Quantum_Flywheel_MIP_Prototype_4_Pages.pdf

1[[PAGE 1]] 2THATAIGUY RESEARCH 3QUANTUM FLYWHEEL / COMPLETED PROTOTYPE 4Exact Normalized Minimum-Information Partitions 5Classical and simulated-quantum search in recurrent neural networks 6Joseph W. Anady 7ThatAIGuy Research 8Abstract 9We executed a reproducible benchmark on 60 synthetic stochastic recurrent networks with 8–14 nodes, exhaustively 10evaluating 163,140 bipartitions. The target is entropy-normalized stochastic interaction, not an unspecified 11consciousness score. Exact-MIP recovery was 18.3% for direct Queyranne search, 85.8% for simulated annealing, 1268.3% for depth-1 simulated QAOA, and 76.2% for depth-2 simulated QAOA; matched 256-draw uniform sampling 13reached 35.7%. Annealing was the strongest tested heuristic. QAOA enriched optimal-partition sampling but 14used an exponentially constructed diagonal cost table, so these results do not establish quantum advantage. The 15completed output is an auditable reference dataset and search pipeline for a subsequent hardware-oriented study. 161. Research question and scope 17Can classical and variational quantum search recover the normalized minimum-information partition (MIP) when 18an exhaustive reference is available? This operationalizes the information-integration question motivating the 19author’s broader manuscript [6], without reusing its historical scores as new evidence. The prototype evaluates 20synthetic linear stochastic recurrent neural-network models; it does not train language models, analyze biological 21recordings, or establish subjective experience. Stochastic interaction is a specific observational information-loss 22measure [1], not the full IIT 3.0/4.0 formalism. 232. Generated network instances 24For n ∈{8, 10, 12, 14}, we generated five independent instances in each of three families: dense, two-module, and 25sparse-with-ring-backbone (15 per size; 60 total). Initial weights are independent N(0, 1/n). Modular cross-block 26weights are multiplied by 0.15. Sparse masks retain entries with probability 0.2, plus the diagonal and two ring 27neighbors. Nodes are randomly permuted; each weight matrix is rescaled to spectral radius 0.9. With independent 28unit-covariance innovations, 29Xt+1 = WXt + εt, 30εt ∼N(0, I), 31Σ = WΣW ⊤+ I. 32We solve for the stationary population covariance analytically. Thus the experiment tests partition search without 33finite-sample covariance-estimation error. Root seed: 20261012; all matrices and seed derivations are retained. 343. Exact normalized objective 35For a nonempty proper subset S and complement ¯S, define [1,2] 36ΦSI(S) = H(Xt+1,S | Xt,S) + H(Xt+1, ¯S | Xt, ¯S) −H(Xt+1 | Xt), 37K(S) = min{H(Xt,S), H(Xt, ¯S)}, 38J(S) = ΦSI(S)/K(S), 39S∗= arg min 40S J(S). 41The optimized quantity J is dimensionless; the unnormalized ΦSI(S∗) is separately saved in nats. All logarithms 42are natural. Differential-entropy normalization depends on variable units: the innovation scale is fixed, not claimed 43invariant to rescaling. “Exact” means exhaustive global search using float64 arithmetic and the tolerance stated on 44page 2, not symbolic exact arithmetic. 45QN-MIP-20261012-v1 4612 October 2026 471 / 4 48 49 50[[PAGE 2]] 51THATAIGUY RESEARCH 52QUANTUM FLYWHEEL / COMPLETED PROTOTYPE 534. Computation and comparison protocol 54Gaussian evaluation and exhaustive reference 55Let G = WΣ and RS = ΣSS −GSSΣ−1 56SSG⊤ 57SS. The implementation uses Cholesky solves and log-determinants, not 58explicit matrix inversion: 59ΦSI(S) = 1 602[log |RS| + log |R ¯S|], 61H(Xt,S) = 1 622[|S| log(2πe) + log |ΣSS|]. 63The full-system innovation determinant is one. We pin node 1 to S to remove complement duplicates, leaving 642n−1 −1 valid bipartitions: 127, 511, 2,047 and 8,191 per instance. Enumeration records every J, numerator, 65denominator and optimal partition. Recovery requires Jreturned ≤J∗+ 10−10 + 10−8|J∗|. No tied optima occurred 66at this tolerance. 67Queyranne: direct normalized-objective search 68We use pendant-pair contraction with a deterministic starting order and cache objective values within each search. 69The minimum candidate is returned without an added local-search step. Queyranne has a guarantee for symmetric 70submodular functions [3]; that guarantee is not assumed for normalized stochastic interaction. Consequently, its 71outputs are judged against enumeration, not treated as reference answers. Each run has a fresh on-demand oracle 72and cannot read the exhaustive table. 73Simulated annealing: independently repeated searches 74Each of ten independent runs per network uses four random restarts and 512 single-bit proposals per restart. 75Metropolis acceptance is min{1, e−∆J/T }. Temperature decreases geometrically from T0 to 10−3T0, with T0 = 76max{SD(32 random pilot scores), 0.001}. All-in-one proposals are rejected and consume a proposal step. The best 77visited valid partition, including pilot points, is retained. Each run uses a fresh cached oracle; it receives neither 78the optimum nor the reference table. Maximum budget: 2,048 proposals plus 36 pilot/initial evaluations. 