Exact Entanglement Entropy and Code Distance for Stabilizer States, Computed Without Floating-Point Arithmetic

Standard quantum circuit simulation represents amplitudes as double-precision complex numbers, so quantities such as entanglement entropy are computed only approximately. We revisit two well-known facts about the stabilizer formalism — that entanglement entropy of a stabilizer state is always an integer, and that the distance of a stabilizer code is a combinatorial quantity — and implement both exactly, using binary linear algebra over F₂ on the stabilizer tableau, with no floating-point step anywhere in the computation. We verify the entropy formula against Qiskit's floating-point von Neumann entropy on canonical states and on 30 random Clifford circuits (all matches exact), reproduce the area-law entanglement of the 1D cluster state, and verify the code-distance procedure against three canonical quantum error-correcting codes (Steane, the 5-qubit code, and Shor's code), recovering their published distances exactly.