“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

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)

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

Transition Energies vs. Applied Field 25 Energy (meV) 20 E10 15 10 el+c ec el 5 0.5 1.0 1.5 2.0 e (MV/m)

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

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.

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

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”).

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

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

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

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