79QAOA: exact statevector simulation, finite-shot output 80With m = n −1 qubits (7–13 here), the circuit alternates diagonal cost phases and transverse-field mixing [4]: 81|ψp⟩= 82p 83Y 84ℓ=1 85e−iβℓPm 86q=1 Xqe−iγℓHC|+⟩⊗m, 87p ∈{1, 2}. 88Valid diagonal entries are J(S)/ max J; the single invalid all-in-one bitstring has cost 2. Three COBYLA starts 89minimize the exact penalized expectation, with 160 evaluations per start at p = 1 and 240 at p = 2. Selection never 90uses optimal-state probability. All p = 2 starts exhausted this budget; convergence is not asserted. After training, 91ten independent 256-shot batches are sampled, retaining the lowest-cost valid observed partition. Invalid shots are 92counted, not replaced. Uniform search uses ten batches of 256 draws from valid partitions. 93Resource accounting. This is a dense-diagonal QAOA simulator, not an efficient QUBO encoding or a 94transpiled hardware circuit. Building its full cost table already performs exhaustive search. QAOA also receives 95noiseless expectation values during training. The comparison measures output quality at stated, unequal 96budgets; it does not demonstrate a speedup. 97Implementation checks 98Before the main run, Queyranne matched enumeration on 70 weighted-cut and 35 Gaussian-mutual-information 99controls. QAOA agreed with independent dense matrix exponentials to 4.66 × 10−16 maximum amplitude error. 100Across the 60 networks, the covariance-equation relative residual was at most 4.54 × 10−15; independent joint- 101versus-conditional log-determinant checks differed by at most 7.11 × 10−15. Independent uncoupled nodes gave 102zero loss. Saved trial outcomes were subsequently audited against the saved tables and shots. 103QN-MIP-20261012-v1 10412 October 2026 1052 / 4 106 107 108[[PAGE 3]] 109THATAIGUY RESEARCH 110QUANTUM FLYWHEEL / COMPLETED PROTOTYPE 1115. Measured results 112Primary endpoint: exact normalized-MIP recovery. Queyranne has one deterministic attempt per network. 113Other methods have ten attempts per network, giving 600 attempts each. For QAOA these are ten readout batches 114from one trained circuit per depth and network, not ten independent trainings. Statistical resampling therefore 115uses networks, not shots or batches, as the unit. 116Method 117Recovered 118Rate 11995% interval 120Mean gap % 121Queyranne, normalized 12211/60 12318.3% 12410.0–26.7% 125154.83 126Simulated annealing 127515/600 12885.8% 12981.5–89.8% 1302.37 131Simulated QAOA, p = 1 132410/600 13368.3% 13464.8–71.7% 1359.62 136Simulated QAOA, p = 2 137457/600 13876.2% 13972.3–79.8% 1403.63 141Uniform, 256 draws 142214/600 14335.7% 14433.3–38.2% 14586.09 146Table 1. Gap is 100(Jreturned −J∗)/J∗, averaged over all attempts, including failures. Intervals use 10,000 stratified cluster-bootstrap 147resamples: five networks resampled within each size × family cell. They describe this synthetic ensemble and fixed protocol, not universal 148algorithm performance. 149Recovery by network size 150Nodes 151Cuts each 152Queyranne 153Annealing 154QAOA 1 155QAOA 2 156Uniform 1578 158127 15933.3% 16099.3% 161100.0% 16298.7% 16387.3% 16410 165511 16620.0% 16791.3% 16886.7% 16984.0% 17042.7% 17112 1722,047 1736.7% 17482.7% 17559.3% 17674.0% 17710.0% 17814 1798,191 18013.3% 18170.0% 18227.3% 18348.0% 1842.7% 185Table 2. Each row contains 15 networks; denominators are 15 for Queyranne and 150 for each repeated method. Increasing QAOA depth 186helped overall but did not monotonically improve every size group under finite optimization and sampling budgets. 187Measured wall time, with preprocessing visible 188Nodes 189Exact table (ms) 190Queyranne (ms) 191Annealing (ms) 192QAOA 2: table + train (ms) 1938 1948.32 1952.94 19611.50 197513.46 19810 19932.74 2004.93 20120.16 202547.96 20312 204131.92 2057.53 20627.50 207744.40 20814 209561.38 21011.64 21135.00 2121,528.62 213Table 3. Medians across instances (annealing: all runs within each size). QAOA includes one full table and all three optimizer starts; readout 214adds about 0.1 ms per batch. Shared covariance setup and JIT warm-up are excluded. Uniform/readout table-lookup times are not presented 215as comparable search runtimes. 216Execution and an inspectable example 217The 60 instance computations totaled 87.24 seconds, excluding initial validation/JIT warm-up. Execution was 218serial with one BLAS thread on a Linux x86-64 environment reporting an AMD EPYC 9V74 CPU; Python 3.13.5, 219NumPy 2.3.5, SciPy 1.17.0 and Numba 0.65.1. Timings are environment-specific. 