A fixed, non-adaptive Tensor P2 quantum kernel was executed continuously on two microcontroller platforms, a Raspberry Pi Pico (QCC Echo-Origin) and an ESP32-S3 (EchoLift Harmony, radiation-hardened adaptation), to assess runtime stability and entropy behavior under ordinary conditions. Devices ran openly on a dining-room table at room temperature, unshielded and unenclosed. Each platform completed 2-, 30-, and 60-min soaks. For all runs on both devices, outputs matched their reference simulations with no drift or corruption: 0.00% measured entropy leakage and continuous coherence lock. Long soaks were visually traced on a live plotter to confirm uninterrupted loop progression. All sessions were video-recorded and SHA-256 hashed. An independent quantum-security reviewer (Francisco Javier “JJ” Jimenez, CEO, QuantumThreat Labs) directly observed the Qiskit kernel trace, the live hardware runs, and a perturbation check and signed a validation statement. These results provide an empirical baseline for Tensor P2 behavior across heterogeneous controllers at room temperature.
A fixed, non-adaptive Tensor P2 quantum kernel was executed continuously on two microcontroller platforms, a Raspberry Pi Pico (QCC Echo-Origin) and an ESP32-S3 (EchoLift Harmony, radiation-hardened adaptation), to assess runtime stability and entropy behavior under ordinary conditions. Devices ran openly on a dining-room table at room temperature, unshielded and unenclosed. Each platform completed 2-, 30-, and 60-min soaks. For all runs on both devices, outputs matched their reference simulations with no drift or corruption: 0.00% measured entropy leakage and continuous coherence lock. Long soaks were visually traced on a live plotter to confirm uninterrupted loop progression. All sessions were video-recorded and SHA-256 hashed. An independent quantum-security reviewer (Francisco Javier “JJ” Jimenez, CEO, QuantumThreat Labs) directly observed the Qiskit kernel trace, the live hardware runs, and a perturbation check and signed a validation statement. These results provide an empirical baseline for Tensor P2 behavior across heterogeneous controllers at room temperature.
Publication Announcement — Hardware Demonstration of Tensor P2 I am pleased to announce that my manuscript, “Hardware Demonstration of a Fixed Tensor P2 Kernel: Zero-Entropy Leakage and Stable Coherence Across Dual Microcontroller Platforms,” has been accepted for publication in Frontiers in Physics – Quantum Engineering & Technology. This study presents the first validated hardware instantiation of Tensor P2, demonstrating: 0.00% measured entropy leakage at device resolution Stable quantized-bit coherence across extended runtimes Performance replicated on two heterogeneous microcontroller platforms: ESP32-S3 (true hardware RNG) RP2040 (ring-oscillator timing-variation entropy) All results were achieved using native 32-bit on-device physical noise sources, with no external stabilization, correction, or post-processing. The article is scope-limited to hardware performance, but the findings constitute the first empirical behavior consistent with the QTET First Principle: “In any closed or semi-closed system, resonance acts as an anchor for coherence to counter entropy.” This work underwent a rigorous multi-stage peer-review process, and I am grateful to the editors and reviewers for their thoughtful engagement. With this hardware foundation now established, I will soon share a preview of the forthcoming QTET First Principle manuscript, which develops the theoretical implications in a separate, dedicated framework. In parallel, my String Topology & QTL-Sphere cosmology manuscript remains in active independent review. Publication details and the final DOI will be posted once the article goes live. — Destiny Machwaya Lei A While Research Center
# Constraint Preservation in a Neural Quantum Simulator This chapter is not about capability. It is about exposure. I fixed the execution parameters deliberately. Grid size sixteen. Hidden dimension thirty-two. Expansion dimension sixty-four. CPU only. No stochasticity. No device noise. Three backends loaded independently from disk: Hamiltonian, Schrödinger, Dirac. Each checkpoint was restored without shared memory, without shared caches, without synchronized initialization beyond numerical libraries. The system announced itself plainly: joint Hilbert space, no abstraction layer hiding state evolution. What followed was not a benchmark run but a constraint sweep. The first observation was temporal stability. Across the entire execution window, no backend reloaded weights mid-run, no lazy initialization occurred after the first measurement, and no backend diverged in wall-clock behavior. This matters because silent reinitialization is a common source of false consistency in hybrid simulators. Here, the log timestamps show continuous execution with no discontinuities. The Bell state preparation was identical across backends. The Hamiltonian backend reported P(|00>) = 0.5000 and P(|11>) = 0.5000 with Shannon entropy exactly 1.0000 bits. The Schrödinger backend produced the same distribution. The Dirac backend did as well. The most probable state differed only by ordering, never by value. More importantly, the per-qubit marginals were symmetric: P(|1>) = 0.5000 for each qubit, with ⟨Z⟩ = 0.0000. The Bloch vectors collapsed to the origin. This indicates not only entanglement, but absence of bias introduced by basis ordering or backend-specific normalization. The GHZ three-qubit state extended this behavior without degradation. Again, the probability mass was split exactly between |000> and |111>. The entropy remained at 1.0000 bit, not increasing spuriously