Transcript No Slide Title

“Quantum computation with quantum
dots and terahertz cavity quantum
electrodynamics”
Sherwin, et al. Phys. Rev A. 60, 3508 (1999)
Norm Moulton
LPS
The hook...
• Other proposed QC architectures involving
quantum dots utilize only nearest-neighbor
interactions
J(t)s3•s4
•At the time of publication, this was the first
proposal for which gate operations might be
performed for an arbitrary pair of dots in the QC.
The approach is analogous to the Cirac-Zoller
approach using laser-cooled trapped ions:
Phonons
THz Resonant Cavity Photons
Laser
Pulses
Voltage pulses applied to
QDots
Both use an “Auxiliary State” to affect quantum gate operations
Proposed system:
•Array of GaAs/AlxGa1-xAs triple-well
nanostructures with electrical gates
•Each QD is charged with 1 and only 1 electron
•Dots are in a sharply resonant THz cavity, l>>Ldot
•CW laser with fixed ll introduced into the side
of the cavity
Stacked self-assembled quantum dots
GaAs
InAs
GaAs
GaAs
Etched quantum well structure
Superconducting electrodes
AlxGa1-xAs
GaAs
AlxGa1-xAs
GaAs
AlxGa1-xAs
GaAs
AlxGa1-xAs
Effective axial potential in the dot
System Hamiltonian

 
 
  



H  ωc ac a  E10e σ 11 E20e σ 22  g01e ac σ 01 σ 10 ac 
Cavity Photons
Projections


Rabi Oscillations


  
  by cavity
driven


 l,01e σ 01 expilt   σ 10 exp ilt   g12e ac σ 21 σ 12 ac 
photons (0-1)




Rabi
Oscillations
Rabi Oscillations driven by
driven by cavity
laser photons (0-1)
photons (1-2)
 
  

 l,12e ac σ 12 expiωlt   σ 21 ac exp iωlt 


Rabi Oscillations driven by
laser+cavity photons (1-2)
Auxiliary state (|2> )driven by two-photon processes


  

Htwo photon   e ac σ 02 expilt   σ 20 ac exp ilt 


~
Where:
g01l,12e  g12l,01e 
e  

ω21e  ωl ω21e  ωc
~
Transition Energies vs. Applied Field
E20
Energy (meV)
25
20
E10
15
10
el+c
5
0
0.5
el
ec
1.0
e (MV/m)
1.5
2.0
i10cc 0c 0tt 10t 1
CNOT Gate Operation: i 0
E20(el+c)
t
E10(el)
E10(ec)
c
c
c
t
p-pulse at ec
2p-pulse at el+c
State vector picks
up phase of i
State vector picks up
phase of -1
CNOT Gate Operation: i 10 cc101 tt 010
E20(el+c)
E10(el)
c
c
E10(ec)
t
c
p-pulse at ec
2p-pulse at el+c
State vector picks
up phase of i
Not on resonance with
E12 so no flopping.
Requirements for Quantum Computation
•Initializing the computer
•Inputting initial data
•Readout
•Error correction
Make
For
Arbitrary
Propose
Enlarge
kBaT<<E
hybrid
the
toone-bit
integrate
cavity
wait
rotations
tonew
of
create
that
less
10 adevice
thaneffected
are
quantum
several
uses
1nearest-neighbor
sec
cavity
well
will
using
detector
modes
ensure
Rabi
inthat
into
theall
qubits
oscillations
the
QD
concepts
cavity.
tunable
areinin
Detector
the
induced
level-spacing
state
cavity.
|0>.
isbytuned
laser
field.
to
range.
cavity
This
resonance
slows things
at thedown
readout
by
reducing
phase
e in
of the
the cavity
calculation.
resulting
in lower .
Requirements for Quantum Computation
•Decoherence
•Electronic State
•Cavity Photons
No experimental data
exists on these dots
Sources:
–Emission of freely
propagating photons
–Interaction with
fluctuating gate potential
(x-talk, Johnson noise)
Frequencies
lower than
When
QD
Prevented
by not
high-Q
E10/, cause
adiabatic
addressed:
3-D
cavity SC electrodes,
changes
the energy
SC path,
SC to
ground->
No
levels En,
to
dissipation
so leading
no thermal
phase errors.
fluctuations.
1
 t  
EneN t dt 

Noise during
switching

will cause errors and will
have to be addressed (“in
a future publication”).
Requirements for Quantum Computation
Sources of decoherence:
–Interaction with metastable
traps in the semiconductor
–Inhomogeneity in the dots
–Cavity photon lifetime
Engineer
Traps
Traps
Rely
Calibrate
on
farfuture
in
the
from
ultra-low
each
volume
quantum
electrode
advances
areproduction
between
in
dot
loss
shielded
prior
THzgate
to
cavity
computation
by
electrodes
technology
the
electrode
pose
a problem
Make cavity from Ultrapure Si
(finite two-phonon losses)
Use QDs with E01 smaller than the
gap of an s-wave superconductor,
make cavity from superconducting
transmission line
Requirements for Quantum Computation
Sources of decoherence:
–Coupling between radial
and and axial wave functions
Calculations for assumed dot
dimensions and properties
show that the Eradial,10=30meV,
larger than the highest electron
energy during a CNOT
(26.5meV).
Interactions with Acoustic Phonons
• Electron relaxation via acoustic phonon emission
– T1 processes: e- scattering from potential fluctuations arising from
local volume compressions and dilations induced by the
phonons.(Deformation-potential approximation)
Relaxation rate (Fermi’s Golden Rule)
2
2p
1
i  f 
 i W  f  E f  Ei  Ek 

k
Numerical calculation based on all
previous assumptions yields =150 ms
– T2 processes:
•Pure dephasing of quantum confined excitons is dominated by
radiative lifetime of exciton at low temperatures
•Polaronic couping to excitons gives DOS peaks nonzero width
•Polaronic effects on electrons in QDs will be more like the effects of
hydrogenic donors.
•Work with CdTe showed that phonon-induced linewidths of transitions
of hydrogenic donors much smaller than those of excitons.
•Sherwin et al. Speculate that the phonon-induced linewidths will be
sufficiently small as to not limit operation of the quantum computer.
CNOT Execution Time
c  11.5meV
nc=3.6
c
lc 
 30mm
nc
max
evac
 49V
m
3
 lc 
Volmin     27mm3
2
el  30.7 kV m
2p=25ns
p=3.3ns
single-bit=few ps (with
laser attenuated so Rabi
frequency can be low
enough.