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Readout of superconducting flux qubits

Frontiers in Quantum Nanoscience A Sir Mark Oliphant & PITP Conference Noosa Blue Resort, 24 January 2006. Readout of superconducting flux qubits. Hideaki Takayanagi 髙柳 英明 NTT Basic Research Laboratories. H. Tanaka, S. Saito, H. Nakano, J. Johansson, F. Deppe,

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Readout of superconducting flux qubits

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  1. Frontiers in Quantum Nanoscience A Sir Mark Oliphant & PITP Conference Noosa Blue Resort, 24 January 2006 Readout of superconducting flux qubits Hideaki Takayanagi 髙柳 英明 NTT Basic Research Laboratories H. Tanaka, S. Saito, H. Nakano, J. Johansson, F. Deppe, T.Kutsuzawa,and K. Semba NTT Basic Research Labs. Tokyo University of Science CREST JST M. Ueda Tokyo Institute of Technology M. Thorwart Heinrich Heine University D. Haviland KTH Posters : Nakano (Berry Phase) Johansson（Vacuum Rabi)

  2. Sample size ～μm • e-beam lithography • Shadow evaporation • Lift-off Loop size SQUID ~ 7 x 7m2 qubit ~ 5 x 5m2 Mutual inductance M ~ 7 pH Josephson junctions Al / Al2O3 / Al Junction area SQUID : 0.1 x 0.08m2 qubit : 0.1 x 0.2 m2, ( a = 0.7 ) 5m IC(SQUID)~ 0.5 mA IC(qubit)~ 0.7 mA M Iq ISQ ~ 3.7 GHz

  3. Multi-photon transition Multi-photon transition between superposition of macroscopic quantum states ｰ ( ) /√21st excited state ＋ ( ) /√2ground state 3 3 2 2 1 1 3 1 2 2 3 1

  4. Analogy of Schroedinger’s cat Macroscopic Quantum state Transition induced by energy difference of single photon. Any superposition state can be prepared by adjusting a duration of resonant MW-pulse. superposition of macroscopically distinct states Qubit Excited state Qubit Ground state Resonant microwave photon Superconducting persistent current ~ 0.5 mA ( ~ 106 cooper pairs ) Φext : magnetic flux

  5. Multi-photon transition 3 2 １ 2 １ １ 3 RF : 3.8 GHz RF : 3.8 GHz 2 2 2 0 dBm -10 dBm 1 1 (nA) (nA) 2 0 0 １ SW SW d I d I -1 -1 -2 -2 1.504 1.496 1.498 1.500 1.502 1.496 1.498 1.500 1.502 1.504 F F / F F / qubit 0 qubit 0 Multi-photon spectroscopy S. Saito et al., PRL 93, 037001(2004) SQUID readout D=0.86GHz 1-photon 2 -photon

  6. Multiphoton Rabi Observation of multiphoton Qubit control by microwave pulse. Two colors Two photons Difference frequency Two colors Two photons Sum frequency Single color Multi photon Sum frequency Y. Nakamura, et al., PRL(2001)

  7. |e> |g> repetition: 3.3kHz ( 300 ms) RF pulse measurement RF pulse t |g> Ibias 70 ns 1200 ns ~100 nA |e> 0 t Discrimination of the signal Vmeas |g> 400 mV switching Vth |e> 0 Non-switching t

  8. Single color & Multi photon 1-photon Rabi 2-photon Rabi 3-photon Rabi 4-photon Rabi 10.25GHz x 3

  9. Two colors, Two photons & Sum frequency 10.25GHz, - 4dBm 10.25GHz, 4dBm 10.25GHz 16.2GHz

  10. Two colors, Two photons & Difference frequency 18.5GHz, 0dBm 18.5GHz, 8dBm 11.1GHz 18.5GHz

  11. Discussion Assume that the microwave is in the coherent state as is the solution of The probability to find the state in the ground state is With the conditions

  12. Comparisions between experiments and calculations Sum freq. Difference freq. a1 = 0.00741[mV-1] a2 = 0.0131 a1 = 0.0118 [mV-1] a2 = 0.00911

  13. Control Gates Rabi Oscillation W: Quantum bit oscillates between and with a frequency that is proportional to the amplitude of irradiated microwave. Any multiple qubit logic gate may be composed from CNOT and single qubit gates. p pulse：width of p/W Rotation Gate p/2 pulse Controlled-not gate A’ A B B’ + A B A’B’ 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 When A=1, B is reversed.

  14. Control of two angles in Bloch sphere q（Rabi）and　 （Ramsey） (t)   latitude Control of Ｒａｂｉ longitude Control of by introduce detuning Ramsey by phase shift ※ in a rotating frame π/2 Pulse π/2 Pulse

  15. Ψ Ψ Detuning method vs. Phase shift method with detuning t ⊿ｔ12 π/2Pulse π/2Pulse Equator Phase shift without detuning t π/2Pulse π/2Pulse ⊿ｔ12 ※ in a rotating frame

  16. Advantage of Phase shift method Ramsey （detuning method dｆ~0.2 GHz） ⊿Φ＝０ T=1/df～5ns ⊿Φ＝π/2 π/2 Pulse π/2 Pulse ⊿Φ＝π Ramsey （phase shift method dｆ=0 Hz） T=1/fR～88ps π/2 Pulse π/2 Pulse fR：RF ~ 11.4 GHz

  17. URF URF Ψ V Measurement scheme ⊿ｔ12 π/2 Pulse π/2 Pulse Read out voltage ｜１＞ ｜０＞ ensemble：１0,000 T=25mK

  18. ３. Fast Oscillation Av：10,000 times TPhaseShift=89 ps Resonant Frequancy １１．４[GHz] π/2 pulse => ５ [ns] Frequancy by fitting 11.18±0.01 [GHz] Dephasing time 1.84[ns] ⊿Φ＝π ⊿Φ＝０ ⊿Φ＝π/2 ⊿Φ＝3π/2

  19. We succeeded in observing Larmor precession ( 11.4 GHz ) of a flux qubit with phase shifted double pulse method. An arbitrary unitary transformation of a single qubit is possible. ・ Advantage ＞We can control qubit phase rapidly ( ~ 10 GHz ). 　　　→　We can save time for each quantum-gate operation 　　　→　Compared with the detuning method (~ 0.1 GHz ), 10 ～ 100 times many gates can be implemented.

