Ion Trap Quantum Computing and Teleportation

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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
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Ion Traps
Cannot trap ions electrostatically (Earnshaws
Theorem) Do it dynamically (Paul trap)
oscillating saddle potential
Effective harmonic well (in all three
directions)
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Phonon Modes
Ions coupled by Coulomb force ? ions
oscillations have normal modes.
D.F.V. James, Appl Phys B 66, 181-190 (1998)
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Trapped Ion Quantum Computers
Harmonic potential
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)
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Historical Timeline
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
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Theory
Cirac Zoller
Cat motional states
cooling 2 ions
heating studies
2 qubit entanglement
4 qubit entanglement
moving qubits
Deutsch-Jozsa Algorithm
geometric gate
Cirac-Zoller gate
sympathetic cooling
GHZ W states
error correction
tomography
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Co-Authors of Deterministic Quantum
Teleportation with Atoms at Innsbruck, 4 May
2004.
Nature 429, 734 (2004)
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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)).
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The Ca ion
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Christian Roos in the lab
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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
wavefront - quantum state
correlated reference beams - entangled pair
Interference on film - Bell state measurement
film - classical information
- Quantum mechanics is a good preparation for
optics (Denis Gabor)
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Quantum Teleportation Theory
three qubits
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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
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Original Proposal

• Bell state preparation on qubits 2 and 3.

• 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
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Teleportation Circuit
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Laser Operations
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Trapped Ion-Phonon Controlled-Z gate
F. Schmidt-Kaler et al., Nature 422, 408 (2003)
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State Readout
what state is the atom in?
cannot detect single photons
over 95 detection efficiency
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Results Fidelity of Teleportation measured for
300 trials
later results with Fidelities over 80 for all
states
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Conclusions
Similar Experiments by Winelands group M. D.
Barrett et al., Deterministic quantum
teleportation of Atomic Qubits, Nature 429, 737
(2004)
Experiment is catching up to theory in
quantum computing
It took TEN years to get here!