Hᵣ/ℏ = [ΔZ + Ω(cos φ X + sin φ Y)]/2; Hₑ/ℏ = δ(ZI − IZ)/4 + j(XX + YY + ZZ)/4; j = J/ℏ; U(t) = exp(−iHt/ℏ)
Assumptions and limits
- One gate-defined electron spin starts in |↓⟩, or a selected pair starts in |↑↓⟩. Basis order is ↑, ↓; Z|↑⟩ = +|↑⟩. Unselected dots are not simulated.
- Resonance uses a rotating frame and the rotating-wave approximation. Exchange uses the mean-Zeeman rotating frame and a constant rectangular exchange pulse; no simultaneous microwave drive.
- Controls use MHz and μs; the solver converts frequency to radians per μs. Values are illustrative effective parameters, not calibrated gate voltages.
- Ideal unitary dynamics exclude valley/orbital leakage, charge and nuclear noise, heating, relaxation, crosstalk and readout errors. Displayed probabilities are Born probabilities, not measured hardware data.
- Geometry is schematic and not to scale. Quantum-dot connectivity is separate from silicon’s diamond-cubic atomic structure. Rings mark the selected subsystem; spin is not a classical rotation of an electron.
Sources · 4 references
