Design and Optimization of a Quantum Dot Qubit System

1
Design and Optimization of a Quantum Dot Qubit
System
Russel Caflisch1, Mark Gyure2, Hans Robinson3 and
Eli Yablonovitch3 1Department of Mathematics,
UCLA 2HRL Laboratories 3Department of Electrical
Engineering, UCLA
Modeling and simulation can be used for design
and optimization of nanosystems, such as solid
state implementation of a qubit for use in
quantum communication and computation.
Overview
Role of Simulation
Quantum Communication and Computing
A Gates
Read-out Channel Depletion Gate (1 of 2)
J Gates
i-InP

• Quantum logic provides for exponential
  parallelism that can greatly enhance
  communication security and computational speed in
  selected applications.
• In this solid state implementation, the qubit
  consists of spin on an electron in a quantum dot
  (QD) and the readout is through a quantum wire
  (QW).
• The dot and wire are confined vertically using a
  layered heterostructure and laterally using
  lithographic gates.

• Simulation is an important guide to experimental
  design of the qubit system, because the
  experiments are difficult to perform and the
  successful design window is small.
• Effective simulation requires a multiscale
  multiphysics strategy fine scale and detailed
  physics for accuracy coarse scale and idealized
  physics for high throughput.

nInP
i-InP
i-Ga0.58In0.42As Qubit Layer
i-InP
i-Ga0.60In0.40As Read-out Layer
i-InP
nInP
i-InP
Quantum repeater design
Qubit Device
Mathematical and Computational Model
Multiscale Simulation
Device Geometry
Validation
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fg
fb

• Detailed computational physics code nextnano3
• Schrodinger-Poisson (SP) for potential f and
  electronic wavefunction ?
• In which U is bandoffset, ? is energy
  (eigenvalue)
• Full-scale numerical solution of SP by Chris
  Anderson, Math Dept, UCLA
• Semianalytic solution of SP, based on
  approximating all potentials as harmonic or
  square-well in each direction, and use of
  resulting explicit Schrodinger solutions

• InP (blue)
• GaInAs lattice-matched (red),
• d-doped layers (light blue)
• Gates (green)
• Design parameters
• 6 layer widths, 2 gate sizes,
• 2 doping densities
• Operation parameters
• 2 gate potentials

• Validation of SP model by comparison to pinchoff
  experiments and to results from nextnano3.
  Excellent fit, after choice of activation
  fraction in doping layers

s1
dz1
dz3
dz2
dz5
dz4
s2
dz6
Pinch-off voltage vs. gate separation.
Electrostatic Potential and Electronic
Wavefunction

• Validation of semianalytic model by comparison
  to full-scale simulation. Excellent fit for
  potential and eigenvalues, without
  self-consistent terms and background doping. Ad
  hoc correction for self-consistency.

• Band offsets in the GaInAs form quantum wells.
• Planar side gates produce potential (light blue)
  that confine electrons to a QW in the bottom
  well.
• Central gate produces potential minimum that
  confines electron to a QD in the upper well.
• Wavefunction (pink) confined to QW and QD.

Potential on centerline for
no SC SC Full-scale x
x Semi-analytic --
--
Device Design
Device Optimization
Search for Optimal Designs
Design Goals
Search for Successful Designs
Robustness

• Double pinchoff design has robustness of only
  than 0.3 SDs, low probability of success
• Search for optimal design is performed by
• Allowing small number (7) of conduction states in
  QW
• analytic determination of nearest failed design
• analysis of optimal doping densities
• Monte Carlo search.
• Resulting optimal design has robustness of 2.8
  SDs, high probability of success

• Optimize design robustness in the presence of
  uncertainty in growth and fabrication i.e. find
  vsmaximizing
• in which vs and vf are successful and failed
  designs, and the distance is
• measured in units of standard deviation (SD) of
  growth and fabrication

• Double pinchoff
• single trapped electron in QD
• Single conduction state in QW
• Mathematical formulation
• ?1d(?g) lt 0 lt ?2 d(?g)
• ?1 w (0) lt 0 lt ?2 w (?g)
• in which
• ?kd(?g), ?kw (?g) k-th eigenvalue in QD, QW
• ?g negative bias on central gate
• ?(0) eigenvalue away from gate
• Correction for electron interactions in dot is
  included

• Monte Carlo search in 10d space of design
  parameters for successful design.
• Semianalytic method enables testing of 106
  candidates, yielding 6 successful designs.

Design window
fside
Example of failure mode collapse of design
window in operation parameter space
fcentral
f
Maximal number of transverse states for different
doping densities
100 mm
?1d(?g) 0 ?2d(?g) 0 ?1w (0) 0 ?2w (?g) 0
W
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z
fb
?
Potential on centerline and eigenvalues
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