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A Robust and Scalable Flux Qubit

Richard Harris

Primary Reference: Harris et al., arXiv:0909.4321

D-Wave Systems Inc.Burnaby, BC Canada

September 2009

Copyright, D-Wave Systems (2009) A Robust and Scalable Flux Qubit September 2009 1 / 53
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Outline

1 Qubit Requirements

2 Compound-Compound Josephson Junction

3 Inductance Tuner

4 Global Flux Bias Line

5 CCJJ rf-SQUID Characterization

6 Qubit Parameters

7 Noise in the CCJJ rf-SQUID

8 Conclusions


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Qubit Requirements

Outline



3 Inductance Tuner



6 Qubit Parameters


8 Conclusions


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Qubit Requirements

Optimization Problem Specification

Let there be an optimization problem that can be mapped onto adimensionless Ising spin Hamiltonian of the form

H(t) = i hi(i)

z +i,j K

i,j

(i)

z

(j)

z (1)

where 1 hi +1 and 1 K +1. Here, the groundstateconfiguration of the spins represents the best solution to the optimizationproblem. The objective is to implement an algorithm in hardware thatreliably finds the groundstate.


Q bi R i

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Qubit Requirements

Quantum Annealing

Introduce quantum mechanical degrees of freedom to create a quantumIsing spin Hamiltonian of the form

H(t) = i

hi(i)z +

i,j

Ki,j(i)z

(j)z

i

f(t)(i)x (2)

Use physical system to find the groundstate by evolving f(t) such that

f(0) hi, Kf(t ) hi, Ki,j

See Farhi et al, Science 292, 472 (2001).


Q bit R i t

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Qubit Requirements

Requirements to Implement a Quantum Ising Spin System

Qubits must map onto a quantum Ising spin with both transverse(x) and longitudinal (z) effective fields - implies bistable systemwith quantum tunneling coupling the two spin states.

Qubits must readily accommodate multiple inter-qubit couplings in

order to solve non-trivial problems.Qubits must work with inter-qubit couplers whose strengths are bothsign- and magnitude-tunable.

Qubits must have a tunnel energy q that can be tuned over orders

of magnitude.All qubit q must be tuned in unison, so qubits need to be identicalto within some precision.


Compound Compound Josephson Junction

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Compound-Compound Josephson Junction

Outline



3 Inductance Tuner



6 Qubit Parameters


8 Conclusions



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The Josephson Junction (JJ)

Ic

j1

e e

e

Isc

h

e

h

e

h

e

h

SC

SC

-Q

+Q

The most basic mesoscopic superconducting quantum device. Let the JJbe characterized by its critical current Ic and capacitance C. The phaseacross the JJ, , and charge on the junction, Q, obey the commutationrelation [0/2, Q] = i. The supercurrent Isc flowing through the JJ

obeys the Josephson equation:Isc = Ic sin ()

The Hamiltonian for this element (with no external current bias) is

H=

Q2

2C

Ic0

2

cos () (3)



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The Simple rf-SQUID

I1

j1

jq

x

jqLbody

A single JJ with critical current I1 and capacitance C1 and a loop ofsuperconducting wire of inductance Lbody. Let the closed loop be subjectedto an external flux bias xq. Express this external flux bias as a phase:

xq

2xq

0Flux quantization dictates phase drop across Lbody, q = 1, and drives apersistent current Ipq about the closed loop:

Ipq = I1 sin (1) =02

q xqLbody



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The Simple rf-SQUID

Hamiltonian of the simple rf-SQUID is a sum of that of a single Josephsonjunction and an inductive potential energy term:

H = Q2q

2Cq+ Uq

q

x

q2

2 Uqcos (q) (4a)

=2LqI1

0(4b)

where Lq Lbody, Cq C1 and Uq (0/2)2 /Lq.



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p p p

The Simple rf-SQUID Flux Qubit

!5 !2.5 0 2.5 5

0

5

10

15

20

25

(q 0/2)/Lq (A)

Energy/h

(GHz)

||

|g

|e

At xq = 0/2, two lowest lying states are quantum superpositions of two

counter-circulating macroscopic persistent current states. Two possiblemodes of mapping a logical basis {|0 , |1} onto the flux qubit:State Energy Basis Flux Basis

|0 |g | = (|g + |e) /2|1 |e | = (|g |e) /2



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p p p

The Simple rf-SQUID Flux Qubit

For arbitrary xq, the low energy Hamiltonian of the simple rf-SQUID can

be mapped onto that of a qubit:

Hq = 12

[z + qx] ; (5)

2 Ipq xq 0q ,where

Ipq | 0q /Lq |, q e|H |e g| H |g and thequbit degeneracy point is defined as 0q = 0/2 for the simple rf-SQUID

flux qubit.

