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Josephson qubits P. Bertet SPEC, CEA Saclay (France), Quantronics group.

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Presentation on theme: "Josephson qubits P. Bertet SPEC, CEA Saclay (France), Quantronics group."— Presentation transcript:

1 Josephson qubits P. Bertet SPEC, CEA Saclay (France), Quantronics group

2 Outline Lecture 1: Basics of superconducting qubits Lecture 2: Qubit readout and circuit quantum electrodynamics Lecture 3: 2-qubit gates and quantum processor architectures 1) Two-qubit gates : SWAP gate and Control-Phase gate 2) Two-qubit quantum processor : Grover algorithm 3) Towards a scalable quantum processor architecture 4) Perspectives on superconducting qubits

3 Requirements for QC Deterministic, On-Demand Entanglement between Qubits High-Fidelity Readout of Individual Qubits 0 1 High-Fidelity Single Qubit Operations III.1) Two-qubit gates

4 Coupling strategies 1) Fixed coupling Entanglement on-demand ??? « Tune-and-go » strategy Coupling effectively OFF Entangled qubits Interaction effectively OFF Coupling activated in resonance for III.1) Two-qubit gates

5 Coupling strategies 2) Tunable coupling Entanglement on-demand ??? A) Tune ON/OFF the coupling with qubits on resonance Coupling OFF ( OFF ) Coupling activated for by ON Entangled qubits Interaction OFF ( OFF ) III.1) Two-qubit gates

6 Coupling strategies 2) Tunable coupling Entanglement on-demand ??? B) Modulate coupling Coupling OFF ( OFF ) Coupling ON by modulating Coupling OFF ( OFF ) III.1) Two-qubit gates IN THIS LECTURE : ONLY FIXED COUPLING

7 How to couple transmon qubits ? 1) Direct capacitive coupling coupling capacitor C c V g,II V g,I I II (note : idem for phase qubits)

8 J. Majer et al., Nature 449, 443 (2007) g g1g1 g2g2 Q I Q II R How to couple transmon qubits ? 2) Cavity mediated qubit-qubit coupling g eff =g 1 g 2 / Q I Q II III.1) Two-qubit gates

9 iSWAP Gate « Natural » universal gate : On resonance,() III.1) Two-qubit gates

10 i(t) 1 mm 200 µm qubits readout resonator coupling capacitor 50 µm Josephson junction frequency control fast flux line Transmon qubit λ/4 JJ coupling capacitor Readout Resonator Example : capacitively coupled transmons with individual readout (Saclay, 2011)

11 qubit 50 µm drive & readout frequency control Example : capacitively coupled transmons with individual readout III.1) Two-qubit gates

12 frequencies (GHz) I,II c c I g/ = 9 MHz Spectroscopy A. Dewes et al., in preparation III.1) Two-qubit gates

13 SWAP between two transmon qubits 5.13 GHz 5.32GHz 6.82 GHz 6.42 GHz Drive QB I QB II QB I f 01 Swap Duration 6.67 GHz 6.03GHz X Swap duration (ns) Pswitch (%) Raw data III.1) Two-qubit gates

14 SWAP between two transmon qubits 5.13 GHz 5.32GHz 6.82 GHz 6.42 GHz Drive QB I QB II QB I f 01 Swap Duration 6.67 GHz 6.03GHz X Pswitch (%) Data corrected from readout errors Swap duration (ns) III.1) Two-qubit gates

15 How to quantify entanglement ?? Need to measure exp Quantum state tomography |0> |1> X Z Y III.1) Two-qubit gates

16 How to quantify entanglement ?? Need to measure exp Quantum state tomography |0> |1> X Z Y /2(X) III.1) Two-qubit gates

17 How to quantify entanglement ?? Need to measure exp Quantum state tomography |0> |1> X Z Y /2(Y) M. Steffen et al., Phys. Rev. Lett. 97, (2006) III.1) Two-qubit gates

