Frontiers in Quantum Nanoscience A Sir Mark Oliphant

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 Posters : Nakano (Berry Phase) Johansson（Vacuum Rabi) 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

Sample size ～μm • • • e-beam lithography Shadow evaporation Lift-off Loop size SQUID ~ 7 x 7 m 2 qubit ~ 5 x 5 m 2 Mutual inductance M ~ 7 p. H 5 m IC(SQUID)~ 0. 5 A IC(qubit)~ 0. 7 A M Iq ISQ ~ 3. 7 GHz Josephson junctions Al / Al 2 O 3 / Al Junction area SQUID : 0. 1 x 0. 08 m 2 qubit : 0. 1 x 0. 2 m 2, ( a = 0. 7 )

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

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 Ground state Superconducting persistent current ~ 0. 5 A ( ~ 106 cooper pairs ) Resonant microwave photon Φext : magnetic flux Qubit Excited state

Multi-photon transition Multi-photon spectroscopy S. Saito et al. , PRL 93, 037001(2004) SQUID readout 2 RF : 3. 8 GHz -10 d. Bm d I SW (n. A) 1 0 3 2 １ D=0. 86 GHz 2 -1 1 -photon １ -2 1. 496 1. 498 1. 500 Fqubit / F 0 2 1. 502 RF : 3. 8 GHz 0 d. Bm d I SW (n. A) 1 0 1. 504 １ 3 2 -1 -2 1. 496 2 1. 498 １ 1. 500 F / F 0 qubit 1. 502 1. 504 2 -photon

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

RF pulse|e> measurement repetition: 3. 3 k. Hz ( 300 s) RF pulse |g> Ibias ~100 n. A t 70 ns 1200 ns |e> 0 t Discrimination of the signal Vmeas 400 V Vth 0 |g> switching |e> Non-switching t

Single color & Multi photon 1 -photon Rabi 10. 25 GHz x 3 2 -photon Rabi 3 -photon Rabi 4 -photon Rabi

Two colors, Two photons & Sum frequency 10. 25 GHz, - 4 d. Bm 10. 25 GHz 16. 2 GHz 10. 25 GHz, 4 d. Bm

Two colors, Two photons & Difference frequency 18. 5 GHz, 0 d. Bm 11. 1 GHz 18. 5 GHz, 8 d. Bm

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 With the conditions is

Comparisions between experiments and calculations Sum freq. a 1 = 0. 00741[m. V-1] a 2 = 0. 0131 Difference freq. a 1 = 0. 0118 [m. V-1] a 2 = 0. 00911

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. Rotation Gate p pulse：width of p/W p/2 pulse Controlled-not gate A’ A B + AB 0 0 0 1 1 B’ A’B’ 0 0 When A=1, 0 1 B is reversed. 1 1 1 0

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

Detuning method vs. Phase shift method 　with detuning t π/2 Pulse ⊿ｔ 12 π/2 Pulse Equator Ψ Phase shift without detuning t ※ in a rotating frame π/2 Pulse ⊿ｔ 12 π/2 Pulse Ψ

Advantage of Phase shift method Ramsey （detuning method dｆ~0. 2 GHz） T=1/df～ 5 ns ⊿Φ＝０ ⊿Φ＝π/2 Pulse ⊿Φ＝π Ramsey （phase shift method dｆ=0 Hz） π/2 Pulse T=1/f. R～ 88 ps f. R：RF ~ 11. 4 GHz

Measurement scheme URF π/2 Pulse ⊿ｔ 12 Ψ π/2 Pulse Read out voltage ｜１＞ ｜０＞ V T=25 m. K ensemble：１ 0, 000

３. Fast Oscillation Av： 10, 000 times TPhase. Shift=89 ps Resonant Frequancy １１．４[GHz] π/2 pulse => ５ [ns] Frequancy by fitting 11. 18± 0. 01 [GHz] ⊿Φ＝０ ⊿Φ＝π/2 ⊿Φ＝π ⊿Φ＝ 3π/2 Dephasing time 1. 84[ns]

• 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.

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

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

Sample I bias Csh V meas I bias V meas M W SQUID qubi t Microwave line 5 m On-chip component 　 [1] LC mode、filtering 　　capacitor( Csh ) resistor ( Ibias, Vmeas ) [2] strong driving： 　　microwave line

Coherent dynamics of a flux qubit coupled to a harmonic oscillator Csh Llead I bias Llead Qubit V meas Microwave line Two macroscopic quantum systems Qubit coupled to a spatially separated LC-harmonic oscillator

Flux-qubit entangled with the LC-oscillator Qubit, two-level system |0 , |1 h. FL LC-harmonic oscillator |0 , |1 , . . . , |N MIq. Icirc microwave field Iqubit, LC> Blue sideband Red sideband p -pulse . . . h wp

Marking the lateral sidebands p-pulse Qubit Rabi oscillations qubit Larmor frequency 13. 96 GHz p-pulse length is determined by Rabi exp. spectroscopy after or without a p-pulse |10 |11 p |00 |10 |01 |11 |01

Red sideband 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 |10 |11 |10 + |01 p |00 |01 Driven, off-resonance, vacuum Rabi oscillations

Blue sideband qubit Larmor frequency 13. 96 GHz, oscillator frequency 4. 19 GHz, blue sideband at 18. 15 GHz |10 |11 |00 + |11 after p-pulse |00 |01 after 2 p-pulse dbm |10 p |11 2 p |00 |01 |11 conditional dynamics

Flux-qubit LC-oscillator system Poster: J. Johansson LC-plasma mode 　　 　 　　qubit 　　　　　 coupling C=10 p. F, L=0. 14 n. H np = 4. 3 GHz ~ 200 m. K >> k. BT~20 m. K

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

p-, 2 p-pulse determined from Rabi oscillations p pulse 10. 25 GHz, -14 d. Bm qubit Rabi oscillation 2 p pulse 14 GHz, -3 d. Bm 20 m. K

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

Vacuum Rabi : measurement scheme I qubit, LC-oscillator >　 |e 1 |e 0 p |g 0 excite qubit by a p-pulse 1→ 2 |e 1 |e 0 |g 1 2→ 3 |g 1 |g 0 shift qubit adiabatically 3⇔ 4 shift qubit adiabatically |g 0 readout qubit state |e 0 4 |g１ |g 0

Vacuum Rabi oscillations Direct evidence of level quantization in a 0. 1 mm large superconducting macroscopic ＬＣ-circuit J. Johansson et al. , submitted

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

connection to cavity QED

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

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

Coupled Flux Qubits

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 and a|01 + b|10

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

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