Quantum Logic via Quantum Dots

1
Quantum Logic via Quantum Dots

• Joon Ho Baek, Happy Hsin, Joshua LaForge, Daniel
  Nedelcu, Tamar Neumann

2
Project Questions

• What physical properties of a quantum dot can be
  used to carry quantum information?
• How do we create simple quantum gates using these
  systems?
• How do we create simple quantum circuits using
  these systems?

3
Quantum Dots

• Semiconductor nanocrystal.
• Prepared using molecular-beam epitaxy or colloid
  techniques.
• Physical boundary of the Qdot confines excitons
  in a 3D well.
• Dimensions on the order of the exciton Bohr
  radius (10nm).

University of New Castle Condensed Matter
Theory http//cmt.phys.ncl.ac.uk/research/dot.php
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Quantum Dots

• The strong confinement in three dimensions
  produces new phenomena not seen in the bulk
  material.
• Useful for quantum computation because of
  environmental isolation, and the reduction of
  internal degrees of freedom that could lead to
  decoherence.

Strouse, G. University of California Santa
Barabara http//www.chem.ucsb.edu/strouse_group/r
esources.html
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Electron Spin

• Pros
• Dephasing time 0.1 µs with gate switching
  speeds of 30 ps
• Spin coherent transport of 100µm
• Expect longer decoherence times than charge
  degrees of freedom since spin is insensitive to
  electrical potential
• Scalable arrays
• Cons
• Cryogenic temperatures for long coherence times.

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Proposed System

• All electrical system
• Qdots defined by electrical gating of 2DEG
• Allows for very fast switching times (ps)
• Scalable to arbitrary size

Golovach VN, Loss D. Semicond. Sci. Technol. 17
(2002) 355366
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Quantum Gates

• Single-qubit operations translate to single spin
  rotations
• Need localized magnetic fields
• 2-qubit gates formed through coupled quantum dots
• Square root of the swap operator used to create
  an XOR (cNOT) gate
• XOR and single qubit operations are universal

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Read-Out

• Tunnel in supercooled paramagnetic dot.
• Use spin-valve to selectively transfer spin to
  another quantum dot, which can be measured using
  an electrometer.

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Spin Off

• Domino Dots
• 5 dots
• 4 electrons
• These states are not
• mutually orthogonal
• Orthogonal states
• Gates can be created by
• increasing tunneling
• The important part
• Any SU(2) rotation can be
• done with H12 and H14
• (note H12H34 and H14 H23)

agt
bgt
cgt
0gt agt
1gt (bgt cgt)/v2
H 12
H 14
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Spin Off

• Domino Dots (take 2, part 2)
• 2-qubit gates
• Combine with single qubit rotation for an
  arbitrary unitary transformation
• Since these all exist in a singlet ground state,
  they are virtually immune to most types of
  decoherence

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Taking Charge

• Domino Dots (take 2) Cellular Automata
• 5 dots
• 2 electrons
• Cascade effect
• (wireless interconnect)
• Majority rule

1gt
0gt
? More energetically favorable
Input cells
Device cells
Vheight of barrier controlled by top gate
Energy of e- coming from source
Mean energy from free e-
?
source
drain
Output cell
V potential at bottom of well controlled by
bottom gate
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Taking Charge

• Logic Gates (examples)
• Inverter
• branch
• And/Or
• 1 fixed input
• 0 for or
• 1 for and
• 2 variable inputs

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Quantum Computing with QD Excitons

• Excitons electron-hole pairs
• Pros
• Easy to initialize
• Scalable
• Easy read-out

• Cons
• decoherence times are relatively short
  (20-100ps)
• BUT it is possible to induce fast unitary
  time-evolution by using a coherent ps or fs laser
  radiation!!

H.Kamada, Quantum Computing with QD Excitons,
NTT Technical Review Online 1 3 (2003)
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Single Qubit Rotation
Rabi oscillations
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Rabi Oscillations
Pump power a T(inf) total pulse
area Excitation of the QD resonance can be
controlled by the strength of the pump pulse
T 6K, Rabi oscillations
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CNOT implementation
Using a coherent laser (p-pulse with energy
EcDEct) will result in a p rotation if and only
if the control bit is in state 1cgt.
What about performing CNOTs on remote QDs?
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Remote CNOT gate
SWAP
agt
bgt
bgt
agt
R1 R2
SWAP SWAP CNOT SWAP SWAP
R1 R2
R1 R2

C T
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Read-out
Probe beam
Statistical distribution of QD size and
composition gives different QD optical responses
? Easy to differentiate btwn QDs BUT
current strategy requires a number of repeated
measurements
QD1 QD2 QD3
QD1
QD3
QD2
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Comparison
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Remarks

• We also looked at other areas, such as
  decoherence of electron spin states due to
  polaron formation, and nuclear spin that we did
  not have time to discuss.
• The methods that we discussed all deserve further
  investigation.

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References

• Stievater, T. H, et al. Rabi oscillations of
  excitons in single quantum dots, PRL 87, 13,
  (2001)
• Kamada, H., Quantum computing with qd exitons,
  NTT Technical Review, vol 1, no. 3, (2003)
• Loss D, DiVincenzo D. Quantum computation with
  quantum dots. Physical Review A 57 (1) (1998)
• Hellberg, C., Robust quantum computation with
  quantum dots, http//www.arxiv.org/quant-ph/030415
  0 v1 (2003)
• Golovach V, Loss D. Electron spins in artificial
  atoms and molecules for quantum computing.
  Semiconductor Science and Technology 17 (2002)
• DiVincenzo D, Loss D. Quantum computers and
  quantum coherence. Journal of magnetism and
  magnetic materials. 200 (1999)