18 0 20 iSWAP X,Y tomo. readouts I II I Z ns I,X,Y How to quantify entanglement ?? 3*3 rotations*3 independent probabilities (P 00,P 01,P 10 ) = 27 measured numbers Fit experimental density matrix exp Compute fidelity III.1) Two-qubit gates

19 |00> |01> |10> |11> measured ideal |00> |11> |10> |01> F=98% F=94% swap duration (ns) switching probability How to quantify entanglement ?? A. Dewes et al., in preparation III.1) Two-qubit gates

20 SWAP gate of capacitively coupled phase qubits M. Steffen et al., Science 313, 1423 (2006) F=0.87 III.1) Two-qubit gates

21 The Control-Phase gate Another universal quantum gate : Control-Phase Surprisingly, also quite natural with superconducting circuits thanks to their multi-level structure F.W. Strauch et al., PRL 91, (2003) DiCarlo et al., Nature 460, (2009) III.1) Two-qubit gates

22 Control-Phase with two coupled transmons DiCarlo et al., Nature 460, (2009) III.1) Two-qubit gates

23 Spectroscopy of two qubits + cavity Qubit-qubit swap interaction cavity left qubit right qubit Cavity-qubit interaction Vacuum Rabi splitting Flux bias on right transmon (a.u.) (Courtesy Leo DiCarlo) III.1) Two-qubit gates

24 Preparation 1-qubit rotations Measurement cavity I One-qubit gates: X and Y rotations x y z Flux bias on right transmon (a.u.) (Courtesy Leo DiCarlo) III.1) Two-qubit gates

25 Preparation 1-qubit rotations Measurement cavity I x y z Flux bias on right transmon (a.u.) One-qubit gates: X and Y rotations (Courtesy Leo DiCarlo) III.1) Two-qubit gates

26 Preparation 1-qubit rotations Measurement cavity Q x y z Flux bias on right transmon (a.u.) see J. Chow et al., PRL (2009) Fidelity = 99% One-qubit gates: X and Y rotations III.1) Two-qubit gates

27 cavity Conditional phase gate Use control lines to push qubits near a resonance Flux bias on right transmon (a.u.) Two-qubit gate: turn on interactions (Courtesy Leo DiCarlo) III.1) Two-qubit gates

28 Two-excitation manifold Two-excitation manifold of system Avoided crossing (160 MHz) Flux bias on right transmon (a.u.) (Courtesy Leo DiCarlo) III.1) Two-qubit gates

29 Flux bias on right transmon (a.u.) Adiabatic conditional-phase gate 2-excitation manifold 1-excitation manifold (Courtesy Leo DiCarlo)

30 Adjust timing of flux pulse so that only quantum amplitude of acquires a minus sign: Implementing C-Phase1 C-Phase 11 (Courtesy Leo DiCarlo) III.1) Two-qubit gates

31 Position: I IIIII0 Find the queen! Implementing Grovers search algorithm Find x 0 ! DiCarlo et al., Nature 460, (2009) First implementation of q. algorithm with superconducting qubits (using Cphase gate) (Courtesy Leo DiCarlo) III.2) Two-qubit algorithm

32 Position: I IIIII0 Find x 0 ! Find the queen! Implementing Grovers search algorithm (Courtesy Leo DiCarlo) III.2) Two-qubit algorithm

33 Position: I IIIII0 Find x 0 ! Find the queen! Implementing Grovers search algorithm (Courtesy Leo DiCarlo) III.2) Two-qubit algorithm

34 Position: I IIIII0 Find x 0 ! Find the queen! Implementing Grovers search algorithm (Courtesy Leo DiCarlo) III.2) Two-qubit algorithm

35 Position: I IIIII0 Classically, takes on average 2.25 guesses to succeed… Use QM to peek inside all cards, find the queen on first try Find the queen! Implementing Grovers search algorithm (Courtesy Leo DiCarlo) III.2) Two-qubit algorithm