A Key Point:

The parameters

Ipq

and q are the definitive parameters of any flux

qubit. It does not matter how one measures these quantities.



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Problems with the Simple rf-SQUID Flux Qubit

The simple rf-SQUID is not useful in any large scale quantum information

processor:One cannot tune q in-situ. As such, one cannot meet one of the keyspecifications for implementing AQO with this device.

q can be exponentially sensitive to fabrication variations in Lbody

and I1 through = 2LbodyI1/0. This makes it impractical tofabricate a large scale device (1000s of qubits) with all devices beingon-target, even with the best of modern fabrication facilities.

Conclusion

The simple rf-SQUID flux qubit (and related variants) is not a practicalqubit for implementing a large scale quantum information processor andhas been abandoned by the majority of research groups in the field.



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Compound Josephson Junction (CJJ) rf-SQUID

I1

j1 jcjj I2

j2x

jqx

jq

Lcjj/2

Lbody

Lcjj/2

Two JJs in parallel with critical currents I1(2) and capacitance C1(2) insidea loop of inductance Lcjj inside a larger loop of inductance Lbody. Let theloops be subjected to external flux biases xcjj and

xq, respectively.

Express external flux biases as phases:xq(cjj)

2xq(cjj)

0Device can be modelled using phases around closed loops cjj 1 2and q

(1 + 2) /2 as the quantum mechanical degrees of freedom.



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CJJ rf-SQUID

Hamiltonian for the CJJ rf-SQUID from device parameters:

H =n

Q2n2Cn

+ Un (n xn)2

2

Uqeffcos

q 0q

, (6a)

where the sum is over n {q, cjj}, Cq C1 + C2, 1/Ccjj 1/C1 + 1/C2and Lq

Lbody + Lcjj/4.

eff = + cos

cjj

2

1 +

+

tan(cjj/2)

2; (6b)

0

q 2

0q

0=

arctan

+tan (

cjj/2) ; (6c)

2Lq(I1 I2) /0 . (6d)Hamiltonian (6a) is similar to that of the simple rf-SQUID modulo thepresence of a cjj-dependent tunnel barrier through eff and a

cjj-dependent flux offset through 0q = 0

0q/2.



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Problems with the CJJ rf-SQUID Flux Qubit

The Good Part:

If Lcjj < Lbody, then cjj xcjj. In this case, eff + cos xcjj/2. Onecan then account for fabrication variations in Lq and I1 + I2 by changingxcjj. One can thereby change q in-situ, which is a significantimprovement over the simple rf-SQUID flux qubit.

The Bad Part:

Any so-called junction asymmetry/+ = (I1 I2)/(I1 + I2) leads to axcjj-dependent offset of the qubit degeneracy point

0q = 0

0q/2. For

asymmetry on the order of 0.01, this leads to an apparent flux offset that

can overwhelm and q if xcjj is altered during operation of the qubit.This is not a trivial effect and would be disastrous in a large scale (1000sof qubits) processor.



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Problems with the CJJ rf-SQUID Flux Qubit

ConclusionsThe CJJ rf-SQUID (and related variants) does provide an in-situ tunableq, but does so at a considerable price. While this device may be useablein few-qubit systems for physics experiments, it is too difficult to control inany practical large scale quantum information processor.

Can one make a better flux qubit?

Ideally, we would like a flux qubit whose imperfections can at least beaccounted for by the application of solely static control signals that can be

applied by a truly scalable architecture using programmable on-chipmemory. This means negligible parasitic coupling between control linesand unintended devices and negligible apparent crosstalk from fabricationvariations such as junction asymmetry.



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Compound-CJJ (CCJJ) rf-SQUID

I1j1 jL

I2

j2x

jqx

jqI3

j3 jRI4

j4x

jccjjx

jl jr Lbody

Lccjj/2Lccjj/2

Two CJJs with loops of negligible inductance denoted as L and R. TheCJJs are connected in parallel inside a loop of inductance Lccjj inside alarger loop of inductance Lbody. Let the loops be subjected to external fluxbiases xL,

xR,

xccjj and

xq. Express external flux biases as phases:

x

n 2xn

0where n {L,R, q, ccjj}. Device can be modelled using phases aroundclosed loops L = 1 2, R = 3 4, ccjj (1 + 2 3 4)/2and q (1 + 2 + 3 + 4) /4 as the quantum mechanical degrees offreedom.



