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Quantum Computing with Trapped Atomic Ions

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Title: Quantum Computing with Trapped Atomic Ions


1
Quantum Computing with Trapped Atomic Ions
Garching
Boulder
  • APS March Meeting - Montréal March 21, 2004
  • Brian King
  • Dept. Physics and Astronomy, McMaster University
  • http//physserv.mcmaster.ca/kingb/King_B_h.html

2
Outline
  • building quantum computers
  • overview of ion trap quantum information
    processor
  • ion trapping
  • initialization and detection
  • single-qubit gates (internal)
  • coupling internal and external qubits
  • directions for the future...

3
Building Quantum Computers
  • Need
  • qubits
  • two-level quantum systems
  • superpositions ? isolated from outside world
  • confined, characterizable, scalable
  • preparation
  • prepare computer in standard start state
  • read-out
  • logic gates
  • controllable interactions with outside world!
  • single- and two-qubits gate sufficient (not nec.!)

4
Why atomic qubits?
  • unparallelled persistence of quantum
    superposition
  • atomic clocks - accuracy, precision
  • control over quantum states - internal and
    external
  • BEC, Fermi degeneracy (controllable), Mott
    insulator transition, quantum squeezing, quantum
    state engineering...
  • atomic ions - demonstration of building blocks
    for scalable quantum computer architecture

the Devil is in the details...
the Devil is in the details...
5
Trapped-Ion QC (Cirac, Zoller('95))
  • a collection (string) of trapped atomic ions
  • qubits (1) internal atomic levels
  • quantum memory
  • tdecoh À tgate
  • T2 gt 10 min.
  • clocks
  • accuracy, stability
  • gt 1/1015

6
How it works...
  • A quantum logic gate between 2 different ions
  • prepare qubits using single-qubit gates
  • map qubit i state to motion with lasers
  • 2-qubit gate between motion and ion j
  • put information from motion back into ion i

i
j
7
Dynamical RF trapping
  • want to confine charged atoms ? E fields!
  • Eherenfest/Gauss ? cant use static fields

? use oscillating fields!
8
Dynamical RF trapping
  • full solution Mathieu equation (same results...)
  • same results
  • quantum harmonic oscillator
  • wavepackets breathe at ?T

9
Linear Ion Traps for QC
  • axial confinement - static!

U0
U0
V0,W
V0,W
  • F(z) (mwz2/2q) (z2/2)
  • wz22aqU0/m a 1 (geom.)
  • radial confinement -dynamic!
  • F(r) (m/2q) (wr2 - wz2/2) (r2)
  • wr2 q2V02/(2mWRFb4r4) b 1 (geom.)
  • wr lt WRF
  • micromotion small, at different freq.

10
Ion Traps - initial micromachining
  • DC U0 10 V
  • RF V0 750 V
  • ? 230 MHz
  • ? wHO 10 MHz
  • pressure lt 210?11 torr
  • single ion lifetime gt 10 h.
  • (cryogenic ? up to 100 days...)

11
Ion Motion in Trap
  • single ion
  • like a mass on a spring

12
Dirty little secrets - motional heating
  • after cooling to the ground state of motion, the
    ion heats back up!
  • timescale for motional manipulation 10 ?s
  • 0? ? 1? in 100 ?s (1998...)
  • motion only sensitive to noise spectrum near ?mot
  • fluctuating patch potentials?
  • RF-assisted tunnelling?
  • heating scales strongly with trap size 10 ? 4
  • heating seems related to atom source ? shield
    trap!

Q.A. Turchette et al. Phys. Rev. A 62, 053807,
2000.
  • 21st century NIST lt 1 /(4 ms)
  • IBM 1/(10 ms)
  • Innsbruck 1/(190 ms)
  • plus sympathetic cooling (multi-species...)

13
Internal-State Qubits
  • long-lived electronic states

Ca, Sr, Ba, Hg
199Hg Qmeas 1.61014 _at_ 282 nm
14
Internal-State Qubits
  • ground-state hyperfine levels

Be (313 nm), Mg (280 nm), Cd (215 nm)
P3/2
g/2p 19 MHz t 8 ns
P1/2
313 nm
?1?
9Be Qmeas 3.41011 _at_ 303 MHz 173Yb Qmeas
1.51013
1.25 GHz
S1/2
?0?
Be
15
State preparation
  • electronic
  • optical qubit - kT ? free!
  • hyperfine qubit optical pumping
  • vibrational Doppler sideband laser cooling

16
Single-qubit logic gate
17
Coupling qubit levels
  • oscillating field induces dipole moment
  • HI ? m E0 ei(kz - wLt)
  • can change electronic level
  • (resonance?)
  • if ion vibrates, interaction strength modulated
  • HI ? m E0 ei(kz0 cos(wzt)- wLt)
  • Quantum HI ? ½mE0 (S S-) ei(kz0 (a a)-
    wLt)
  • W (S S-) ei(h (a a)- wLt)
  • can change motion!
  • (k z0?nvib z0 / l ?nvib) (... and
    resonance...)

18
CZ Realized
  • motion-dependent spin transitions (conditional
    logic)

1ñm
?ñº 1ñe
0ñm
1ñm
ñº 0ñe
1ñm
0ñm
auxñ
0ñm
19
CZ Realized - a two-ion logic gate!
F. Schmidt-Kaler, et al., Nature 422, 408 (2003)
  • two 40Ca ions - CZ scheme
  • but no aux? needed...

theoretical
measured F 70
20
CZ Realized - a two-ion logic gate!
  • doesnt use aux? - uses clever NMR trick!

