Quantum Information Processing with Atoms and Light

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Quantum Information Processing with Atoms and
Light
Daniel F. V. James Group T-4, Los Alamos
National Lab University of Toronto,
Canada Monday, 28 March 2005
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Research Interests
- coherence-induced changes in spectra (and other
things)
- novel synthetic aperture imaging techniques
- properties of polarized light and ellipsometry
- characterizing quantum states and processes
- physical boundaries of entanglement and entropy
(MEMS states)
- realizing quantum gates and detectors
- spin-based quantum solid-state quantum
computing architectures
- read-out techniques (optics, MRFM,cantilevers)
and tomography
- quantum dynamics of trapped ions (modes,
heating, motion...)
- quantum algorithms teleportation, factoring...
- scalable architectures
- quantum simulations (chaos, phase transitions
etc.)
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Collaborators
-Quantum Optics Experiments Paul Kwiat
Andrew White Michael Di Rosa, Fio
Omenetto -Ion Trap Experiments Rainer
Blatt Ferdinand
Schmidt-Kaler -Solid State Quantum Technology
Marilyn Hawley Robert Clark -Classical and
Quantum Optics Theory Emil Wolf Gerard
Milburn Peter Milonni, Eddy Timmermans,
Gennady Berman, Gerardo Ortiz, Juan-Pablo Paz,
James Gubernatis
-LANL Postdocs John Grondalski Sergey
Ponomarenko
-Los Alamos Summer School David Etlinger,
Rochester/Northwestern David Hume,
Kentucky/Colorado Miho Ishibashi,
Salisbury/Stanford Matt Krems, Missouri
Rolla
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Quantum Computing Basic Ideas
Classical digital computers Each register is
either 0 or 1
Quantum Computers Each register (qubit) can
be in a superposition of two states 0? and 1?
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Quantum Memories
State of one quantum data register (qubit)
a??? b?1?
State of two qubits
a?????? b????1? ? c?1???? d?1??1?
State of three qubits
a????????? b???????1? ? c????1???? d????1??1?
e?1??????? f?1?????1?
? g?1??1???? h?1??1??1?
a, b??c and d etc. are the probability
amplitudes.
n qubits 2n pieces of information
Quantum memories are BIG
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Quantum Parallelism
Operations on one qubit effect ALL of the data
in the quantum register.
Example bit flip on second qubit a??????
b????1? ? c?1???? d?1??1? ? b??????
a????1? ? d?1???? c?1??1?
Quantum computers perform complex operations on
very large registers very efficiently
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Quantum Logic Gates
You can do ANYTHING if you can do the following
two things
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Measurement and Readout
Projective measurement of each
qubit i.e. A?0? B?1? ? ?0? (probability
P0A2) OR A?0? B?1? ? ?1? (probability
P1B2)
N qubits store 2N bits of information and process
them efficiently, BUT you can only read out N
bits to get the final answer.
Restricts types of algorithms that can be
executed on a quantum computer global
mathematical properties like periodicities.
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Killer App Factoring
Shors Algorithm what are the factors of the
integer n?
Period Finding ? Factoring
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Classical factoring evaluate fn,x(a) for a
large number ( 2L-1 ) of values of a until you
can find r.
2L operations replaced by 1 operation
Quantum Fourier Transform and measurement gives
r.
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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 of Trapped Ion QC
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
2005
Theory
Cirac Zoller
Cat motional states
cooling 2 ions
differential mode heating (James King et al.)
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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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 wave front
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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• -Continuous Variables photon number rather than
  polarization
• Kimble et al., Science 282, 706 (1998).
• Lam et al., Phys. Rev. A 67, 032302 (2003).

• NMR no entanglement, no projective measurement,
  no pure states
• Nielsen et al., Nature 396, 52 (1998).

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The Tricky Part Bell State Detection
Measurement of the output gives a Bell state
detector
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Teleportation Circuit
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The Ca ion
D.F.V. James, Appl Phys B 66, 181-190 (1998)
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Laser Operations
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How to do a Controlled-Z gate
phonon
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Trapped Ion-Phonon Controlled-Z gate
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State Readout
what state is the atom in?
cannot detect single photons
over 95 detection efficiency
M.A. Rowe et al. (Wineland group) Nature 409,
791-794 (2001) - detection loophole
D. F. V. James and P. G. Kwiat, Phys. Rev.
Lett. 89, 183601 (2002) - photon detection
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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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Whats Next ? 15 5 x 3 (we hope!)
p/2
p/2
Z
p/2
p/2
Z
p/2
Z
Z
p/2
p/2
argument register (2 qubits)
function register (2 or 3 qubits)
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Prospects for Trapped Ion QIP
Next year or two
- experiments with 5 qubits
- larger entangled states
- primitive versions of factoring
- error mitigation techniques (error correction,
DFS etc.)
- proof-of-principle quantum simulators
Scalability of ion traps?
- moving ions around (Boulder, Michigan, Ulm etc.)
- connected micro-traps (Innsbruck, Michigan)
- other paradigms ?
Does the final technology have to be solid
state?
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Research Interests
- coherence-induced changes in spectra (and other
things)
- novel synthetic aperture imaging techniques
- properties of polarized light and ellipsometry
- characterizing quantum states and processes
- physical boundaries of entanglement and entropy
(MEMS states)
- realizing quantum gates and detectors
- spin-based quantum solid-state quantum
computing architectures
- read-out techniques (optics, MRFM,cantilevers)
and tomography
- quantum dynamics of trapped ions (modes,
heating, motion...)
- quantum algorithms teleportation, factoring...
- scalable architectures
- quantum simulations (chaos, phase transitions
etc.)