High-Fidelity Josephson qubit gates – winning a battle against decoherence

• “Quantum Integrated Circuit” – scalable• New breakthroughs:

Improved fidelityUniversal gates, with tomography

• 50 qubit – easy to couple

Nadav Katz

Work done while at UCSB with Prof. John Martinis and group.

Contact: katzn@phys.huji.ac.ilExt: 84133

Racah Institute of Physics Colloquium, Nov. 2007

Experimental Quantum Information Processing (QIP)

a perplexing explosion of different systems

Experimental QIP – a guide for the perplexed

Smaller

IonsNeutral AtomsNMR

Semiconductor SpinsQuantum Dots

Superconducting Circuits

Easier to isolate Easier to couple & construct

Bigger

• NMR: 2 to 7 qubits; scalability?• Ions: up to 8 qubits & scalable

• Dots: LONG T1 (T2?)• Coherent Oscillations • No dissipation

• Pretty good coherence times• Coupled qubits• Decoherence??

Goal - reach the fault tolerant threshold – F > 99.95%

The Josephson JunctionSC

SC

~1nm barrier

Silicon or sapphire substrate

Al top electrode

Al bottom electrode

AlOx tunnel barrier

Josephson junction

“Josephson Phase”2

2ie

1 2

0 / 2V

0 sin( )JI I

0 / 2h e

11

ie

Electrical notation

Idc

The Qubit (phase)

IdcI RC

Idc + C V + V / R = I.

Kirchoff’s Laws:

V

equation of motion

Controllable

“kinetic” energy potential energy

0 / 2V

0 sin( )JI I

1 2 0 / 2h e

2 2

0 0 0 00

1cos( ) 0

2 2 2 2 dcC I IR

damping

Transform to Hamiltonian rep. Quantize ( is an operator)…

Superconducting Qubits

Phase Flux Charge

104 102 1

Area (µm2): 10-100 (1) 0.1-1 0.01

Potential &wavefunction

EngineeringZJ=1/10C 30 103 105

Yale, Saclay, NEC, Chalmers

Delft, IBM, Berkeley

UCSB, NIST, Maryland, Wisconsin, Jerusalem

0 02

/ 2

/ 2J

C

E I

E e C

Our Qubit

microwave drive

Junction

Flux bias

SQUID

~ 100 microns

Idc

Qubit

Flux bias

VSQ

SQUID

Iµw

inductor

Operation of the Phase Qubit

Qubit basis states |0, |1

Tune qubit state energies E10 with dc current Idc

Control qubit states with microwave current Iµw at 10

Measure state occupation by selective tunneling

Minimize fluctuations and dissipation for qubit coherence

Idc

Qubit

Flux bias

VSQ

SQUID

Iµw

10|0

|1

01

0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Measure Pulse amplitude (V)

Sw

itchi

ng p

roba

bilit

y

|0

|1

(1) State Preparation Wait t > 1/10 for decay to |0>

Josephson-junction qubit

dt

e 01

|0>

|1>

I = Idc + dIp(t) + Imwc(t)cosw10t + Imws(t)sinw10t

phase

pote

ntia

l

pulse height of dIp

Pro

b. T

unne

l

|0> : no tunnel

|1> : tunnel

|0>|1>

3 ns Gaussian pulse96%

mwcI

mwsI

dIp(t)(2) Qubit logic with current bias

(3) State Measurement: U(Idc+dIp) Fast single shot – high fidelity

GHz) 6 ; ;mK (20 10kT

U

ExperimentalApparatus

V source

20dB 4K

20mK

300K

30dB

I-Q switch

Sequencer & Timer

mwaves

IsIfVs

fiber optics rf filters

mw filters

~10ppm noise

V source~10ppm noise

20dB

20dB

Z, measure

X, Y

Ip

Imw

Is

Iftime

Reset Compute Meas. Readout

Ip

Imw

Vs

0 1

X Y

Z

Repeat 1000xProbability 0,1

10ns

3ns

~5 ns pulses

GHz DAC Electronics

Old analog system:

time (ns)

mw

ave

amp

litu

de

I Q

mw

14 bits, 2x Gs/sFPGA memory, ~2k$

-8 -6 -4 -2 0 2 4 6 8

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

measured waveform

Spectroscopy

Bias current I (au)

10/ U

saturate

Ip

Imw

meas.

