Quantum in a superconducting flux Yasunobu Nakamura NEC Fundamental Research Laboratories Frontier Research System, RIKEN Irinel Chiorescu, Kees Harmans, Hans Mooij Department of NanoScience, TU Delft Collaborators

TU Delft NEC/RIKEN () Hannes Majer (®Yale) Yuri Pashkin Adrian Lupascu Tsuyoshi Yamamoto Kouichi Semba (NTT) Oleg Astafiev Raymond Schouten JawShen Tsai Alexander ter Haar Fumiki Yoshihara Lieven Vandersypen Michio Watanabe

Discussions with CEA Saclay Daniel Esteve Abdel Aassime Denis Vion Cristian Urbina Motivation

• Coherent control of an artificial two-level system in solid-state device • Understanding the mechanism of decoherence

f

2 mm Charge qubit and flux (phase) qubit

Cooper-pair box RF-SQUID

n Variety of Josephson-junction small large

charge phase (flux) phase (flux) phase Cooper-pair box 3-junction loop RF-SQUID Current-biased JJ

NEC Tsukuba Delft IBM Yorktown Kansas Chalmers/Yale Heights NIST Boulder

Saclay (large EJ/EC) coherent/Rabi osc. Rabi osc. coherent osc. Rabi osc. Ramsey, echo Ramsey, echo coupled qubits Cooper-pair box: a charge qubit

f • sensitive to charge fluctuations • decoherence time ~ ns

Single Cooper-pair Tunnel tunneling Reservoir junction

SQUID loop Gate Box Probe

Nakamura et al. Nature 398, 786 (1999) Rabi oscillations in “Quantronium”

Vg

55

t meas. 50 Ä Fex 45

40

• Large switching probability (%) 35 • Operation at optimal point

• Long decoherence time ~ 0.5 ms 30 0.0 0.5 1.0 RF pulse duration t (ms)

CEA Saclay Vion et al. Science 296, 886 (2002) Optimal operation point

control

readout Rabi Oscillations in a Large Josephson-Junction Qubit John Martinis, S. Nam, J. Aumentado (NIST Boulder) ; C. Urbina (CNRS/CEA Saclay)

1 Qubit Rabi Oscillations

mwaves 0.8 17 ns

0.6 Isolates qubit w10 w21 from dissipation of leads 0.4

100 mm (occupation prob.) 0.2 1 p tcoh ~ 10-20 ns

0 Josephson junction qubit: 0 1 2 3 4 5 6 7 1/2 nonlinear LC resonator (P10) (power, a.u.)

LJ C • Demonstrated qubit operation U • State preparation - fidelity of >99% = 0 = 1 mV • State manipulation - Rabi oscillations w measurement pulse |1> 21 • State measurement - fidelity of 85% w10 Rabi oscillations |0> • Scalable system - large junctions, microfab. • ~1 ms coherence times at Saclay, U. Kansas 3-Josephson-junction loop qubit

Loop inductance is not necessary Þ small loop can be used cf. RF-SQUID (single-junction loop) requires ~100-mm loop Mooij et al. Science 285, 1036 (1999) Energy levels

• Two-level approximation holds in a narrow range of gq • Relatively immune to charge fluctuations

100 15 10

5 0 0 Ene rgy ( GH z)

Energy (GHz) -5

-100 -10 0.8 1.0 1.2 0.98 0.99 1.00 1.01 1.02 / gq p gq/p Sample qubit + readout SQUID

2 mm Qubit signal: Energy levels and circulating current

Optimal operation point (no signal)

100

0

Readout point (large signal) Ene rgy ( GH z)

-100 0.8 1.0 1.2 / gq p Qubit operation at optimal point

and readout after adiabatic bias phase shift

gqubitg=qubit p psi1 at operation point psi1 at readout point

-42

adiabatic shift

C -44

psi0 E / psi0 -46

bias -48

operation read-out -50 point point

0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53 0.54 frustration Bias phase shift

Automatic phase shift is induced by SQUID bias current increase

~ 0.01p

critical current Qubit readout: switching current measurement

Ideally Þ Switching with probability Þ No switching with probability

Ib pulse ~50 ns rise/fall time

time 100 ns 500 ns

10 ms

Vm signal threshold

histogram

0 no switching switching Switching probability curves: ideal case

- nominal ground state - under saturation - nominal excited state

switching probability P vs. Ib derivative

100 6000

80 5000 No RF No RF p-pulse 4000 60 3000 long (%/V) 40 b pulse 2000 long

dP/dI pulse 20 p-pulse 1000 switching probability (%) 0 0 2.7 2.8 2.9 3.0 2.7 2.8 2.9 3.0 pulseIb pulse height height @ AW (arb.unit generator) (V) pulseIb pulse height height @ AW ( arb.unitgenerator) (V) Switching probability curves

