING MICROWAVE RESONATOR: ANALOG OF FABRY-PEROT CAVITY ν ~ 10GHz w~20μm Al or Nb Si or Al2O3 length ~ 1cm, but photon decay length ~ 10km! can get Q up to 10 6 ( in bulk: Q ~ ) CHIP ~ IN OUT ADC VERY SMALL MODE VOLUME 1/2 photon: ~1nA ~100nV 31

32 SUPERCONDUCTING CAVITY = FABRY-PEROT 10mm 3mm Nb 100μm qubit goes here "QUANTRONIUM" IN MICROWAVE CAVITY CPW ground READOUT JUNCTION ISLAND 10µm CPW ground 32

33 HIGH FREQUENCIES, LOW TEMPERATURES 2-20 GHz mk QUANTRONIUM IN MICROWAVE CAVITY OFF-RESONANT NMR-TYPE PULSE SEQUENCE FOR QUBIT MANIPULATION 33

34 QUANTRONIUM IN MICROWAVE CAVITY READOUT PROBING PULSE or 0> 1> QUBIT STATE ENCODED IN PHASE OF TRANSMITTED PULSE QUANTRONIUM IN MICROWAVE CAVITY Metcalfe et al. Phys. Rev. B (2007) 0> 200ns 40ns 40ns t 1> t AWG ~ ADC IN OUT 34

35 QUANTRONIUM IN MICROWAVE CAVITY Metcalfe et al. Phys. Rev. B (2007) 0> 200ns 40ns 40ns t 1> t AWG ~ ADC IN OUT latching effect due to bifurcation of cavity mode CAVITY BIFURCATION : ANALOG OF OPTICAL BISTABILITY 35

36 HYSTERESIS 0 Ω/2π = 4.2GHz T=15mK 1 ms sweep 1 MEASUREMENT OF READOUT FIDELITY π pulse U rf Relaxation induced by readout Slope 3 times too small compared with thy U rf TOO MANY READOUT PHOTONS? 36

37 JOSEPHSON PARAMETRIC AMPLIFIER SIGNAL Bergeal et al. 08 Josephson ring modulator Φ 0 /2 180º hybrid coupler Design goals: T N < hf/k B Gain > 20 db Bandwidth > 5 MHz Dynamic range > 20 db chip IDLER OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit 6. Coherence of Josephson circuits 7. Quantum bus concept 37

38 CAVITY QUANTRONIUM RABI OSCILLATIONS 0 1 ν Larmor =14.5GHz M. Metcalfe et al. RAMSEY FRINGES 60% 40% 20% T2 =500ns ns 0 acquisition time (s) 1 38

39 DISTRIBUTION OF RAMSEY DATA method A of van Harlingen et al Lopsided frequency fluctuations (Karlsruhe) E J /E C = 3.6 SN g 1/f Charge noise amplitude 2 α 3 ( ω) =, α e ω value OK DISTRIBUTION OF RAMSEY DATA van Harlingen et al Lopsided frequency fluctuations (Karlsruhe) Need larger E J /E C SN g 1/f Charge noise amplitude 2 α 3 ( ω) =, α e ω value OK 39

DECOHERENCE TIME ( T 2 ) Δt ν Larmor =18.984GHz Q φ = ω Larmor T 2 '02 Vion et al. 50,000 '05 Siddiqi et al. 30,000 '05 Wallraff et al. 19,000 '06 Metcalfe et al. 70,000 '08 Houck et al.

