Spin Qubit Exchange Coupling — 2D Anticrossing & Bloch-Circle View

Two electron spins trapped in neighbouring gate-defined quantum dots form a "singlet-triplet" qubit whose splitting is set purely electrically, by the Heisenberg exchange interaction J between the spins. This 2D build diagonalizes the same real two-level charge Hamiltonian as the 3D version to compute J(ε), draws it as the anticrossing energy diagram physicists actually publish, and evolves the same 3D Bloch-vector precession internally, projected onto a 2D meridian plane so the precession cone induced by the field gradient ΔB_z is directly visible as the state pulling in off the unit circle.