distributing entanglement in a multi-zone ion-trap * division 891 t. schätz d. leibfried j....
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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