40 DECOHERENCE TIME ( T 2 ) Δt ν Larmor =18.984GHz Q φ = ω Larmor T 2 '02 Vion et al. 50,000 '05 Siddiqi et al. 30,000 '05 Wallraff et al. 19,000 '06 Metcalfe et al. 70,000 '08 Houck et al. 100,000 Δt (ns) 1 param. fit T 2 = 300ns Siddiqi et al, 06 SENSITIVITY OF BIAS SCHEMES TO NOISE (EXP D ) CHARGED IMPURITY TUNNEL CHANNEL junction noises bias ΔQ off ΔE J ΔE C charge flux ELECTRIC DIPOLES phase charge qubit flux qubit phase qubit 40

41 OUTLINE 1. Motivation: Josephson circuits and quantum information 2. Quantum-mechanical superconducting LC oscillator 3. A non-dissipative, non-linear element: the Josephson junction 4. The Cooper pair box artificial atom circuit 5. Readout of the Cooper pair box qubit 6. Coherence of Josephson circuits 7. Quantum bus concept QUANTUM BUS CONCEPT FOR SOLID STATE QUBITS Nature, 27 Sept microwave transmission line resonator artificial atom coupling element 41

42 Msmt. of qubit-cavity avoided crossing cavity STRONG QUBIT-CAVITY COUPLING qubit vacuum Rabi splitting 2g = 250 MHz! ~ ~ ADC IN OUT CPB RESOLVING PHOTON NUMBER IN CAVITY P( n) = ( n) n! n e n Mean shifts Peaks are Poisson distributed Peaks get broader n Houck et al., Nature 07 42

43 RESOLVING PHOTON NUMBER IN CAVITY CONDITIONAL QUBIT ROTATION POSSIBLE! SCHEMATIC OF 2 COOPER PAIR BOXES IN A MICROWAVE CAVITY Blais A. et al., Phys. Rev. A 75,

SWAPPING INFORMATION BETWEEN QUBITS Nota Bene: (Using first generation transmon with short T2=100 ns.) Background due to off-resonant driving by the Stark tone J.

Chow et al, Nature, 449, 443 (2007) Similar results with phase qubits: Sillanpaa et al, Nature, 449, 438 (2007) PERSPECTIVES QUANTUM COMPUTATION violation of Bell's

44 SWAPPING INFORMATION BETWEEN QUBITS Nota Bene: (Using first generation transmon with short T2=100 ns.) Background due to off-resonant driving by the Stark tone J. Majer, J. M. Chow et al, Nature, 449, 443 (2007) Similar results with phase qubits: Sillanpaa et al, Nature, 449, 438 (2007) PERSPECTIVES QUANTUM COMPUTATION violation of Bell's inequalities teleportation error correction algorithms Q φ ~ 10 7 NEW MATERIALS? MEASUREMENTS AND CONTROL OF QUANTUM ENGINEERED SYSTEMS amplification at the quantum limit quantum noise squeezing (1-mode and 2-mode) quantum feedback single photon detection for radioastronomy charge counting for metrology Q φ ~ 10 4 OK 44

45 Circuit Quantum Electrodynamics Groups Depts. Applied Physics and Physics, Yale P.I.'s Grads Post-Docs Res. Sc. Undrgrds Collab. M. D. R. VIJAY C. RIGETTI M. METCALFE V. MANUCHARIAN I. SIDDIQI (UCB) E. BOAKNIN (Mtrl) N. BERGEAL P. HYAFIL S. FISSETTE D. ESTEVE (Saclay) R. SCHOELKOPF J. CHOW B. TUREK J. SCHREIER B. JOHNSON A. WALRAFF (ETH) H. MAJER (Vienna) A. HOUCK D. SCHUSTER L. FRUNZIO J. SCHWEDE P. ZOLLER (Innsbruck) S. GIRVIN T. YU L. BISHOP J. KOCH J. GAMBETTA F. MARQUARDT (Munich) A. BLAIS (Sherbrooke) A. CLERK (McGill) 45

JOSEPHSON QUBIT CIRCUITS AND THEIR READOUT

JOSEPHSON QUBIT CIRCUITS AND THEIR READOUT Michel DEVORET, Applied Physics and Physics, Yale University Sponsors: W.M. KECK Final version of this presentation available at http://qulab.eng.yale.edu/archives.htm