Electrostatically defined quantum dot

A small electron island confined laterally by depletion gates in an already vertically confined two-dimensional electron gas. Tunnel barriers couple it to reservoirs, and a plunger gate tunes charge occupation. Coulomb blockade and orbital confinement resolve individual electron additions.

A single confined electron's two spin states form a qubit when initialization, coherent rotations and measurement are controlled. Local driving rotates one spin; gate-controlled exchange can entangle neighboring dot spins. Spin-to-charge conversion permits electrical readout. Observing charge blockade alone does not demonstrate coherent qubit operation.

Two capacitively and tunnel-coupled electron islands with separately tunable occupations. Detuning controls which dot holds an electron and whether two-electron charge states such as $(1,1)$ and $(0,2)$ are accessible.

A single electron shared by two dots has a left/right charge basis. In that basis, a two-level model is $H=(\epsilon {\sigma }_z+2t_c{\sigma }_x)/2$, where detuning sets the energy imbalance and tunnelling mixes the states. Electrical control and charge sensing are direct, but electric-potential fluctuations also couple strongly to the encoded information.

An effective coupling that separates the two-electron singlet state and triplet states by energy $J$. For a symmetric two-site Hubbard model with weak tunnelling $t_c$ and charging cost $U$, $J\simeq 4t_c^2/U$. Gate-controlled detuning and tunnelling change the interaction; the simple expression does not hold at arbitrary detuning or strong charge hybridization.

A measurement method in which spin-dependent tunnelling or allowed charge transfer maps a spin outcome onto a distinguishable dot charge state. Quantum-dot charge sensing then records that charge. The measurement axis or singlet/triplet observable must be specified.

Map states with unequal escape rates ${\Gamma }_f\gg {\Gamma }_s$ onto distinct charge outcomes after an interval between their characteristic escape times. Both removal energies can lie above the reservoir chemical potential, so their splitting need not be thermally resolved. A useful rate difference must have a physical origin: a demonstrated single-dot example uses a two-electron singlet state and triplet state with different occupied orbitals. A bare single-electron Zeeman pair in the same orbital does not automatically provide the required rate contrast.^[ref]

For independent exponential escape, equal prior probabilities and no state relaxation, the mean classification error is $P_e(\tau )=[e^{-{\Gamma }_f\tau }+1-e^{-{\Gamma }_s\tau }]/2$. Setting its derivative to zero gives the displayed interval. The error increases both when the fast state is not given enough time to escape and when the slow state is given too much. Detector bandwidth, relaxation and reloading require an expanded measurement model.

Suppression of charge transfer by spin symmetry and the Pauli exclusion principle. For a double quantum dot, a $(1,1)$ singlet state can enter the lowest $(0,2)$ singlet, whereas a $(1,1)$ triplet state is blocked if the required $(0,2)$ triplet lies above the accessible energy window. Spin mixing or relaxation can lift blockade.

Place the reservoir chemical potential between the lower and higher Zeeman-split one-electron dot levels. The excited state can leave while the ground state remains trapped; a time-resolved charge sensor detects the temporary empty state. Thermal errors, missed fast tunnelling and relaxation before escape limit fidelity.

Detection of a dot's charge through its capacitive influence on a nearby quantum point contact or single-electron transistor. Discrete charge changes shift the sensor response, allowing individual tunnel events to be resolved even when direct current through the dot is too small to measure.