1. “Quantum computation with quantum dots and terahertz cavity quantum electrodynamics” Sherwin, et al. Phys. Rev A. 60, 3508 (1999)
Norm Moulton
LPS

2. 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.

3. 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

4. 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

5. Stacked self-assembled quantum dots
GaAs
InAs
GaAs
GaAs

6. Etched quantum well structure
Superconducting electrodes
AlxGa1-xAs
GaAs
AlxGa1-xAs
GaAs
AlxGa1-xAs
GaAs
AlxGa1-xAs

8. Effective axial potential in the dot

9. Rabi Oscillations driven by cavity photons (0-1)
System Hamiltonian
Cavity Photons
Projections
Rabi Oscillations driven by cavity photons (0-1)
Rabi Oscillations driven by cavity photons (1-2)
Rabi Oscillations driven by laser photons (0-1)
Rabi Oscillations driven by laser+cavity photons (1-2)

10. Auxiliary state (|2> )driven by two-photon processes
Where:

11. Transition Energies vs. Applied Field25
Energy (meV) 20
E10 15 10
el+c ec el 5
0.5
1.0
1.5
2.0
e (MV/m)

12. State vector picks up phase of i p-pulse at ec
CNOT Gate Operation:
E20(el+c) t
E10(el)
E10(ec) c c c c c t
p-pulse at ec
State vector picks up phase of i
p-pulse at ec
State vector picks up phase of i
2p-pulse at el+c
State vector picks up phase of -1

13. State vector picks up phase of i p-pulse at ec
CNOT Gate Operation:
E20(el+c)
E10(el)
E10(ec) c c c c t c
p-pulse at ec
State vector picks up phase of i
p-pulse at ec
State vector picks up phase of i
2p-pulse at el+c
Not on resonance with E12 so no flopping.

14. Requirements for Quantum Computation
Initializing the computer
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 W.
Make a hybrid device that uses nearest-neighbor concepts in the cavity.
Propose to integrate new quantum well detector into the cavity. Detector is tuned to cavity resonance at the readout phase of the calculation.
Arbitrary one-bit rotations are effected using Rabi oscillations induced by laser field.
For kBT<<E10 a wait of less than 1 sec will ensure that all qubits are in state |0>.
Inputting initial data
Readout
Error correction

15. Requirements for Quantum Computation
Cavity Photons
Electronic State
No experimental data exists on these dots
Decoherence
Sources:
Frequencies lower than E10/h, cause adiabatic changes to the energy levels En, leading to phase errors.
When QD not addressed: SC electrodes, SC path, SC ground-> No dissipation so no thermal fluctuations.
Prevented by high-Q 3-D cavity
Emission of freely propagating photons
Interaction with fluctuating gate potential (x-talk, Johnson noise)
Noise during switching will cause errors and will have to be addressed (“in a future publication”).

16. Requirements for Quantum Computation
Sources of decoherence:
Calibrate each quantum dot prior to computation
Engineer ultra-low loss THz cavity
Rely on future advances in production technology
Traps in the volume between gate electrodes pose a problem
Traps far from electrode are shielded by the electrode
Interaction with metastable traps in the semiconductor
Inhomogeneity in the dots
Cavity photon lifetime
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

17. Requirements for Quantum Computation
Sources of decoherence:
Calculations for assumed dot dimensions and properties show that the Eradial,10=30meV, larger than the highest electron energy during a CNOT (26.5meV).
Coupling between radial and and axial wave functions

18. 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)
Numerical calculation based on all previous assumptions yields t=150 ms

19. 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.

20. CNOT Execution Time
nc=3.6
t2p=25ns
tp=3.3ns
tsingle-bit=few ps (with laser attenuated so Rabi frequency can be low enough.