220For the first fixed instance, n08_dense_r00, the exact partition is {1, 2, 3, 7} | {4, 5, 6, 8}: J∗= 0.2578092851, 221ΦSI = 2.1867917397 nats and K = 8.4822070674 nats. Queyranne instead returns {1, 2, 3, 6} | {4, 5, 7, 8} with 222J = 0.2788420313. Every other instance, including unsuccessful searches, is retained in the companion data. 223QN-MIP-20261012-v1 22412 October 2026 2253 / 4 226 227 228[[PAGE 4]] 229THATAIGUY RESEARCH 230QUANTUM FLYWHEEL / COMPLETED PROTOTYPE 2316. Interpretation and limits 232Normalization materially changes this benchmark. A separately labeled post-run diagnostic found that 233Queyranne recovered all 60 unnormalized stochastic-interaction minima, versus 11 normalized minima. Normal- 234ization changed the exact minimizing partition in 37/60 networks. An exhaustive post-run check of 6,804,480 235elementary submodularity inequalities found violations in all 60 normalized objective tables. Thus the direct 236normalized search cannot inherit an exactness guarantee merely from success on a related objective. These post-run 237diagnostics leave the primary results unchanged. 238Quantum sampling enrichment is not quantum advantage. Depth-2 QAOA exceeded uniform recovery by 23940.5 percentage points (paired bootstrap interval 36.7–44.3), but annealing exceeded it by 9.7 points (5.5–13.7). 240The median optimal-state probability was 7.93 times the valid-uniform probability, with some instances below 241uniform. The dense cost table, classical optimizer, exact expectations and statevector simulation are substantial 242resources. There was no QPU execution, noise model, efficient cost-oracle synthesis, or BlueQubit cloud job in this 243prototype. 244Scientific boundary. The result concerns this specified Gaussian, entropy-normalized bipartition problem. It 245does not establish a general hardness theorem, an efficient hardware implementation, performance on trained 246nonlinear networks, a measurement of full IIT Φ, or evidence of machine consciousness. Sampling enrichment is 247not a substitute for full resource accounting. 2487. Proposed three-month extension 249The completed prototype supplies the exact-answer testbed for a proposed quantum-optimization study, aligned 250with Quantum Flywheel’s three-month research structure [5]. 251Compute should be used to test a genuinely 252implementable encoding, not simply to enlarge the current exponential lookup table. 253Month 1 — encoding and controls. Develop sparse Ising/QUBO surrogates or an explicitly costed reversible 254numerical oracle. Measure distortion against exact normalized tables and retain the true objective for scoring. 255Freeze held-out seeds; add normalization and parameter-budget controls. 256Month 2 — scaling and robustness. Extend exact references where feasible, including 16–20-node instances. 257Compare deeper QAOA, annealing and stronger classical methods at matched budgets. Measure optimizer 258variability, noise, state-preparation and phase-oracle costs; heuristic agreement is not an exact reference. 259Month 3 — hardware-ready evidence. For viable encodings, compile small circuits, report two-qubit gate 260counts and depth, and run matched simulator/QPU tests subject to granted access. Deliver the benchmark release 261and preprint, including negative findings. Advance only on full-pipeline cost and held-out accuracy. 2628. Reproducibility and sources 263AI assistance covered implementation, experiment orchestration, numerical checks and report assembly. The 264companion bundle contains the frozen protocol, source code, all 60 weight/covariance matrices, every objective 265table, optimized angles, optimizer traces, sampled bitstrings, 2,400 trial records, and validation artifacts. The main 266implementation and protocol were hashed before execution. Run python code/benchmark.py in a fresh result 267directory, then python code/analyze.py; existing results are preserved. No manuscript benchmark numbers were 268imported into this experiment. 269[1] J. Kitazono, R. Kanai and M. Oizumi. Efficient Algorithms for Searching the Minimum Information Partition in Integrated Information 270Theory. Entropy 20, 173 (2018). DOI: 10.3390/e20030173. 271[2] A. B. Barrett and A. K. Seth. Practical Measures of Integrated Information for Time-Series Data. PLoS Comput. Biol. 7, e1001052 272(2011). DOI: 10.1371/journal.pcbi.1001052. 273[3] S. Hidaka and M. Oizumi. Fast and exact search for the partition with minimal information loss. PLoS ONE 13, e0201126 (2018). 274DOI: 10.1371/journal.pone.0201126. 275[4] E. Farhi, J. Goldstone and S. Gutmann. A Quantum Approximate Optimization Algorithm. arXiv:1411.4028 (2014). 276[5] BlueQubit. Quantum Flywheel grant-program announcement. Official program release, 14 September 2026. 277[6] J. W. Anady. Measurable Artificial Consciousness Through Fibonacci Dynamics: A Mathematical Framework with Empirical Validation. 278Author-supplied 17-page manuscript; background motivation only. 279QN-MIP-20261012-v1 28012 October 2026 2814 / 4 282