2ñm
1ñm
?ñº 1ñe
0ñm
use (p,x) (p/?2,y) (p,x) (p/?2,y)
1ñm
ñº 0ñe
0ñm
21
Scaling up
  • problem
  • as Nions ?
  • ion string gets heavier ? gates get slower!
  • more motional modes ? greater noise
  • optical multiplexing

R. DeVoe, PRA 58, 910 (98) J.I. Cirac, et al. PRL
78, 3221 (97)
22
Solutions (1) - optical
  • MPQ, Garching (Ca) 4 2S1/24 2P1/2
  • G.R. Guthöhrlein, et al., Nature 414 (01)

res. l/10
  • U. Innsbruck (Ca) 4 2S1/23 2D5/2
  • A.B. Mundt, et al., quant-ph/0202112

red shift
blue shift
  • sweep PZT
  • Þ Doppler shift
  • Pex. gt 0.5 Þ coherent
  • positioning
  • node/antinode
  • res. l/100
  • differential coupling to motional sidebands

23
Scaling up
  • problem
  • as Nions ?
  • ion string gets heavier ? gates get slower!
  • more motional modes ? greater noise
  • quantum CCD
  • quantum CCD
  • Wineland, et al. J. Res. NIST 103, 259 (98)
  • D. Kielpinski, et al. Nature 417, 709 (02)

24
Solutions (2) - physical multiplexing
M. Rowe, et al., Quantum Information and
Computation 1, x (01).
  • transporting ions between traps

(1) Ramsey interferometer
  • no transport 96.8 0.3 contrast
  • line triggered 96.6 0.5 contrast!
  • 60 Hz fields...

spin echo 96 contrast
(2) separating ions
Dn200 quanta (2.9 MHz) for 10 ms sep.
time (separation electrode too wide!)
95 sep. eff. (5000 shots)
25
Solutions (2) - physical multiplexing
  • gold foil traps
  • silicon traps
  • easily micro-machined, smooth

26
Ion Trap QC Wither thou?...
  • single-qubit logic gates (40s) (gt98 fidelity)
  • single-ion 2-qubit logic gate (95) (80
    fidelity)
  • C. Monroe et al. Phys. Rev. Lett. 75, 4714
    (95).
  • 2-ion 2-qubit logic gates ? 2 (80 / 97
    fidelity)
  • Gulde et al. Nature 422, 408 (03).
  • Leibfried et al. Nature 422, 412 (03).
  • Deutsch-Jozsa algorithm
  • Gulde et al. Nature 421, 48 (03).
  • state preparation (fidelity gt 98)
  • spin qubit t / tgate gt 1000
  • motional data bus/qubit
  • heating lt 1/(4, 10, 190 ms) (NIST, IBM, Innsbruck)

NIST Boulder, MPQ, IBM Almaden, U. Innsbruck,
Oxford, U. Michigan, McMaster
http//physserv.mcmaster.ca/kingb/King_B_h.html
27
References
  • Cirac Zoller New Frontiers in Quantum
    Information With Atoms and Ions, Physics Today
    57, 3, 38 (March '04).
  • Steane Appl. Phys. B 64 , 623 ('97).
  • Ghosh Ion Traps, (Clarendon Press, '97),
    ISBN 0198539959.
  • Leibfried et al. Quantum dynamics of single
    trapped ions, Rev. Mod. Phys. 75, 281 ('03).
  • Wineland, et al. Quantum information processing
    with trapped ions, Phil. Trans. Royal Soc.
    London A 361, 1349, ('03).
  • Wineland, et al., Experimental Issues in
    Coherent Quantum-State Manipulation of Trapped
    Atomic Ions, J. Research NIST 103, 259 ('98).
  • Monroe, et al. Experimental Primer on the
    Trapped Ion Quantum Computer, Forschr. Physik
    46, 363 ('98).
  • http//jilawww.colorado.edu/pubs/recent_theses/
  • D. Kielpinski, Entanglement and Decoherence in a
    Trapped-Ion Quantum Register
  • B.E. King, Quantum State Engineering and
    Information Processing withTrapped Ions

28
Nobel Sidebar - Ramseys expt.
  • superpositions - how do we characterize phase?

t
29
2 is better than one!...
D. Leibfried, et al., Nature 422, 412 (2003)
  • spin-dependent motional Berrys phase
  • 2 lasers with dwL ? 0 create standing wave
  • dipole force

30
2 is better than one!...
  • resonant oscillating force displacement
    operator in phase space
  • a set by strength of force
  • phase set by phase between motion and lasers

31
2 is better than one!...
  • stretch mode
  • need different force on each ion to drive
  • can only excite if ions in different electronic
    levels!
  • move ions in closed loop in phase space

walking standing wave has different strengths
for ?,?
32
2 is better than one!...
  • IF ions in different electronic states, move
    quantum motional state in closed loop in phase
    space
  • ? motional Berrys phase ? phase shift
  • ???????Y? ???????? Y ?
  • ??????? Y ? ? eip/2??????? Y ?
  • ??????? Y ? ? eip/2 ??????? Y ?
  • ??????? Y ? ???????? Y ?
  • e-ip (eip/2 ???) ( eip/2???)? Y ?
  • controlled-Phase single-qubit rotations (F
    97)

33
and some 2s are better than others
in the lab
  • 2-qubit gates utilize the motion
  • gt cough, cough, mumblelt
  • higher motional n gives faster gates
  • ?? shining laser on only one ion!
  • Motional gates (Mølmer-Sørensen, Milburn, etc.)
    can be done illuminating all ions!
  • - keep n high ? fast motional gates
  • - with expt. gate, can have different
    illuminations
  • single-qubit operations can be done with weak
    trap
  • the accordion quantum computer!

34
Coupling qubit levels
  • laser-ion interaction messy details
  • in interaction picture
  • rotating-wave approximation
  • expand exponential
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