Fermions (Majorana Jordan-Wigner mapping)
Majorana-fermion → qubit (Jordan-Wigner) mapping, one qubit per two
Majorana modes: chi_{2j-1} = (prod_{k<j} Z_k) X_j,
chi_{2j} = (prod_{k<j} Z_k) Y_j. Each chi_i is Hermitian and unit-
normalized (chi_i^2 = I), and the anticommutation relation
{chi_a, chi_b} = 2*delta_ab*I holds exactly — verified against the
actual matrices, not assumed from the textbook formula alone.
Combine the returned Pauli term with
pauli_hamiltonian_to_matrix to build any
Majorana-operator Hamiltonian as a dense matrix, e.g. a sparse
Sachdev-Ye-Kitaev (SYK) model: H = sum_{ijkl} J_ijkl * chi_i*chi_j*chi_k*chi_l.
::: dense_evolution.physics.fermions
See also: entropy and trotter, the
other two modules promoted alongside this one from a real traversable-
wormhole-inspired quantum teleportation reproduction (Gao-Jafferis-Wall
theory, arXiv:2604.10090) — see the MCP Server section
and Dense-Evolution-Discovery
for the real experiments built on top of these three modules.