- nominal ground state - under saturation - nominal excited state switching probability P vs. Ib derivative

100 No RF No RF p-pulse B=4.55 Gs 2000 (3 ns) 80 F=5.63GHz 1500 60 1 ms pulse 1 ms pulse

[ %/ V ] 1000 40 b p-pulse 500 20 (3 ns) dP/dI

s w it ch i ng probab ilit y [ % ] 0 0 1.6 1.7 1.8 1.9 1.6 1.7 1.8 1.9 puIblsepulse height height @ AWG ( arb.unitTE3362) [ V ] pulIbsepulse height height @ AWG ( arb.unitTE3362) [ V ] Spectroscopy and the bias phase shift

Calculated energy levels Isw: Ib pulse height which gives 50% switching

( %) 1 40 step 16 GHz

/ I 0 )

20 bg 16 GHz

- I -1 sw I ( D Dgq=0.008 p 0 15

Energy ( GHz) 10 -20

Dgq F ( GH z) 5 Spectroscopy = 3.4 GHz -40 0 D 0.92 0.96 1.00 1.04 1.08 -0.005 0.000 0.005 gq / p DFext / F0 Rabi oscillations: power dependence pulse length

Decay time » 150 ns readout time

0.6 80

60

0.5

40 A = 0 dBm 0.4 80

60 0.3 Rabi frequency (GHz)

40 A = -6 dBm 0.2 80 switching probability (%) 60 0.1

40 MW amplitude A = -12 dBm 0.0 0 10 20 30 40 50 60 70 80 90 100 0.0 0.5 1.0 1.5 2.0 pulse length (ns) 10^(A/20) (a.u.) Rabi oscillations

Readout efficiency > Maximum amplitude ~ 60%

100 90

90 Psw (%) 60 80

70 30 0 10 20 30 RF pulse length (ns) 60

50 62

40 60 Switching probability (%)

Psw (%) 58 30 RF pulse length (ns)

20 500 510 520 530 0 50 100 150 200 250 300 350 400 450 500 RF pulse length (ns) Ramsey interference (or Free-induction decay)

p/2 p/2 ~ 2 ns

delay Readout

80

70

60

50

p/2 p/2 Dephasing time T *» 20 ns

switching probability (%) 2

0 5 10 15 20 25 30 35 distance between two p/2 pulses (ns) Relaxation time

p

delay time Ib pulse time operation read-out

100

80

8.3 ns, A=-12dBm 6 ns, A=-9dBm 60 4.5 ns, A=-6dBm 3.2 ns, A=-3dBm 2.445 ns, A=0 dBm

switching probability (%) T ~ 900 ns 40 exp fit of A=-12dBm 1 T 1 = 870 ns

0 1 2 3 4 5 delay time (ms) Possible decoherence sources magnetic-field noise?

trapped vortices?

paramagnetic/nuclear spins?

charge fluctuations?

environment circuit modes?

phonons? tunneling?

?

charge/Josephson-energy fluctuations? Design of electromagnetic environment

• Large shunt capacitor – Filter noise • Symmetric plasma mode – Avoid coupling between control pulse and SQUID plasma excitation • On-chip resistor – Suppress parasitic resonance in the leads Current bias line 160 W I b I RF Cs ~ 5 pF

Ground

Overlap capacitance 20 mm

Vm 1 kW RF control line Voltage measurement line Impedance of surrounding circuit

bonding resistor at wire 160W mixing chamber ~2mm 1nH 0W 1kW

bonding 600pH 10pF pad 1pF

Cu coaxial cable ~ 10cm Cu-powder filter On-chip + coaxial cable Off-chip (inside cavity) (treated as 50W impedance) Spin echo 30 ns 60 detuning 40 ns 50 T2 » 30 ns 50MHz 100MHz 40 200MHz 50 ns F = 5.64 GHz 30 res F = 297.6 MHz Rabi 65 ns 20

10 70 ns

0 s w it ch i ng probab ilit y [ % ] 0 20 40 60 80 100 80 ns distance between two p/2 pulses [ ns ] 90 ns

p/2 p p/2 70 60 P [% ] 50 Ib pulse 0 20 40 60 80 100 distance between p-pulse and operation readout time second p/2-pulse [ ns ] Charge noise and phase noise resonant frequency resonant peak width

phase bias charge bias

CEA Saclay D. Vion et al. Fortschritte der Physik, 51, 462 (2003). Summary coherent control of 3-junction-loop • Rabi-oscillation period >~1.5 ns • High readout efficiency ~60%

• Relaxation time T1~0.9 ms * • Dephasing time T2 ~20 ns

Future works • Identification of the decoherence sources • Operation at the optimal point • Understanding switching dynamics in the readout • Optimization of the parameters

Chiorescu, Nakamura, Harmans, Mooij, Science 299, 1869 (2003).