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Compares caller-supplied Alice and Bob bases, retains matching-basis positions, calculates the quantum bit error rate over caller-selected revealed positions, and returns only a digest and count for remaining demonstration bits. It neither exchanges quantum states nor creates a secret key: all submi

Estimates logical qubits and logical gates from algorithm family and key size, applies a caller-supplied error-correction overhead, and reports capacity and runtime ratios. The formulas are coarse planning heuristics, not cryptanalytic proof or a forecast of when cryptographically relevant quantum c

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.

Treats a caller-supplied odd-length bit word as a classical repetition code, majority-decodes one logical bit, and reports the corrected word and adjacent XOR syndrome. This narrow demonstration is not a surface-code simulation and does not model coherent quantum errors, measurements or fault-tolera

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.

Uses lattice dimension, log2 determinant and an assumed root-Hermite factor to estimate Gaussian-heuristic and reduced-basis vector lengths in log2 units. It does not execute lattice reduction, validate an LWE instance or provide a cryptographic security level.

Counts zeros, ones and runs, reports a normalized monobit imbalance, and compares observed runs with the IID Bernoulli expectation. It generates no random number and is not a NIST test-suite replacement, entropy estimate or certification of cryptographic randomness.

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.

Enumerates every selection of exactly k assets for at most 16 assets, maximizing summed expected return minus a caller-selected covariance penalty. It runs no quantum circuit and provides a deterministic classical optimum for testing a corresponding binary QAOA or QUBO formulation; it is not investm

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