36 Grovers algorithm unknown unitary operation: Challenge: Find the location of the -1 !!! (= queen) oracle Previously implemented in NMR: Chuang et al. (1998) Linear optics: Kwiat et al. (2000) Ion traps: Brickman et al. (2005) (Courtesy Leo DiCarlo) III.2) Two-qubit algorithm

37 Begin in ground state: bcdf e g oracle Grover step-by-step DiCarlo et al., Nature 460, 240 (2009) (Courtesy Leo DiCarlo)

38 Create a maximal superposition: look everywhere at once! bcdf e g oracle Grover step-by-step DiCarlo et al., Nature 460, 240 (2009) (Courtesy Leo DiCarlo)

39 Apply the unknown function, and mark the solution bcdf e g oracle Grover step-by-step DiCarlo et al., Nature 460, 240 (2009) (Courtesy Leo DiCarlo)

40 Some more 1-qubit rotations… Now we arrive in one of the four Bell states oracle bcdf e g Grover step-by-step DiCarlo et al., Nature 460, 240 (2009) (Courtesy Leo DiCarlo)

41 Another (but known) 2-qubit operation now undoes the entanglement and makes an interference pattern that holds the answer! oracle bcdf e g Grover step-by-step DiCarlo et al., Nature 460, 240 (2009) (Courtesy Leo DiCarlo)

42 Final 1-qubit rotations reveal the answer: The binary representation of 2! Fidelity >80% bcdf e g oracle Grover step-by-step DiCarlo et al., Nature 460, 240 (2009) (Courtesy Leo DiCarlo)

43 III.3) Architecture Towards a scalable architecture ?? 1) Resonator as quantum bus …. |0> | register >

44 III.3) Architecture Towards a scalable architecture ?? 1) Resonator as quantum bus 2) Control-Phase Gate between any pair of qubits Qi and Qj …. |0> | register >

45 III.3) Architecture Towards a scalable architecture ?? 1) Resonator as quantum bus A) Transfer Qi state to resonator 2) Control-Phase Gate between any pair of qubits Qi and Qj …. SWAP

46 III.3) Architecture Towards a scalable architecture ?? 1) Resonator as quantum bus A) Transfer Qi state to resonator 2) Control-Phase Gate between any pair of qubits Qi and Qj …. B) Control-Phase between Qj and resonator C-Phase

47 III.3) Architecture Towards a scalable architecture ?? 1) Resonator as quantum bus A) Transfer Qi state to resonator 2) Control-Phase Gate between any pair of qubits Qi and Qj …. B) Control-Phase between Qj and resonator C) Transfer back resonator state to Qi SWAP

48 III.3) Architecture Problems of this architecture …. 1) Off-resonant coupling Qk to resonator Uncontrolled phase errors

49 III.3) Architecture Problems of this architecture …. 1) Off-resonant coupling Qk to resonator Uncontrolled phase errors 2) Effective coupling between qubits + spectral crowding g eff

50 RezQu (Resonator + zero Qubit) Architecture q qq q memory resonators qubits coupling bus resonator frequency q single gate memory coupled gate measure (tunneling) damped resonators zeroing (courtesy J. Martinis)

51 RezQu Operations Idling Transfers & single qubit gate |g reduces off coupling (>4 th order) Store in resonator (maximum coherence) i-SWAP C-Z (CNOT class) Measure tunnel time Intrinsic transfer % |g (courtesy J. Martinis)

52 Perspectives on superconducting qubits 1) Better qubits ?? Transmon in a 3D cavity H. Paik et al., arxiv:quant-ph (2011) REPRODUCIBLE improvement of coherence time (5 samples) T 1 =60 s T 2 =15 s

53 Perspectives on superconducting qubits Quantum feedback : retroacting on the qubit to stabilize a given quantum state « Non-linear » Circuit QED Resonator made non-linear by incorporating JJ. Parametric amplification, squeezing, back-action on qubit Quantum information processing : better gates and more qubits ! Hybrid circuits CPW resonators : versatile playground for coupling many systems : Electron spins, nanomechanical resonators, cold atoms, Rydberg atoms, qubits, … PhDs, Postdocs, WANTED


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