Quantum Information Processing with Trapped Ions

E. Knill

C. Langer

D. Leibfried

R. Reichle

S. Seidelin

T. Schaetz

D. J. Wineland

NIST-Boulder Ion QC group

Be+ Be+

R. OzeriM. BarrettJ. BrittonB. R. BlakestadJ. ChiaveriniW. M. ItanoD. HumeJ. D. Jost

Overview

• Trapped ions Experimental System– The trap– Initialization, detection.– Coherent control of the ion-qubit– Deterministic entanglement

• Deterministic Teleportation Between Atomic Qubits.

• Quantum Error-Correction.

Linear RF Paul trap

RF electrode

High dc potentialcontrol electrode

Low dc voltagecontrol electrode

Positive ion

• Drive freq ~ 100-150 MHz• RF amp ~ 200-400 V• Secular freq

– Radial ~ 15 MHz– Axial ~ 4 MHz

Multi-zone ion trap

control

controlrf

rf

view along axis:

~1 cm

rf filter board• Gold on alumina

construction• RF quadrupole

realized in two layers

• Six trapping zones• Both loading and

experimental zones

• One narrow separation zone

• Closest electrode ~140 m from ion

segmentedlinear trappingregion

Ion transport

100 m

6-zone alumina/gold trap(Murray Barrett, Tobias Schaetz et al.)

200 mseparation zone

• Ions can be moved between traps.– Electrode potentials

varied with time

• Ions can be separated efficiently in sep. zone– Small electrode’s

potential raised

• Motion (relatively) fast– Shuttling: several 10 s– Separating: few 100 s

Electronic levels in 9Be+

2P1/2

2P3/2

2S1/21.25 GHz

F = 1

F = 2

2P Fine structure

Hyperfine structure

Turn on small B field

(P also has hfs, but it’s negligible)197 GHz

Qubit levels in 9Be+

2P1/2

2P3/2

2S1/2

1.25 GHz

Vibrational modequantum number

mF = -2mF = -1

mF = 0mF = 1

mF = 2

F = 1

mF = 1

mF = 0mF = -1

F = 2

Cooling and initialization

2P1/2

2P3/2

2S1/2

1.25 GHz

mF = -2mF = -1

mF = 0mF = 1

mF = 2

mF = 1

mF = 0mF = -1

Raman side-band cooling + Optical pumping =Ion initialized in the with better than 99% efficiency.

Qubit detection by resonance fluorescence

2P1/2

2P3/2

2S1/2

1.25 GHz

  F = 2, mF = -2  F = 1, mF = -1

Detection ()

313 nmDetection efficiency >99%

0 5 10 15 20 250

100

200

300

Exp

erim

en

ts

Photons collected

Ion in state , 200 us

0 5 10 15 20 250

25

50

75

100 Ion in state , 200 us

Exp

eri

me

nts

Photons collected

Coherent control of qubits

2P1/2

2P3/2

2S1/2

1.25 GHz

~ 80 GHz

Raman

313 nm

kk

Vib. modequantum #

Coherent qubit rotations

Any single qubit rotation can be composed of 1-3 pulses

i i

Bloch sphere

Entanglement on demand

Geometric phase gate:

FF

Polarization gradient “walking-standing” wave

Long. motional modes:

1st mode (COM)

2nd mode (stretch)

Set ion spacing such that stretch is not excited for

or .Can give opposite spin

states a phase relative to same spin states.Brennen, et al. PRL 1999

Jaksch, et al. PRL 1999Mandel, et al. Nature 2003

Phase gate

A

or

or

x

x

p

p

Tune from stretch mode,displace for

Start withPerformDobtain,with fidelity=0.97:

( i)

(Didi Leibfried et al. Nature 2003)

(Universal 2-qubit gate)

Good year for the ions!

• Creation of and spectroscopy with GHZ states. (NIST & Innsbruck)

• Enhanced state detection efficiency with QIP .

• Quantum Dense coding

• Deterministic teleportation between atomic qubits. (NIST & Innsbruck)

• Quantum error-correction with atomic qubits.

• Implementation of a semmi-classical Quantum Fourier transform.