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CCJJ rf-SQUID

It is shown in arXiv:0909:4321 that one can find pairs of static flux biases(x

L,x

R) such that the CCJJ Hamiltonian can be written as

H =n

Q2n2Cn

+ Un(n xn)2

2

Uqeffcos

q 0q

, (7a)

where the sum is over n {q, ccjj}, Cq C1 + C2 + C3 + C4,1/Cccjj 1/(C1 + C2) + 1/(C3 + C4) and Lq Lbody + Lccjj/4 and

eff = +(xL,

xR) cos

ccjj 0ccjj

2

, (7b)

where +(xL,

xR) = 2LqI

cq(

xL,

xR)/0 with

Icq(xL,

xR) (I1 + I2) cos

xL0

+ (I3 + I4) cos

xR0

.



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CCJJ rf-SQUID

For small xR, if one chooses xL using

xL =2

0arccos

R,+L,+

cos

xR0

, (8)

then the q and ccjj apparent flux offsets will be given by

0q =0

0q

2=

0L + 0R

2; (9)

0ccjj =0

0ccjj

2= 0L 0R , (10)

where 0L and 0R are purely functions of (

xL, I1, I2) and (

xR, I3, I4),

respectively. As such, the qubit degeneracy point is independent of xccjj.



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Summary - Advantages of the CCJJ rf-SQUID Flux Qubit

The CCJJ is robust against fabrication variations in junction critical

currents within a qubit as one can choose pairs of (xL,

xR) to

eliminate any junction-asymmetry driven xccjj-dependent qubitdegeneracy point offset.

The CCJJ is robust against fabrication variations in junction criticalcurrents between multiple qubits in that one can choose pairs of(xL,

xR) to homogenize the net critical current I

cq amongst a set of

such devices while preserving the advantage cited above.

The compensation signals xL and xR are static quantities that can

be applied to the CCJJ rf-SQUID using a truly scalable architecture in

which the biases are supplied to a plurality of such devices by on-chipmemory that is programmed by only a handful of lines (see Johnsonet al., arXiv:0907.3757).


Inductance Tuner

O

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Outline



3 Inductance Tuner



6 Qubit Parameters


8 Conclusions


Inductance Tuner

I d (L) T

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Inductance (L)-Tuner

1

n

LTx

Mco,1 Mco,n

Qubit inductance Lq can be subject to fabrication variations and is also a

function of inter-qubit coupler settings - see Harris et al., PRB 80, 052506(2009). Insert a large JJ dc-SQUID into the qubit body to provide in-situtunable Josephson inductance:

Lq = L0

qi M2

co,ii +

LJ0

cos(xLT/0) , (11)

where LJ0 0/2IcLT, IcLT is the net critical current of the two junctionsin the L-tuner and xLT is an externally applied flux bias. We can thencontrol Lq during qubit operation by changing

x

LT

.


Global Flux Bias Line

O li

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Outline



3 Inductance Tuner



6 Qubit Parameters


8 Conclusions



Gl b l Fl Bi Li

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c1

Ig

Fg1

x

cnFgn

x

Recycle the inter-qubit coupler to couple individual qubits to a global biasline that carries a an arbitrary time-dependent signal Ig. One can pass asign- and magnitude-scaled copy of Ig to each qubit using static flux biaseson the couplers xgn. This is a very scalable means of providing

time-dependent signals to flux qubits as it uses only one analog bias lineand one can use programmable on-chip memory to control the couplers.

It will be demonstrated in tomorrows hardware performance presentationthat a scaled global bias is essential to implement AQO with flux qubits.


CCJJ rf-SQUID Characterization

O tli

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Outline



3 Inductance Tuner



6 Qubit Parameters


8 Conclusions



D i A hit t

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Device Architecture

Data from qubit q1 in an 8-qubit network of coupled CCJJ rf-SQUIDs.

q0 q1 q2 q3

q4

q5

q6

q7RO

CCJJLTCO

a)



Device Architecture

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Device Architecture

SEM cross section of fabrication profile and an optical image of a portion

of an 8-qubit device completed up to Nb metal layer WIRB.

