Coherence and decoherence in Josephson junction qubits

Yasunobu Nakamura, Fumiki Yoshihara, Khalil HarrabiAntti Niskanen, JawShen Tsai

NEC Fundamental and Environmental Research Labs.RIKEN Frontier Research SystemCREST-JST

•Decoherence of qubit, bias dependence•Tunable coupling scheme based on parametric coupling

using quantum inductance

Josephson junction qubits

small large

Josephson energy = confinement potentialcharging energy = kinetic energy quantized states

typical qubit energy

typical experimental temperature

Flux qubitCharge qubit Phase qubit

Energ

y

Examples of Josephson junction qubits

2 m

charge qubit/NEC flux qubit/Delft

charge qubit (quantronium)/Saclay

phase qubit/NIST/UCSB

~100 m

SQUID readout of flux qubit

0

switch

I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij, Science 299, 1869 (2003)

Ib pulse~30 ns rise/fall time

time~1 s

~20 ns To hold voltage stateafter switching

0 1

qubit+underdamped SQUID

qubit

SQUID

100

80

60

40

20

0

Sw

itch

ing

prob

abil

ity

(%)

1.361.341.321.30I bias (a.u.)

w/o -pulse

w/ -pulse

Coherent control of flux qubit

resonant microwave pulse

visibility~79.5%

Rabi oscillations

Study of decoherence

environment

interaction

qubit

= Characterization of environment

tunable tunable

Possible decoherence sources

phonons?

photons?

magnetic-field noise?

charge fluctuations?

paramagnetic/nuclear spins?

trapped vortices?

charge/Josephson-energy fluctuations?

quasiparticletunneling?

environment circuit modes?

Flux qubit: Hamiltonian and energy levels

J.E. Mooij et al. Science 285, 1036 (1999)

0.8 1.0 1.2- 100

0

100

Ene

rgy

(GH

z)

q/ f/f* f*=0.5

Sensitivity to noises

relaxation

dephasing

transverse coupling

longitudinal coupling

Energy relaxation

relaxation and excitation

for weak perturbation: Fermi’s golden rule

• qubit energy E variable• relaxation S(+) and excitation S(-) quantum spectrum analyzer

ex. Johnson noise in ohmic resistor R

spontaneous emission

absorption

zero-point fluctuation of environment

T1 measurement

80

70

60

50

Sw

itch

ing

prob

abil

ity

(%)

1.61.20.80.40.0Time (s)

initialization to ground state is better than 90% relaxation dominant classical noise is not important at qubit frequency ~ 5GHz

~ 4ns

delay readout pulse

T1 vs f~ 4ns

delay readout pulse

1 vs E

assuming flux noise (not assured)

• Data from both sides of spectroscopy coincide

• Positions of peaks are not reproduced in different samples

• Peaks correspond to anticrossings in spectroscopy

1 vs E: Comparison of two samples

sample3 sample5

Random high-frequency peaks. Broad low-frequency structure and high-frequency floor.

Dephasing

free evolution of the qubit phase

dephasing

for Gaussian fluctuations

sensitivity of qubit energy to the fluctuation of external parameter

information of S() at low frequencies

Dephasing: T2Ramsey, T2echo measurement

~2ns

t

correspond to detuning

readout pulse

Ramsey interference (free induction decay)

0.01 0.1 1 10 100freq.

0.2

0.4

0.6

0.8

1

thgiew

~ 4ns

t/2

readout pulse

~2ns

t/2

spin echo

0.01 0.1 1 10 100freq.

0.2

0.4

0.6

0.8

1

thgiew

Optimal point to minimize dephasing

Ibf• two bias parameters

– External flux: f =ex/0

– SQUID bias current Ib

f

E (GHz)

Ib

G. Burkard et at. PRB 71, 134504 (2005)

T1 and T2echo at f=f*, Ib=Ib*

T1=54516ns

Pure dephasing due to high frequency noise (>MHz) is negligible

Echo decay time is limited by relaxation

Echo at ff*, Ib=Ib*

assuming 1/f flux noise

do not fit

does not fit

2Ramsey, 2echo vs f

cf. 7±3x10-6 [0] for 2500-160000 m2 F.C.Wellstood et al. APL50, 772 (1987)

~1x10-4 [0] for 5.6 m2 G.Ithier et al. PRB 72, 134519 (2005)

Red lines: fit

For

for 3.17 m2

Optimal point to minimize dephasing

f

E (GHz)

Ib

Ibf• two bias parameters

– External flux: f =ex/0

– SQUID bias current Ib

T1, T2Ramsey, T2echo vs Ib

can be obtained experimentally

at Ib=Ib*

at |Ib-Ib*|=large

Echo at f=f*, IbIb*

at Ib=Ib*

at |Ib-Ib*|=large

exponential fit Gaussian fit

-echo does not work-exponential decay white noise (cutoff>100MHz)

Sammary

• T1, T2 measurement in flux qubit, T1,T2~1s• dependence on flux bias and SQUID-current bias condition characterization of environment

Optimal point f=f*, Ib=Ib*

T1 limited echo decayPure dephasing due to low freq. noise

We do not understand yet -T1 vs flux bias-dephasing at optimal point-origin of 1/f noise

ff*, Ib=Ib*

1/f flux noise dominant

f=f*, IbIb*

‘white’ Ib noise dominant

Optimal point and quantum inductance

• At optimal point– Dephasing is minimal– Persistent current is zero

• Inductive coupling ~ xx; effective only for 12

• Current readout should be done elsewhere– Quantum inductance is finite

• Depend on flux bias tunable parametric coupling• Depend on qubit state nondemolition inductance readout

current inductance

Tunable coupling between flux qubits

• Use nonlinear quantum inductance of high-frequency qubit3 as transformer loop

• Drive the nonlinear inductance at |1-2| and parametrically induce effective coupling between qubit1 and qubit2

Effective coupling; can be zero at dc

At the optimal point for qubit1 and qubit2

Tunable coupling between flux qubits

• Advantages– Qubits are always biased at o

ptimal point– Coupling is proportional to MW

amplitude; can be effectively switched off

– Induced coupling term also has protection against flux noise

Simulated time evolution vs. control MW pulse widthDouble-CNOT

within tens of ns

A.O. Niskanen et al., cond-mat/0512238

|10 |01

|10 |01

Simple demonstration of tunable coupling between flux qubits

• Three qubits and a readout SQUID

Easy to distinguish |00 and |11 (not |01 and |10)

qubit1 qubit2

qubit3

|1-2|

1

|00 |10 |10+|01 |00+|11

readout

t

Psw

t

|00

|11

A.O. Niskanen et al., cond-mat/0512238

Future

Single qubit control

Tunable coupling

Nondemolition readout

Long coherence time