Post on 12-Jan-2016
description
“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
•CW laser with fixed l introduced into the side of the cavity
•Dots are in a sharply resonant THz cavity, >>Ldot
GaAs
InAsGaAs
Stacked self-assembled quantum dots
GaAs
Etched quantum well structure
AlxGa1-xAs
GaAs
AlxGa1-xAs
GaAs
AlxGa1-xAs
GaAs
AlxGa1-xAs
Superconducting electrodes
Effective axial potential in the dot
System Hamiltonian
aac
cω 22201110 σσ
eEeE
cc aaeg 100101 σσ
titie lll expσexpσ 100101,
cc aaeg 122112 σσ
tiatiae lclcl ωexpσωexpσ 211212,
H
Cavity Photons ProjectionsRabi Oscillations driven by cavity
photons (0-1)
Rabi Oscillations driven by laser+cavity photons (1-2)
Rabi Oscillations driven by cavity
photons (1-2)
Rabi Oscillations driven by laser photons (0-1)
tiatiaeH lclc expσexpσ 2002
~
photontwo
Auxiliary state (|2> )driven by two-photon processes
c
l
l
l
e
eg
e
ege
ωωωω 21
01,12
21
12,01~
Where:
Transition Energies vs. Applied Field
e (MV/m)
ecelel+c
0 0.5 1.0 1.5 2.05
10
15
20
25
Ene
rgy
(meV
)
E20
E10
t
c
c
c
t
-pulse at ec
State vector picks up phase of i
2-pulse at el+c
State vector picks up phase of -1
-pulse at ec
State vector picks up phase of i
c
c
E10(ec)
E10(el)
E20(el+c)
CNOT Gate Operation: 001tc100tc
i 100tc
i 001tc
c
c
c
-pulse at ec
State vector picks up phase of i
2-pulse at el+c
Not on resonance with E12 so no flopping.
-pulse at ec
State vector picks up phase of i
c
c
E10(ec)
E10(el)
E20(el+c)
CNOT Gate Operation: 011tc110tc
i 110tc
i 001tc
t
Requirements for Quantum Computation
•Initializing the computer For kBT<<E10 a wait of less than 1 sec will ensure that all qubits are in state |0>.
•Inputting initial data
Arbitrary one-bit rotations are effected using Rabi oscillations induced by laser field.•Readout
Propose to integrate new quantum well detector into the cavity. Detector is tuned to cavity resonance at the readout phase of the calculation.•Error correction
Enlarge the cavity to create several cavity modes in the QD tunable level-spacing range. This slows things down by reducing e in the cavity resulting in lower
Make a hybrid device that uses nearest-neighbor concepts in the cavity.
Requirements for Quantum Computation
•Decoherence
•Cavity Photons
•Electronic StateNo experimental data exists on these dots
Sources:
–Emission of freely propagating photons
Prevented by high-Q 3-D cavity
–Interaction with fluctuating gate potential (x-talk, Johnson noise)
Frequencies lower than E10/, cause adiabatic changes to the energy levels En, leading to phase errors.
tdteEt Nn
1
When QD not addressed: SC electrodes, SC path, SC ground-> No dissipation so no thermal fluctuations.
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
Traps far from electrode are shielded by the electrode
Traps in the volume between gate electrodes pose a problem
Rely on future advances in production technology
–Inhomogeneity in the dots
Calibrate each quantum dot prior to computation
–Cavity photon lifetime
Engineer ultra-low loss THz cavity
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)
kkiffifi EEEW
21 2
Relaxation rate (Fermi’s Golden Rule)
Numerical calculation based on all previous assumptions yields =150 s
– 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
meV5.11c
mn
c
cc
30
nc=3.6
mVevac 49max
33
min 272
mmVol c
mkVel 7.30
=25ns
=3.3ns
single-bit=few ps (with laser attenuated so Rabi frequency can be low enough.