distributing entanglement in a multi-zone ion-trap

*Division 891

T. SchätzD. LeibfriedJ. ChiaveriniM. D. BarrettB. Blakestad J. BrittonW. Itano

J. JostE. KnillC. LangerR. OzeriT. RosenbandD. J. Wineland

NIST, Boulder QC Group

*

at “entanglement and transfer of quantum information”: September 2004

multiplexed trap architecture

interconnected multi-trap structuresubtraps decoupled

guiding ions by electrode voltages

processor sympathetically cooledonly three normal modes to coolno ground state cooling in memory

no individual optical addressingduring two-qubit gatesgates in tight trap

readout / error correction /part of single-qubit gates in subtrapno rescattering of fluorescence

D. J. Wineland et al., J. Res. Nat. Inst. Stand. Technol. 103, 259 (1998);D. Kielpinski, C. Monroe, and D. J. Wineland,Nature 417, 709 (2002).Other proposals: DeVoe, Phys. Rev. A 58, 910 (1998) .Cirac & Zoller, Nature 404, 579 ( 2000) .L.M. Duan et al., arXiv-ph\0401020

one basic unitsimilar to Cirac/Zoller, but:

modularity

NIST array N4N:● no new motional modes ● no change in mode frequencies

individually working moduleswill also work together

“only” have to demonstrate basic module

reminder:

2 wafers of alumina (0.2 mm thick)gold conducting surfaces (2 m)

6 zones, dedicated loading zone

2 zones for loading4 zones for QIP

heating rate 1 quantum/6 ms(two-qubit gate in 10 s)

Electrodes computer-controlledwith DACs for motionand separation

rf

rfdc

dc

200 m

Filter electronics on board (SMD)

(later: multiplexers, fibers , MEMS mirrors, detectors, sensors?)

current trap design

universal set of gates

universal two qubit gate(controlled phase gate):

implemented with 97% fidelity.D. Leibfried et al., Nature 422, 414 (2003)

single qubit rotations (around x,y or z-axis):experimentally demonstrated co-carrier rotations with> 99% fidelity.

individual addressing despite tight confining

3m

30mlaser beam waist

individual addressing gate

phase plot

/2 pulse

effectiveindividual

Raman beams

universal two-qubit gate

,

Stretch mode excitation

only for states

Center-of-mass mode, COM

Stretch mode, s

2

1

k1

k2

ktrap axis

stretch

mdk

FF

12

2

2

d

Fwalking standing wave

coherentdisplacement

beams

(e.g two qubits on stretch mode)

universal geometric phase gate

Gives CNOT or phase gate with add. single bit operations

1 0 0 0

0 00

0 0 0

0 0 01

G ei2

ei2

exp(i )

exp(i)

Gate (round trip) time,

g = 2/

Phase (area),

= /2

via detuning

via laser intensity

experiments

1) distribution and manipulation of entanglement2) quantum dense coding

3) QIP- enhancement of detection efficiency

4) GHZ-spectroscopy

5) teleportation

6) error correction

“playing” with entanglement of massive particles

two

thre

e q

ub

its

moving towards scalable quantum computation

implement ingredients for multiplex architecture

T.Schaetz, M.D. Barrett, D.Leibfried et al., PRL (2004)

T.Schaetz, M.D. Barrett, D.Leibfried et al., PRL submitted (2004)

D.Leibfried, M.D. Barrett, T.Schaetz et al., Science (2004)

M.D. Barrett, J.Chiaverini, T.Schaetz et al., Nature (2004)

J. Chiaverini, D.Leibfried, T.Schaetz et al., Nature submitted (2004)

DETECTOR

individual addressing and entanglement distributed over two zones

22

GatePhase

ii

22 )()( 2222

i triplet singlet

2I )()(22

parity oddor rotate not does singlet

entangled pair distributed and manipulatedentanglement survives

distribution of entanglement

DC-electrodes

RF-electrode

Fidelity: F= = 0.85

No adverse effects from moving,individual rotation and separation

Distribution and manipulation of entanglement: results

controltripletsinglet

Singlet (do individ. pulse after separation) = -

no rotation from final pulse, odd parity

Triplet (no individ. pulse after separation)+= +

rotates to - ei even parity

Control (preparation only, no motion) + rotates to - ei even parity

no adverse effects from moving,individual rotation and separation

Fidelity: F= = 0.85

quantum dense coding

one of fourlocal operations

on one qubitreceiving

two bits ofinformation

sending one qubit

entangled state

General scheme:

Theoretically proposed by Bennett and Wiesner (PRL 69, 2881 (1992))

Experimentally realized for ‘trits’ with photons by Mattle, Weinfurter, Kwiat and Zeilinger (PRL 76, 4656 (1996))only two Bell states identifiable, other two are indistinguishable ( trit instead of bit)non deterministic (30 photon pairs for one trit)(but: photons light and fast)

AB

I x y z

0.84 0.07 0.06 0.03

0.02 0.03 0.08 0.87

0.07 0.01 0.84 0.08

0.08 0.84 0.04 0.04

average fidelity 85%

quantum dense codingproduce Alice’s entangled pair/2-pulse and phase gate on both qubits

rotate Alice’s qubit onlyx, y, z or no-rotation (identity) on Alice’s qubit, identity on Bob’s qubit

Bob’s Bell measurement phase gate and /2-pulse on both qubits

Bob’s detectionseparate and read out qubits individually

resu

lts:

