Interpolates a caller-supplied start and end temperature across a bounded number of steps using either a linear or geometric rule. It does not run an annealer, optimize a problem Hamiltonian or tune a schedule from hardware measurements.

Cancels adjacent identical self-inverse gates on identical ordered targets and folds adjacent RX, RY or RZ rotations on identical targets. It preserves only these local identities; it does not commute gates, model hardware topology, synthesize arbitrary unitaries or prove global optimality.

Converts ++, +−, −+ and −− counts into a correlation for each of AB, AB′, A′B and A′B′, then computes S = E(AB) + E(AB′) + E(A′B) − E(A′B′). A value above the classical bound in supplied data does not by itself demonstrate entanglement or close detection, locality, sampling or significance loopholes.

Computes all pair distances and a single-parameter Lennard-Jones 12-6 potential using caller-supplied epsilon and sigma. It does not perform quantum chemistry, infer element-specific force fields, relax geometry, model bonds or predict experimental molecular behavior.