500 nmb)

q0

q1

q2

q3

q4100 m

c)



Extracting Information FromI

p Measurements

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Extracting Information From Ipq Measurements

We can calibrate many CCJJ rf-SQUID parameters by measuring themagnitude of the persistent current

Ipq =

02

q xq

L

q

as a function of externally controlled flux biases xL, xR,

xccjj,

xq and

xLT. Here, q, which can be predicted from the full quantum mechanicalCCJJ rf-SQUID Hamiltonian (7a), is a function of the device parametersLq

, Lccjj

, Cq

and Icq

.

A full description of the experimental methods can be found inarXiv:0909.4321.



rf SQUID Inductance and Critical Current

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rf-SQUID Inductance and Critical Current

Measured Ipq versus

xccjj with

xL/0 = 0.0984,

xR/0 = 0.0893 and

x

LT/0 = 0.344.

!1.5 !1 !0.5 0 0.5 1 1.51

1.5

2

2.5

3

xccjj

/0

Ip q

(A)

Data

Fit

Fit data to CCJJ rf-SQUID Hamiltonian. This particular fit yieldedLq = 265.4 1.0pH, Lccjj = 26 1pH and Icq = 3.103 0.003A.Copyright, D-Wave Systems (2009) A Robust and Scalable Flux Qubit September 2009 30 / 53


CCJJ Calibration

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CCJJ Calibration

Measured (xL,xR) such that the qubit degeneracy point has no

xccjj-dependence.

!0.2 !0.1 0 0.1 0.20

0.04

0.08

0.12

0.16

0.2

xR/0

x L/0

a)

Data

Fit

Data have been fit to

xL =2

0arccos

R,+L,+

cos

xR0

, (12)

with L,+/R,

+= (I

1+ I

2)/(I

3+ I

4) = (4.1

0.3)

103.



CCJJ Calibration

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CCJJ Calibration

MeasuredIpq

versus pairs (xL,xR) that balance the CCJJ with

xccjj/0 =

1 and xLT/0 = 0.344.

!0.2 !0.1 0 0.1 0.22.4

2.5

2.6

2.7

2.8

x

R/0

Ip q

(A)

b)DataFit

Data have been fit to CCJJ rf-SQUID Hamiltonian with the substitution

Icq(xR,

xL) = I

0c cos

xR0

(13)

with I0c = 3.25

0.01A.



L-Tuner Calibration

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L Tuner Calibration

MeasuredIpq

versus xLT with xL/0 = 0.0984,

xR/0 = 0.0893 and

xccjj/0 =

1. Given Lccjj and I

cq, convert results into Lq using CCJJ

rf-SQUID Hamiltonian and plot relative to value obtained with LxLT = 0.

!0.4 !0.2 0 0.2 0.40

4

8

12

16

x

LT/0

L

q

(pH

)

a)

Data

Fit

Fit results to

Lq =LJ0

cosxLT/0

, (14)with LJ

0= 19.60

0.04pH.



rf-SQUID Capacitance

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rf SQUID Capacitance

Spacing of energy levels as a function of xq is very sensitive to Cq. Locate

resonances as a function of

x

q using macroscopic resonant tunneling(MRT) - see Harris et al., PRL 101, 117003, (2008) for experimentaldetails.

!2 !1 0 1 20

10

20

30

40

50

60

(q x

q)/Lq (A)

U/h(GHz)

2

1

3

a)



rf-SQUID Capacitance
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rf SQUID Capacitance

0 5 10 15 2010!

5

10!4

10!3

10!2

10!1

100

101

x

q(m0)

(s1

)

a)

0

1

2

3

4

5

6

7

8

9

10

11

12

0 2 4 6 8 10 120

5

10

15

20

n

np/2|

Ip q|

(m0)

c)

Fit MRT rate versus rf-SQUID flux bias xq peak positions np/2

Ipq toCCJJ rf-SQUID model with Lq, Lccjj and I

cq fixed. This procedure yielded

Cq = 190 2fF.Copyright, D-Wave Systems (2009) A Robust and Scalable Flux Qubit September 2009 35 / 53


Summary of Device Calibration
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Summary of Device Calibration

Functionality of the novel CCJJ and L-tuner structures inserted intoan rf-SQUID have been demonstrated.

Tools for calibrating the device parameters Lq, Lccjj, Cq and Icq havebeen demonstrated - there are no unknowns in the quantummechanical CCJJ rf-SQUID Hamiltonian.


