Jordan-Wigner Fermion-to-Qubit Encoding — 2D Circuit View

Before a quantum computer can run any molecular algorithm — VQE, QAOA-style ansatze, or phase estimation on a Hamiltonian — the chemistry has to be translated from fermionic creation/annihilation operators into qubit gates. The Jordan-Wigner transform does that translation, and its defining quirk is the "parity string": a chain of Z gates that has to run between any two orbitals an excitation moves an electron across, so that the qubit circuit reproduces the anti-symmetric sign fermions are required to carry. This 2D simulator draws a small spin-orbital register as a row of qubit discs plus a live circuit-diagram panel underneath, lets you set a Hartree-Fock reference determinant or any custom occupation, and applies a single-excitation operator a†_pa_q between any two orbitals — visualizing exactly which qubits the Z-string threads through and computing the resulting fermionic sign flip live.