  20. Artificial Atom in a Cavity Cavity QED I. Chiorescu et al, Nature 431, 159 (2004) A. Wallraff et al, Nature 431, 162 (2004)

  21. Measurement system E/M shielding (-100 dB) & Three-fold m-metal shield Dilution refridgerator (~ 20 mK) RF-line Ibias-line Vm-line sample package RF-line Ibias -line Vm-line

  22. Sample 5m SQUID qubit Vmeas Ibias Ibias Vmeas Csh MW On-chip component [1] LC mode、filtering capacitor( Csh ) resistor ( Ibias, Vmeas ) [2] strong driving： microwave line Microwave line

  23. Coherent dynamics of a flux qubit coupled to a harmonic oscillator Csh Csh Llead Llead Qubit Ibias Vmeas Microwave line Two macroscopic quantum systems Qubit coupled to a spatially separated LC-harmonic oscillator

  24. Flux-qubit entangled with the LC-oscillator Blue sideband Red sideband p -pulse Qubit, two-level system LC-harmonic oscillator |0, |1 |0, |1, ..., |N . . . MIqIcirc hFL hwp microwave field Iqubit, LC>

  25. Marking the lateral sidebands p-pulse |11 |10 p |01 |00 |11 |10 |01 |00 Qubit Rabi oscillations • qubit Larmor frequency 13.96 GHz • p-pulse length is determined by Rabi exp. • spectroscopy after or without a p-pulse

  26. Red sideband |11 |10 |10+ |01 p |01 |00 • Rabi oscillations |10  |01 for various powers, • after a p pulse |00  |10 • qubit Larmor frequency 13.96 GHz, oscillator frequency 4.31 GHz, red sideband at 9.65 GHz Driven, off-resonance, vacuum Rabi oscillations

  27. Blue sideband |11 |10 p |01 |00 conditional dynamics 2p • qubit Larmor frequency 13.96 GHz, oscillator frequency 4.19 GHz, blue sideband at 18.15 GHz |11 |10 |00+ |11 after p-pulse |01 |00 after 2p-pulse dbm |11

  28. Flux-qubit LC-oscillator system Poster: J. Johansson LC-plasma mode qubit coupling C=10 pF, L=0.14 nH  np = 4.3 GHz ~ 200 mK >> kBT~20 mK

  29. for cavity QED ( ENS Paris ) Qubit n=50, 51 Single mode cavity

  30. p-, 2p-pulse determined from Rabi oscillations p pulse 2p pulse 14GHz, -3dBm qubit Rabi oscillation 10.25GHz, -14dBm 20 mK

  31. spectroscopy under weak excitations anti-crossing is observed with help of the dumping pulse J. Johansson et al., in preparation

  32. Vacuum Rabi : measurement scheme |e1 |e0 p |g1 |g0 |e1 |e0 |g1 |g0 I qubit, LC-oscillator > |e1 |e0 |g1 2 → 3 |g0 excite qubit by a p-pulse shift qubit adiabatically shift qubit adiabatically readout qubit state 3 ⇔ 4 1 → 2 |e0 4 |g１ |g0

  33. Vacuum Rabi oscillations Direct evidence of level quantization in a 0.1 mm large superconducting macroscopic ＬＣ-circuit J. Johansson et al., submitted

  34. Influence of higher level occupation J. Johansson et al., submitted

  35. connection to cavity QED

  36. Harmonic oscillator ... qubit 2 qubit 1 readout SQUID for qubit 1 readout SQUID for qubit 2 : Josephson junction Multi qubit operation scheme Control signal ：RF line LC-resonator as a qubit coupler ・・・ ・・・ qubit 1 qubit 2 ・・・ n

  37. |e, 2> |e, 1> (b) |e, 0> (b) (a) (c) |g, 2> (a) |g, 1> |g, 0> ( b2 ) p/√ p/2 ( b2 ) p/√ p/2 (c) p/2 p (c) p/2 0 qubit 1 Map Map-1 harmonic oscillator qubit 2 ( b1 ) p 0 ( b1 ) p p angle phase qubit 1 ( b2 ) p 0 ( b2 ) p 0 2 2 qubit 2

  38. Coupled Flux Qubits

  39. Summary • Multi-photon Rabi oscillation • - between Macroscopically distinct states • Faster (q,j)-control  To make best use of the coherence time • - q-control : Rabi with strong driving • - j-control by composite pulse : Z(j)=X(p/2)Y(j)X(-p/2) • Coupling between qubit and LC-oscillator - Conditional spectroscopy of the coupled system • - Entanglement with an external oscillator • - Vacuum Rabi oscillations • Generation of “two qubit”-like states • a|00 + b|11anda|01 + b|10

  40. Flux-qubit, Atom chip team at NTT-BRL Atsugi

  41. MS+S2006 at NTT AtsugiFebruary 27-March 2, 2006 Int. Symp. on Mesoscopic Superconductivity & Spintronics ~ In the light of quantum computation ~ http://www.brl.ntt.co.jp/event/ms+s2006/ MS+S2004, March 2004

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