Scaling up a Josephson JunctionQuantum Computer

• Basic elements of quantum computer

have been demonstrated

• 4-5 qubit algorithms within reach

• 8-10 likely

• With improvement in coherence,

further scaling up

John Martinis, UCSB

Quantized Voltages and Currentsof Microfabricated Circuit

100m

Qubit

(old NIST design)

control port

controlport

readoutport

Josephson Junction forms non-linear LC resonator

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

Josephson-Junction Qubit

I = Idc + Idc(t) + Iwc(t)cos10t + Iws(t)sin10t

|0> : no tunnel

|1> : tunnel

3 ns pulse

wcI

wsI

Idc(t)

(2) Qubit logic with current bias

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

GHz) 6 ; ;mK (20 10kT

U()

E0

E1

E2

|0>

|1>

ExperimentalApparatus

V source

20dB 4K

20mK

300K

30dB

I-Q switch

Sequencer & Timer

waves

IsIVs

fiber optics rf filters

w filters

~10ppm noise

V source~10ppm noise

20dB

20dB

Z, measure

X, Y

Ip

Iw

Is

Itime

Reset Compute Meas. Readout

Ip

Iw

Vs

0 1

X Y

Z

Repeat 1000xProbability 0,1

10ns

3ns

~5 ns pulses

Qubit Characterization

~350ns

Meas.time

T1 ~400ns

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

Single Qubit Gate Errors: Measurement Errors

1610 1614 1618 1622

6.8

7

7.2

Flux Bias [mV]

Fre

qu

en

cy [G

Hz]

3 ns

Iw

Iz

8 ns

nothing or -pulse

measure

measurement

TLS leakage

Spectroscopy

|1> (misidentified as |0>)• 4.5% splitting at 7GHz• 3-5% other splittings• 1% T1 during measurement

0 0.5 1

0

0.5

1

7.22 GHz

0 0.5 1

0

0.5

1

6.75 GHz

Imeas / Ic

thy: 96.6%exp: 85.0%

thy: 96.6%exp: 89.5%

|0> (misidentified as |1>)• 3.4% stray tunneling

Error Budget

|0>|1>

Tun

nelin

g P

rob.

Single-Qubit Gate Errors: Limited by T1

measureIw

Iz

8 ns 8 ns

X X

0 20 400

10

20

P1 [%]

separation

3.4%stray tunneling

pulse separation [ns]

4% error at separation 11 ns

T1 decaypulsenon-linearity

double - error:

4%single-qubit gate fidelity:

98%

Vary the time between pi pulses to separate gate fidelity from decoherence due to T1 decay.

(limited by T1)

Direct measure of probabilityChecks on measurement & -gates

Coupled Qubits

Cc

C

011010012/ 10 C

CS c

0 0

1 0 0 1

1 1

On Resonance:

Straightforward to implement: simple coupling tunable fast readout simultaneous measurement

Cc

Entangling 2-Qubit Gate (Universal)

0 50025050 100 150 200 300 350 400 4500

20

40

60

80

100

t [ns]

Pro

bab

ilit

y o

f |0

1>,

|10>

, o

r |1

1> [

%]

|00>

Entanglement of Formation

0.2635 ebit

real imag

t

0 0

1 0 0 1

1 1S

DATA

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

Re [] Im [] Process Tomography of 2-Qubit Gate

SIM

Fidelity:Tr(thyexp) = 0.427

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

qu

en

cyOn-Off Coupling to TLS Memory

• 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(thymeas)

= 79%

Summary and Future Prospects

•Demonstrated basic qubit operations with fidelity

Initialize, gate operations, simultaneous measurement

10 to 50 logic operations

Tomography conclusively demonstrates entanglement

•Decoherence mechanism understood

Optimize dielectrics, expect future improvements

•Working on Bell violation, advanced CNOT gates (+ tunable)

•Simulating 4-5 qubit algorithms

•Scale-up infrastructure designed (“brute force” to ~100 qubits)

Very optimistic about 4 -10 qubit quantum computer

Single-Qubit Gate Errors: Tomography Check

detu

ning

[M

Hz]

measureIw

Iz

8 ns 8 ns

X

detuning (both pulses)

phase [/]theory

experimentGoal:Measure fidelity of pi-pulse (longest single-qubit gate) separately from measurement errors.

Idea: Two pi-pulses bring state back to |0>, where the only measurement error is stray tunneling. Remaining error is due to pi-pulses only.

Tomography Check: On resonance, phase of second pulse has no effect, as expected for pi-pulses.

0

1

P1

P1

|2> Errors from Fast Pulses

Zoom in on 2-state errors for many pulse lengths

0.4 0.8 1.2 1.60

50

100

Measure Pulse Amplitude [V]

P o

f T

unne

ling

[%]

|0>

4ns

5ns

6ns

8ns

Two State Errors

Measure

(FWHM)

X

Gaussian pulses:Minimum width in time and frequency

frequency

pu

lse

po

wer

1021

4ns

8ns

10

21

6.05 6.15 6.250

60

Microwave Frequency [GHz]

P |1

> [%

]

25 30 35 40 450.2

0.4

0.6

0.8

1

Delay between 01 pulses [ns]

P |2

> [

%]

- Pulses Give Low Background & Error Filtering

Measure |2> State

5 ns

|2> Error Two Photon Qubit

200MHz

delay

Ramsey Fringe Filtering of |2> state

4P2-error

X X

Delay timedelay [ns]

High Power Spectroscopy

Error vs. Gaussian Pulse Width

0 1 2 3 4 5 6 7 810

-6

10-5

10-4

10-3

10-2

10-1

100

[ns]

|2

erro

r

0 1 2 3 4 5 6 7 810

-6

10-5

10-4

10-3

10-2

10-1

100

[ns]

|2

erro

r

10-4S-curve-

FT theorySpectrum analyzerQuantum simulation