10(I)

26

P1 = grayscale

Qubit Characterization

T2 ~350ns

Meas.time

T1 ~450ns

0 100 200 300 400 500 600

time [ns]

T~100ns

Rabi

time

x/2

time

x/2

x/2 x/2y

Ramsey

Echo

time

xlifetime

P1

0

1

0

1

Standard State Tomography (Z, Y, X meas.)

time (ns)

P1

I,X,Y

I

XY

0

1

10 10 i

Z

Y/2

State prep.

0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Measure Pulse amplitude (V)

Sw

itchi

ng p

roba

bilit

y

|0

|1

Measurement in detail

Idc

Imw pulse

What is the quantum state after a partial measurement (p<1) ?

Question:

Full measurement (p=1) projects to either or 1 0

12sin02cos 000

2cos2sin 02

002

1 pp

p~1

p=0.5

Partial measurement evolution

Theory: A. Korotkov, UCRFollowing Dalibard et al. PRL

68, 580 (1992).

N

pe Mi 110M

Prob. = p/2tunnel out

Prob. = 1-p/2

Apply state tomography to test theory

2/tan1tan2 01 pM

2

10

Answer:

2sin

2sin112/sin102/cos

02

0200

0

pwellqubitofouttunnel

pN

pe Mi

M

M

M

2sin

2sin112/sin102/cos

02

0200

0

pwellqubitofouttunnel

pN

pe Mi

M

1

0

0 0.2 0.4 0.6 0.8 10

50

100

Partial measurement probability

Pol

ar a

ngle

M

(D

eg)

Partial measurement - results

2/tan1tan2 01 pM

0 0.5 10

500

1000

1500

2000

Measure pulse amplitude (V)A

zim

utha

l rot

atio

n

(Deg

)

But can the effect of such a partial measurement be undone?

High fidelity zrotations

Quantum erasure

Partialmeasure

Erasure

Erasure(0.9)

01

tomography & final measure

statepreparation

7 ns

partial measure p

Iw

Iz

p

t10 ns

partial measure p

p

10 ns 7 ns

x

0 1

2

i 0 1

2

Probablistic recovery of quantum state even with strong measurement

Nontrivial sequence – Very good control

Process tomography ofthe erasure (~85% fidelity)

Im Re

0.05 0.7p

Coupled Qubits

Cc

C

0110100110 C

CH c

coupling

0 0

1 0 0 1

1 1

On Resonance:

Straightforward to implement: simple coupling tunable fast readout simultaneous measurement

eg. UMaryland

Cc

0 100 200 300 4000

0.2

0.4

0.6

0.8

1

osc

(ns)

Pro

babi

lity

P10

P01

P11

0 100 200 300 4000

0.2

0.4

0.6

0.8

1

osc

(ns)

Pro

babi

lity

P10

P01

P11

0 100 200 300 4000

0.2

0.4

0.6

0.8

1

osc

(ns)

Pro

babi

lity

P10

P01

P11

Simultaneous Measure of Coupled Qubits: i-SWAP gate

)2sin(01)2cos(10

01100110

oscosc

21

21 osc

SiS

e iS

0 0

p

1 0 0 1

1 1S

i-SWAP gate

p PABA

B

tosc

z-gate

/2 z-gate

P10

P01

P11

0110 i0110 i

0110 0110 i

Eigenstate, Bell singlet

Tomography: Direct Proof of Entanglement

pA

B

p/2

state tomographyI,X,Y

I,X,Y

01 10 i

Re Im

00

10

01

11 0010

0111

00

10

01

11 0010

0111

) 0101 1010 )(2/1(incoh

) 1001 0110

0101 1010 )(2/1(

)0110)(0110(coh

ii

ii

fidelity = 0.86expect = 0.87

Process Tomography

y tomographstateswap01 i

10,10,1,010,10,1,0 ii

4 initial states / qubit

pA

B

i-swap

state tomographyI,X,Y

I,X,Y

Samples Bloch sphere enough to describe gate for ANY initial state

(i-swap)1/2 is a universal gate

16 Density Matrices:16 Density Matrices:Data Data (3 min.)(3 min.)

Process Tomography

DATA

T1 = 450nsCM = 8% CuW= 5%vis = 85%g/ππ = 20MHz

Re [] Im [] Preliminary Data

SIM

Fidelity:Tr( thy exp) = 0.427

Qubit Coherence: Where’s the Problem?

