Two electrons confined in a double quantum dot form a two-electron spin qubit. Loaded with one electron per dot — charge state (1,1) — the joint spin state is either the singlet
|S⟩ = (|↑↓⟩ − |↓↑⟩)/√2 (antisymmetric spin)
|T₀⟩ = (|↑↓⟩ + |↓↑⟩)/√2 (symmetric spin)
|T₊⟩ = |↑↑⟩ , |T₋⟩ = |↓↓⟩
Pulsing the interdot detuning ε pushes the ground orbital toward the (0,2) configuration — both electrons in the same dot, same orbital. The Pauli exclusion principle forces the two-electron wavefunction to be antisymmetric overall, so only the spin-antisymmetric singlet can occupy (0,2); every triplet is Pauli-blocked and stays stuck in (1,1). This is Pauli spin blockade (PSB), the readout mechanism behind real singlet-triplet spin qubits (Petta et al. 2005; Ono et al. 2002).
Tunnelling through the S(1,1)–S(0,2) anticrossing is modelled as a rate process over the pulse duration τ:
Γ_S = (t_c / t_ref)² / τ_ref
P_tunnel(S) = 1 − exp(−Γ_S · τ)
P_tunnel(T) = P_tunnel(S) × leakage_fraction
A nearby charge sensor — a quantum point contact (QPC) or single-electron transistor capacitively coupled to the dots — reads a higher conductance when dot B holds two electrons than one, converting the invisible spin state into a measurable electrical signal. The small non-zero leakage models real imperfections: spin-orbit coupling and hyperfine coupling to the host-nuclear spin bath (the pale flickering cloud around the dots) slowly mix triplet and singlet character, occasionally letting a triplet leak through and capping real-device readout fidelity below 100%.
- S / T₀ / T₊ / T₋ — prepare the two-electron spin state before the pulse.
- tc, τ — set how strongly-coupled and how long the readout point is held; both raise the singlet tunnelling probability.
- Leakage — the blockade-breaking probability from spin-orbit/hyperfine mixing.
- Run Readout Pulse — samples one projective readout shot and updates the running fidelity statistics.