Qubit Parameters

Outline

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O



3 Inductance Tuner



6 Qubit Parameters


8 Conclusions


Qubit Parameters

Recap: What Defines a Flux Qubit?

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p Q

The low energy Hamiltonian of the simple rf-SQUID can be mapped onto

that of a qubit: Hq = 12

[z + qx] ; (15)

2 Ipq

xq 0q ,

whereIpq | 0q /Lq |, q e|H |e g| H |g and the

qubit degeneracy point is defined as 0q.

A Key Point:

The parametersIpq and q are the definitive parameters of any flux

qubit. It does not matter how one measures these quantities.


Qubit Parameters

Measurement Methods

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Why dont we do Rabi Oscillations?

Our apparatuses have many (currently 128) relatively low bandwidth biaslines ( 5 MHz) to facilitate running AQO on large-scale devices - nomicrowaves! It would be impractical to build an apparatus with a largenumber of high bandwidth bias lines as the qubits would probably then be

overwhelmed by environmental noise.

How Can We Demonstrate a Qubit?

Perform experiments that only require low bandwidth bias signals tomeasure the flux qubit parameters Ipq and q. Given independentlycalibrated device parameters Lq, Lccjj, Cq and Icq, show that predicted

Ipqand q from the quantum mechanical CCJJ rf-SQUID Hamiltonian agreewith experimental results.


Qubit Parameters

q from Macroscopic Resonant Tunneling (MRT)

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q p g ( )

Initialize qubit in the lowest state in one well, measure rate at which ittunnels into lowest state in other well as function of = 2 I

pqxq.

() =1

8

2qW

exp

( p)

2

2W2

(16)

+

For experimental details see Harris et al., PRL 101, 117003, (2008).


Qubit Parameters

q from Landau-Zener (LZ)

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q ( )

Initialize qubit, sweep xq through degeneracy point with bias ramp rate= 2 I

pq

dxq/dt and look for probability of occupying the excited state:

PLZ = exp

2q

2

. (17)

e

Initial Final

Dq

For experimental details see Johannson et al., PRB 80, 012507 (2009).


Qubit Parameters

q from Groundstate Persistent Current

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q

A novel 2-qubit experiment that works for CJJ or CCJJ rf-SQUID flux

qubits. Use a pair of coupled source and detector qubits. Use feedback toadjust flux bias on detector dq until P0 = 1/2. See arXiv:0909.4321 fordetails.

Detector

Qubit

Meff

Coupler

Source

Qubit{

Fqs

Fqd

Fcjjs

Fcjjd

!5 0 50

10

20

30

40

(q dq)/Lq (A)

Energy/h

(GHz)

!5 0 50

10

20

30

40

(q s

q)/Lq (A)

Energy/h

(GHz)

-F0/2

t

Fqs(t)

i ii iii iv v

-F0

0

Fcjj(t)s

Fcjj(t)d

Fqd(t)


Qubit Parameters

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Trace dq versus sq and fit to an analytical formula. Model as a system in

thermal equilibrium in which d 0. We have a full finite temperatureexpression that we use in practice. For T = 0:

d

1

2( + 2J)

2 + 2q

1

2(

2J)2 + 2q (18)

2Ipqxq d 2 Ipddq J MeffIpq Ipd

Weak Coupling Limit is a Projective Measurement

Notably, in the limit q J:

dq MeffIpq

2 + 2q

= Meffgq| Ipq |gq


Qubit Parameters


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!4 !2 0 2 4!1

!0.5

0

0.5

1

xq (m0)

x d

(m0

)

1+

1-

2+

2-

3+

3-

slope 1(2J)2+2

q

slope

2Meff|Ipq |

An example plot of detected flux versus source qubit flux bias withxccjj/0 = 0.6513. Fitting yielded

Ipq

= 0.72 0.04A andq/h = 2.64 0.24 GHz.Copyright, D-Wave Systems (2009) A Robust and Scalable Flux Qubit September 2009 44 / 53

Qubit Parameters

Qubit ParametersIpq and q

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!0.67 !0.665 !0.66 !0.655 !0.65 !0.6450.4

0.6

0.8

1

1.2

1.4

x

ccjj/0

|

Ip q

|

(A)

a)DataTheory

!0.67 !0.665 !0.66 !0.655 !0.65 !0.64510

5

106

107

108

109

1010

x

ccjj /0

q

/h

(Hz)

b)kbT/h

MRT Data

LZ Data

g| Ipq |g Data

Theory

A summary of the flux qubit parametersIpq and q data and predictions

from CCJJ rf-SQUID Hamiltonian with independently calibratedparameters Lq, Lccjj, Cq and I

cq - there are no free parameters.