Enhanced detection by QIP

coherent operations @ high fidelitystate detection (read out) @ low fidelity

detection asbottleneck?

out0 |000…0> + 1 |000…1> + … + 2(N-1) |111…1>

measurementprojection in one of the 2N eigenstates with probability |k|2

one qubit read out Fdet 1 state read out FNdet <

e.g. Fdet = 0.70 and N = 20 FNdet < 0.0008

e.g. Fdet = 0.99 and N = 20

output of an algorithm (e.g. Shor’s)

FNdet = 0.82

measurement not only after an algorithmscalable QC needs error correction measurement as part of the algorithm

Enhance detection – how? statistical precision by repetition(run algorithm many times)

statistical precision by reproduction(copy primary qubit many times)

statistical precision by amplification(QIP on primary qubit and ancillae)

measure M+1 qubits(+ take majority vote)

for Fdet < 1 FN shrinks exp.<

for Fdet ~ 1 still bad iftdet < talgorithm<

no cloning theorem

(| + | )

qubit (control)

ancillae (targets)

|a1|a2 … |aM +

|a1|a2 … |aM | |a1|a2 … |aM

M+1 tries

QIP

e.g. CNOT’s

D.P. DiVincenzo, S.C.Q. (2001) error reduction > 40 % [only one ancilla (max. 99%)]results:

0

= (| + ei0t|) ·(| + ei0t|)···(| + ei0t|)/2N/2

= (|··· + exp(-iNt) |···)/21/2

0

entangled“superatom”

Entangled-states for spectroscopy (J. Bollinger et al. PRA, ’96)

non-entangled

Experimental demonstration (two ions)

(V. Meyer et al. PRL, ’01)

GHZ state (spectroscopy)

projection noise limited:

Heisenberg limited:

o ~ 1/ N

o ~ 1/ N

GHZ state : results-i 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 -i 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 -i 0 0

0 0 0 0 0 0 -i 0

0 0 0 0 0 0 0 1

P3 =

…

GHZ state preparation

entanglement enhanced spectroscopy [gain by factor 1.45(2) over projection limit]

GHZ spectroscopy

G3 = (/2) () P3 (/2):

GHZ = + i

Total fidelity: F= GHZGHZ = 0.89(3)

-i 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 -i 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 -i 0 0

0 0 0 0 0 0 -i 0

0 0 0 0 0 0 0 1

(also in Innsbruck)

Prepare ions in state and motional ground stateCreate entangled state on outer

ions

Alice prepares state to beteleported

Alice performs Bell basis decodingon ions 1 and 2

Alice measures ion 1Alice measures ion 2Bob performs conditionalrotation dep. on meas.Bob recovers onion 3 and checks the state

Entire protocol requires ~2.5 msec (also in Innsbruck)

Teleportation: Protocol

Error correction basics

• Encode a logical qubit state into a larger number of physical qubits (here 1 logical qubit in (3 – large?) physical qubits)

• Make sure that your logical operations leave the state in one part of the total Hilbert space while your most common errors leave that part

• Construct measurements that allow to distinguish the type of error that happened

• Do those measurements and correct the logical state according to their outcome

classical strategy: redundancy by repetition (0 00…0, 111…1 and majority)

quantum analog: repetition code(see e.g. Nielsen and Chuang)

● experimental error correction with classical feedback from measured ancillas● no classical analog

3 qubit bitflip error-correction

encoding/decoding gate (G) implemented withsingle step geometric phase gate example data

(error angle)2

Infid

elity

(1-

F)

J. Chiaverini et al., submitted

Experiments

“playing” with entanglement of massive particles

moving towards scalable quantum computation

1) separation and transfer of qubits between traps2) maintaining entanglement 3) individual addressing (in tight confinement)4) single and two qubit gates5) use of DFS (Decoherence Free Subspace)6) use of ancilla qubits (trigger conditional operations) 7) pushing QIP fidelities principally towards fault tolerance8) non-local operations / teleportation (including “warm gate”)9) step towards fault tolerance ( 3 qubit error correction)10) (sympathetic cooling)

It is not over, just a start… (fault tolerance)

reduce main sources of error (e. g. beam intensity) ,demonstrate error correction and make it routine tool

test new traps using reliable ways of “mass fabrication”, (lithography, etching, etc.)

incorporate microfabricated electronics and optics(multiplexers, DACs, MEMS mirrors ect.)

IV. “scale” electronics and optics to be able to operate in larger arrays

III. build larger trap arrays

II. reach operation fidelity of > 99.99%, incorporate error correction

I. incorporate all building blocks with sympathetic cooling in one setup

more complicated algorithms

New Trap Technology

Approaches to the necessary scale-up for trap arrays…

almost arbitrary geometries

very small precise features

atomically smooth mono-crystalinesurfaces

incorporate active and passiveelectronics right on boardfilters, multiplexers, switches,detectors

incorporate opticsMEMS mirrors, fiberports…

Back to the Future:Boron-Doped Silicon

Joe Britton

Future techniques II

Control electrodes on outside easy to connect

• “X” junctions more straightforward

Field lines:

dc rf dc rf dc

Pseudopotential:

Planar 5 wire trap

John Chiaverini

Planar Trap Chip

DC Contact pads

RF

Gold on fused silica

John Chiaverini low pass filters

trapping region