Optical Quantum Computing Using Spin Qubits

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Optical Quantum Computing Using Spin Qubits
Brendon Lovett
brendon.lovett_at_materials.ox.ac.uk
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Outline

• Non-interacting spin systems
• Long lived storage qubit.
• Fast two qubit gate using exciton states.
• Continuously interacting spins
• Passivate interaction by using excitons.

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Quantum Dots Introduction
Let us look at some optically active dots those
grown by molecular beam epitaxy in the
Stranski-Krastanow mode.
TEM
AFM

• Two semiconductors of differing band-gap.
• Different lattice constants cause spontaneous
  formation of quantum dots.

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Quantum Dots Electronic Structure
DOTS
BULK

• The degeneracy is lifted by confinement.
• Some light-heavy hole mixing is usually present,
  but well ignore that for now!

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Spins in Quantum Dots

• In SK dots, it is hard to contact samples, and
  wouldnt really want to anyway.
• Extra electron spins can be added by lightly n
  doping samples.
• Good evidence that systems have been made with
  exactly one extra electron.

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Interaction with a Laser Pauli Blocking

• Pauli Blocking describes how an exciton state can
  be created depending on the spin of an excess
  electron in the quantum dot by using circularly
  polarized light.

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Interactions Between Dots
Lovett, Reina, Nazir and Briggs, Physical Review
B 68, 205319 (2003) Nazir, Lovett, Barrett, Reina
and Briggs, Physical Review B, in press (January
2005)

• Foerster transfer interaction is mediated by
  electromagnetic vacuum.
• It is a dynamic dipole-dipole coupling.
• It is a non-magnetic interactions which conserves
  spin.

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Interactions Between Dots

• Exciton-exciton static dipole coupling.
• Typically 1-10 meV.

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The Hamiltonian

• Pauli Blocking causes the Hamiltonian to split
  into four uncoupled subspaces.

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Performing a CPHASE Gate
Nazir, Lovett, Spiller, Barrett, Briggs, Physical
Review Letters 93, 150502 (2004)
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What is Happening During the Gate?
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Energy Transfer Interactions - Again
Benjamin, Physical Review Letters 88, 107904
(2002) Nazir, Lovett and Briggs, Physical Review
A 70, 052301 (2004)

• Energy transfer interactions allow energy to move
  back and forth between resonant qubits.
• When the qubits are off resonance, the energy
  transfer is blocked, since energy cannot be
  conserved.

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Control of Always-On Interactions
Benjamin and Bose, Physical Review Letters 90,
247901 (2003) Physical Review A 70 032314 (2004)

• By altering the energy of the barrier qubit we
  can do a two qubit operation between X and Y.

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Mathematical Description
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Gate Details
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Level Shifting With a Laser
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Pictorial Representation
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Quantum -v- Classical Radiation
I have shown that levels shift when an atom is
coupled to a quantized laser field. This analysis
can be carried over to the classical case with
the help of Floquets theory for converting a
time-dependent Hamiltonian to a time independent
one. See Shirley, Phys. Rev. 138 B979 (1965) and
Cohen-Tannoudji, et al. J. Phys. B 6 L214 (1973)
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Tuning the Qubit Energy with a Laser
A laser is tuned to the 0-T transition
It splits and shifts both of these levels
The level 1gt is not affected, since it does not
couple due to frequency or polarization
selectivity
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Qubit-Barrier Scheme Using Lasers
Benjamin, Lovett and Reina, Physical Review A 70
060305 (2004)

The barrier energy can be altered by applying a
laser tuned to the third higher level. This
effectively turns off the energy transfer
interaction, since the qubit no longer has a
resonant energy. This allows for a simple
quantum gate.
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Quantum Dynamics
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• Good performance even with an unstable Tgt level.
  (Decay introduced using optical master equation).
• Even works when the laser is pulsed rather than
  continuous.

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Potential Physical Embodiments

• Endofullerenes in nanotubes
• Self assembled quantum dots

(Picture courtesy of Sheffield University)
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Summary

• Have shown how to do fast gates in spin systems
  by using optical coupling to strongly interacting
  excitons.
• Continuously interacting spins can be used to
  build quantum information processors by
  passivating their interaction using optics.

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Thanks to

• Simon Benjamin
• Andrew Briggs
• Ahsan Nazir
• Tim Spiller
• Sean Barrett
• John Henry Reina
• Ehoud Pazy
• Sougato Bose