Ene

rgy

D. of States

Inductors & Junctions

Capacitors

Superconductors: Gap protects from dissipation X-tal or amorphous metal Protected from magnetic defects

2D~4Tc

eV

Circuits

Good circuit design (uwave eng.)

resonator

(X-tal) (amorphous)

Many low-E statesOnly see at low T

Qubit Improvements(dielectric loss)

P1

(p

roba

bili

ty)

1st gen.

T1 = 500 ns

tRabi (ns)

2nd gen.

3rd gen.

T1 = 40 ns

T1 = 110 ns

40%

60%

90%

No Si waferSiO2 -> SiNx

Small junction+ shunting C

(loss of SiNx limits T1)

60 m

SiNx capacitor

0 100 200 300 400 500 600 700 800 900 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T1 = 474 ns

Wave Delay (ns)

P1

New Qubit DataP

1 (p

roba

bili

ty)

tRabi (ns)

4th gen.

T1 = 470 ns

90%

Interdigitated C – (topologically protected)

sapphire dielectric (radiation from large size?)

T ~ 300 ns

Optimistic for further dramatic improvements • We know crystals are “superinsulators”• How to fabricate?

5th gen.a-Si:H dielectric (Q ~ 40000)

T1 = 450 ns

time16 ns

X

12 ns 12 ns

swap swaphold

time16 ns

TLS

X interact with TLS

1610 1614 1618 1622

6.8

7

7.2

Flux Bias [mV]

Fre

qu

en

cy [G

Hz]

0 1 2 3 4 0

0.5

1

time [s]

0 0.5 10

0.5

1

time [s]

T1,TLS ~ 1.2s

0 50 1000

1

time [ns]

Tswap ~ 12ns

• Strong interaction with TLS (S = 40MHz)• Long-lived TLS is quantum memory

P1

P1

excite qubit off-resonancez-pulse into resonance

“on”

“off”

measure

offon

TLSoffon

Bias

Fre

quen

cyTLS Resonance – not a bug, a feature…

• On-Off coupling with change in bias

8%

Quantum Memory with Process Tomography

)Im(

)Re(

16ns16 ns

TLS

init

12 ns 12 ns

store loadmem

1 2 3

1 – InitializeCreate states over the entire Bloch sphere.

2 – StoreSwap state into TLS. Qubit now in ground state.

3 – LoadAfter holding for 16ns, swap again to retrieve state from TLS.

Process tomography:identity operation dominates process

Fidelity:Tr(thmeas)

= 79%

New Frontier: 50 atoms

• “Atom” with 50 W impedance|Zqubit| =1/w10C

Zqubit ()

11K1M

phasequbitQ F

atoms

377 50

Z mismatch makes coherence easier

Z match makes coupling easier

Error threshold

Unlimited range 10-3 – 10-4

2D lattice nearest-neighbor 10-5

1D lattice nearest-neighbor 10-8

Architecture

• 50 enables long distance coupling Much better error threshold !

Future Prospects

•Demonstrated basic qubit operations

Initialize, gate operations, controlled measurement

10 to 100 logic operations

Tomography conclusively demonstrates entanglement

•Decoherence mechanism understood

Optimize dielectrics, expect future improvements

Problem is NOT (only) T1 !!

•Future: tunable coupling, CNOT gate with process tomography

•New designs and regimes (cavity QED and microbridges)

•Scale-up infrastructure designed (“brute force” to ~40 qubits)

Very optimistic about 4 -10 qubit quantum computer