Qubit Parameters

Summary of Qubit Parameters

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A suite of tools for measuring q that uses low bandwidth biascontrols has been demonstrated and the results from theseexperimental methods have been shown to be self-consistent.

The CCJJ rf-SQUID can justifiably be identified as a flux qubit as themeasured

Ipq and q agree with the predictions of a quantummechanical device Hamiltonian whose parameters have beenindependently calibrated.


Noise in the CCJJ rf-SQUID

Outline

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3 Inductance Tuner



6 Qubit Parameters


8 Conclusions



T1 and T2 Noise in AQO

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Noise affects AQO, albeit in different ways than in gate model QC.

Fqx

dwn

dFn

Ge

|g>

|e> E/h

Noise Type Physical Consequence

T1 Spectral broadening e, loss of superposition states.T2 Flux bias drift n, loss of precision in problem specification.



Flux Noise in the CCJJ rf-SQUID

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10!4

10!3

10!2

10!1

100

10!11

10!10

10!9

10!8

Frequency (Hz)

S

(f)(

2 0

/Hz)

Use methods described in Lanting et al., PRB 79, 060509(R) (2009) tomeasure low frequency flux noise in the CCJJ rf-SQUID. Data yield fluxnoise spectral density of the form S(f) = A

2/f(+wn) with 1/f flux noiseamplitude at 1 Hz

S(1,Hz) = 1.3

+0.70.5 0/

Hz above the statistical

white noise floor wn 1010 A2/Hz.Copyright, D-Wave Systems (2009) A Robust and Scalable Flux Qubit September 2009 49 / 53


Flux Noise in the CCJJ rf-SQUID

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So How Do Our Qubits Compare?

It has been established that 1/f flux noise is the dominant source of

dephasing in superconducting phase and flux qubits.

S(1,Hz) is viewedas a critical metric in the field.

Fabrication and Reference Wiring Dimensions

S(1,Hz)

VTT, PRL 97, 167001 (2006) 0.25m

10m

10/

Hz

NTT, PRL 98, 047004 (2007) 0.25m25m 10/HzUCSB, PRL 99, 187006 (2007) 1m1000m 40/

Hz

D-Wave, arXiv:0909.4321 (2009) 2m1800m 1.30/

Hz

D-Wave flux qubits, despite their physical size and complexity, areamongst the quietest flux qubits reported upon in the literature.Moreover, the D-Wave qubit is the only one in the above table made fromNb, which has several advantages over Al, but had been shunned by manyresearchers due to 1/f flux noise in historical measurements.



What is T2 ?

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The answer depends upon at least three experimental details:

At what CCJJ bias, xccjj? Recall that CJJ and CCJJ flux qubits can

be tuned to reach both the coherent and incoherent regime with thesame device. Clearly dephasing time will be variable.

At what flux bias, xq? Dephasing times show a strong dependenceupon this parameter, as shown in the literature.

What experimental protocol? Rabi, free induction decay (FID orRamsey), spin-echo, . . .

We cannot measure dephasing times directly with our experimentalapparatuses purely because of bandwidth constraints. Using the measured1/f flux noise and established theoretical formulae from the literature, weestimate the FID time for the CCJJ flux qubit to be T2 150 ns fornominal device parameters such that

Ipq 0.7A, q 2 GHz - seearXiv:0909.4321 for details. This result is comparable to T2 reported inthe literature for flux qubits with comparable 1/f flux noise amplitudes.


Conclusions

Outline

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3 Inductance Tuner



6 Qubit Parameters


8 Conclusions


Conclusions

Conclusions

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The CCJJ rf-SQUID with L-tuner and tunable coupling to a globalbias line is a truly robust and scalable flux qubit design.

It has been experimentally demonstrated that the CCJJ rf-SQUID canjustifiably be referred to as a flux qubit as the measured flux qubitparameters Ipq and q agree with the predictionsof a quantummechanical device Hamiltonian whose parameters were independentlycalibrated.

It has been experimentally demonstrated that the CCJJ rf-SQUID fluxqubit shows 1/f flux noise levels that are comparable to the best such

devices reported upon in the literature. This is despite the fact thatthe CCJJ rf-SQUID flux qubit design is relatively complex and thedevice has been fabricated from Nb.


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