BQP = P = NP? Quantum-to-Classical Dictionary Selection and Exact HKD Compression | IJCT Volume 13 – Issue 5 | IJCT-V13I5P45

This paper tests a narrow quantum-to-classical translation for lossless compression. Candidate phrase selection is written as a quadratic unconstrained binary optimization (QUBO) problem suitable for the Quantum Approximate Optimization Algorithm (QAOA). A classical HKD implementation instead searches candidate dictionaries and, for each fixed dictionary, computes a globally minimum tokenization by dynamic programming on an acyclic weighted transition system. The supplied ultra-search harness was reproduced with Prediction by Partial Matching (PPM) candidates and exact decoding checks. On its own 9,669-byte Python source, the best PPM candidate used 2,620 bytes versus 3,094 bytes for bzip2, a 15.320% reduction. On a deterministic synthetic auction-log corpus, an HKD phrase preconditioner followed by bzip2 reduced 410 bytes to 315 bytes at 1,600 records, a 23.171% reduction, but required 1.409 s versus 0.019 s for bzip2. All reported outputs decoded exactly. These experiments establish corpus-specific compression improvements, not quantum advantage, polynomial worst-case dictionary selection, guaranteed profit, or BQP=P=NP. The title is therefore a research question: the equality would require independent universal complexity proofs absent from the present work.