1. Ion Trap Quantum Computing and Teleportation
Daniel F. V. James
Group T-4, Los Alamos National Lab
2005 CQCT ANNUAL WORKSHOP
BELLBIRD RESORT, AVOCA BEACH, NSW
8 FEBRUARY 2005

2. Ion Traps • Cannot trap ions electrostatically (Earnshaw’s Theorem)
• Do it dynamically (Paul trap)
oscillating
saddle
potential
• Effective harmonic well (in all three directions)
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

3. Phonon Modes
Ions coupled by Coulomb force  ions’ oscillations have normal modes.
• Lowest mode: center-of-mass (CM):
• Next mode is “stretch” mode:
Number of modes in each direction = number of ions.
D.F.V. James, Appl Phys B 66, (1998)
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

4. Trapped Ion Quantum Computers
Harmonic potential
• Perform Rabi flips between and : local gates.
• Excite phonons of the vibration modes: quantum bus for multi-qubit gates.
• Efficient projective measurement
J. I. Cirac and P. Zoller , Phys Rev Lett 74, 4091 (1995)
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

5. Deutsch-Jozsa Algorithm
Historical Timeline
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Theory
Boulder
CNOT demonstrated
(ion + phonon)
Innsbruck
Multi-ion addressing
Cirac & Zoller
“Cat” motional states
cooling 2 ions
heating studies
2 qubit entanglement
“Hot”
Gates
Poyatos,Cirac & Zoller
Mølmer & Sørensen
Schneider, James &
Milburn
ion heating !!!
4 qubit entanglement
moving qubits
Deutsch-Jozsa Algorithm
geometric gate
Cirac-Zoller gate
sympathetic cooling
GHZ & W states
teleportation
error correction
tomography
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

6. Left to Right: Prof. Rainer Blatt (group leader), Dr
Left to Right: Prof. Rainer Blatt (group leader), Dr. Daniel James (guest professor from Los Alamos), Dr. Hartmut Häffner (postdoc), Dr. Christoph Becher (faculty member), Prof. Ferdinand Schmidt-Kaler (faculty member), Mr. Jan Benhelm (PhD student), Dr. Timo Körber (postdoc), Dr. Gavin Lancaster (postdoc), Dr. Christian Roos (faculty member), Dr. Wolfgang Hänsel (postdoc), Mr. Mark Riebe (PhD student).
Co-Authors of “Deterministic Quantum Teleportation with Atoms” at Innsbruck, 4 May 2004.
Nature 429, 734 (2004)

7. Innsbruck Ion Trap
made from four blades (a), two tips (b) and a supporting structure (c). (from F. Schmidt-Kaler et al., Appl. Phys. B 77, 789 (2003)).
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

8. The Ca+ ion Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

9. Christian Roos in the lab

10. What is Quantum Teleportation?
• Quantum wavefunction Reconstruction:
- the quantum state of a particle is transferred to another particle by means of a classical communication and a shared correlated resource
• Analogy with Holography:
- optical wavefront reconstruction
film
reference
beam #2
reconstructed
wavefront
wavefront - quantum state
reference
beam #1
object
film
correlated reference beams - entangled pair
Show figure from p.509 of Born and Wolf
Interference on film - Bell state measurement
film - classical information
- “Quantum mechanics is a good preparation for optics” (Denis Gabor)
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

11. Quantum Teleportation: Theory
three qubits:
the maximally entangled ‘Bell State Basis’ is:
re-write state of first two qubits using this basis:
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

12. Single operation on output qubit recreates input state
• Bell state analysis: measure which Bell state the first two qubits are in, projecting third qubit into one of four possible states:
Single operation on output qubit recreates input state
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

13. i.e. A three qubit quantum computer•
Charles H. Bennett, Giles Brassard, Claude Crepeau, Richard Jozsa, Asher Peres, and William Wootters, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels”, Phys. Rev. Lett. 70, (1993) [1385 citations].
Original Proposal •
three qubits, with good coherence properties, which we can address individually.
What is needed to do it experimentally?
Bell state preparation on qubits #2 and #3.
Asher Peres died on New Year’s Day 2005.
He was born “Aristide Pressman” in France in 1934; He changed his name when he moved to Israel, and was given the choice of “Asher Peres” or “Asher Afarsamon” (Peres means Eagle; Afarsamon is a fruit); he said he regretted his choice in later life, since the teleportation paper would have been “Afarsamon et al.” rather than “Bennett et al.” See quant-ph/
Bell State measurement (or equivalently C-Z gate and single qubit measurements) on qubits #1 and #2.
Operation on qubit #3 conditional on outcome of Bell state measurement.
Confirmation of result.
i.e. A three qubit quantum computer
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

14. Teleportation Circuit
2. input state to be teleported
4. measurement in the computational basis
3. Controlled-Z gate: the ‘flux capacitor’ of quantum computers
1. prepare the Bell state
6. confirm outcome
5. reconstruction
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

15. [ ] ( ) Laser Operations | … Blue sideband pulse: ˆR R = exp ↠()
(center of
mass mode)
(stretch mode) …
Laser Operations
Blue sideband
pulse:
blue
sideband ˆR [ ] R
= exp â†
() n + i â | e i 
–i S D 2 ( )
Carrier pulse
on n-th ion
carrier
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

16. Trapped Ion-Phonon Controlled-Z gate
pulse 1
pulse 2
pulse 3
pulse 4
BUT:
F. Schmidt-Kaler et al., Nature 422, 408 (2003)
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

17. • what state is the atom in? • cannot detect single photons
State Readout
• what state is the atom in?
• cannot detect single photons
• over 95% detection efficiency
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

18. Results: Fidelity of Teleportation measured for 300 trials
76%
74%
73%
75%
later results with Fidelities over 80% for all states
Dr. Daniel F.V. James
MS B283, PO Box 1663, Los Alamos NM 87545

19. Conclusions • Similar Experiments by Wineland’s group
M. D. Barrett et al., “Deterministic quantum teleportation of Atomic Qubits,” Nature 429, 737 (2004)
First teleportation with material qubits in pure states.
First qubit teleportation with complete projective Bell-state analysis.
First qubit deterministic teleportation (in any system).
• Teleportation Firsts
• Experiment is catching up to theory in quantum
computing
• It took TEN years to get here!