(D. Leibfried et al. Science 2004)

(T. Schaetz et al. PRL 2004)

(M. Barrett et al. Nature 2004)

(T. Schaetz et al. PRL 2004)

(M. Riebe et al. Nature 2004)(C. F. Roos et al. Science 2004)

(J. Chiaverini et al. Nature 2004)

(J. Chiaverini et al. Submitted)

Quantum teleportation

Resources required: 2 cbits + entangled pair

Transmit classical information

Bell state measurement

Entangle pairDistribute entanglement

Apply conditionaloperation

Arbitrary state to beteleported

Bennet et al., 1993

Properties of Q. Teleportation

• Effectively transmit a qubit– Use a classical channel

• Actually transmit only 2 cbits– To classically define qubit: infinite # of cbits

• No information contained in 2 cbits

• Information in the correlations

• Entangled pair can be distributed anytime

• Initial qubit contains no info afterward

QT in the lab

Prepare ions in state and motional ground state

Create entangled state on outerions

Alice prepares state to beteleported

Alice performs Bell basis decodingusing phase gate on ions 1 and 2Alice measures ion 1

Alice measures ion 2Bob performs conditionalrotation dep. on meas.

Bob recovers onion 3 and checks the state

(Murray Barrett et al., Nature 04)

Entire protocol requires ~2.5 msec

(also demonstrated at Innsbruck with ions)Photons: Bouwmeester et al., Nature (1997) Furusawa, et al., Science (1998)

Teleportation results

• Average fidelity 78(2)%

• Best possible without entanglement: 2/3

A range of states was teleported:

i i

0 100 200 300 400 500 600 700

0

0.2

0.4

0.6

0.8

1

ramsey phase (deg) [relevant for superposition only]

teleported state measurement

pro

ba

bili

ty(d

ow

n)

downupsuperposition

Classical error correction

• Decoding or parity check allows reconstruction

• With a noisy line, “B” is hard to distinguish from “C”• A solution is to encode these letters in longer words• B becomes Bravo, C becomes Charlie

0 000 1 111Digitally:

Send eachencoded bit

An error occurs Decode usingmajority rule

111

101

Repetitioncode

Classical error checkingMeasurementresult

Error action Correctionoperation

Flip bit 1

None 000 or 111 No qubits flipped

1st bit flipped

2nd bit flipped

3rd bit flipped

100 or 011

010 or 101

001 or 110

Flip bit 2

Flip bit 3

Probability that more than 1 bit flips:

So rep. code provides an improvement when

Quantum error correction

• Problems in converting from classical– Can’t look at the quantum info.– No cloning of an unknown quantum state– Errors are continuous (not just a bit flip)

• Solution– Use entanglement– Make meas. that tell nothing about state

(QND).

Three bit repetition codeEncode state in three qubits via entanglement

||

Now an error E (rotation around x axis) occurs in one of the qubits

Apply E I I to our state

Three bit repetition code

Now measure the ancilla qubits

Decode

Ancilla qubits

Error correction with rep. code

Measurementresult

Syndrome Correctionoperation

X I I

I I I

I X I I I X

|

|

|

|

No qubits flipped

1st qubit flipped

2nd qubit flipped

3rd qubit flipped

If we get |, we

apply X I I to

Correction is independent of , , and

Error correction protocol

• G includes a three-ion entangling gate that gives all states but and a phase of

• Error rotation e applied to all qubits

• Ancilla qubits are measured after decoding

• R is either X, Y, or I dep. on measurement

e

e

e R

G G-1

Results

• Uncorrected infid. ~ e2, corrected infid. ~ e

4

• Qubits genuinely protected for e ~ 1 rad.

(J. Chiaverini et al. Nature 2005)

Summary

o Initialization and detection efficiency > 99%o Memory coherence time > 10 sec.o Trapped ion qubit can be coherently manipulated,

Fidelity > 99%.o Two or more qubits can be deterministically entangled,

fidelity > 97%.o Entanglement can be distributed across different traps

(~mm).o sympathetic cooling with 24Mg+ ions demonstrated .o Going for more ions!

From left to right:

Joe Britton, Jim Bergquist, John Chiaverini, Windell Oskay, Marie Jensen, John Bollinger, Vladislav Gerginov, Taro Hasegawa, Carol Tanner, Wayne Itano, Jim Beall, David Wineland, Dietrich Leibfried, Chris Langer,Tobias Schaetz, John Jost, Roee Ozeri, Till Rosenband, Piet Schmidt, Brad Blakestad

NIST Ion Storage Group, March, ‘04