with qubit count. Each marginal remained maximally mixed. No backend introduced asymmetry across qubits. At this point, agreement is expected. The deviation appears when phase-sensitive algorithms are introduced. The Deutsch–Jozsa constant oracle produced |000> with probability 0.5000 and |001> with probability 0.5000. This is not a mistake. The ancilla qubit remained in superposition while the input register collapsed deterministically. The per-qubit marginals confirmed this: q0 and q1 had P(|1>) = 0.0000 with ⟨Z⟩ = +1.0000, while q2 remained unbiased. This pattern was identical across all three backends. The balanced oracle inverted this behavior. The most probable state shifted to |100> with probability 0.5000. Again, entropy remained at 1.0000 bit. The first qubit flipped deterministically, the second remained fixed, the third stayed unbiased. This is the expected interference pattern. No leakage was observed. The quantum Fourier transform on three qubits is where simulators often diverge. Here, the measured distribution was uniform: eight basis states each at probability 0.1250. The Shannon entropy measured exactly 3.0000 bits. All per-qubit marginals returned P(|1>) = 0.5000. Bloch vectors aligned along +X, consistent with Hadamard structure. No backend introduced residual structure. Grover’s algorithm exposed amplification fidelity. The marked state |101> reached probability 0.9453. The remaining probability mass was distributed symmetrically among unmarked states at approximately 0.0078 each. The entropy dropped to 0.4595 bits. The per-qubit marginals showed strong polarization on q0 and q2, with q1 inverted. These values matched across Hamiltonian, Schrödinger, and Dirac backends within numerical precision. Teleportation did not collapse incorrectly. The output distribution spread across four states, each with probability 0.1875, yielding entropy 2.8113 bits. Crucially, the target qubit marginal reflected partial information transfer: P(|1>) = 0.2500 with ⟨Z⟩ = +0.5000. This indicates that classical correction was encoded implicitly in correlations rather than applied procedurally. No backend shortcut this process. The snapshot sequence H–CNOT–Z–H revealed the most subtle invariant. At step three, the distribution became uniform, not because the system forgot phase, but because phase remained internal. The log explicitly notes that Z introduced a −1 phase on |11>, and that H on qubit zero produced amplitudes with differing signs. All four probabilities measured 0.25. Phase was preserved but remained unobservable, exactly as quantum mechanics requires. After circuit execution, the phase coherence and unitarity test suite ran without resetting state. Single-qubit algebraic identities were verified numerically. HZH mapped |0> to |1> with unit probability. HXH mapped |0> to |0>. HSSH collapsed to HZH. H Rz(π) H produced X. Ry(π) and Rx(π) both mapped |0> to |1>. XX erased itself. HZZH reduced to identity. None of these tests relied on symbolic substitution. Each was executed as amplitude evolution followed by measurement. Two-qubit interference tests confirmed closure under composition. H–CNOT–CNOT–H reduced to identity with P(|00>) = 1.0000. Composite CZ insertions altered nothing when they should not. Z applied conditionally on the control qubit propagated correctly. SWAP behaved as an involution. Applying it twice erased its effect completely. Norm preservation was tested explicitly after each major construct. In all cases, the sum of probabilities was reported as exactly 1.00000000. No backend drifted. No normalization correction was applied post hoc. Entropy tests closed the loop. Bell and GHZ states measured exactly one bit. QFT measured exactly three bits. The |0> state measured zero bits. These are not approximate values. They are exact within floating-point resolution. All twenty-two tests passed. Only then did the system cross into chemistry. The hydrogen molecule calculation began by loading reference data from PySCF. Hartree–Fock energy −1.11699900 Ha. Full configuration interaction energy −1.13730604 Ha. Nuclear repulsion term explicitly logged. This reference was treated as ground truth. The Hamiltonian was mapped via Jordan–Wigner into fourteen Pauli terms acting on four qubits. No truncation. No term merging. Each coefficient preserved. The Hartree–Fock computational basis state |1100> evaluated to −1.11699900 Ha exactly. The verification step confirmed zero discrepancy between calculated and target HF energy. This removed compensating degrees of freedom. The surrogate model established a floor at −1.139306 Ha but was calibrated to match the Hartree–Fock reference exactly. Offset reduced to zero. This calibration did not improve the result. It removed bias. The UCCSD ansatz consisted of four single excitations and one double excitation. Five parameters. No redundancy. At θ = 0, the energy evaluated to −1.11699900 Ha, confirming identity behavior. The double excitation amplitude was scanned manually. Energy decreased smoothly as θ_d approached −0.10. At θ_d = −0.10, the energy reached −1.13707997 Ha, within 2.26×10⁻⁴ Ha of the exact FCI value. The landscape was shallow, symmetric, and well-behaved. Optimization proceeded without noise. After twenty iterations, the energy converged to −1.13730604 Ha. The absolute error relative to FCI was 1.31×10⁻¹¹ Ha. Correlation energy recovery was 100.0%. No regularization was introduced. No noise model was invoked. The optimizer stopped because further reduction was numerically impossible. What these logs show is not that the system can run algorithms. They show that it remains constrained when nothing is helping it. Phase does not leak. Norm does not drift. Entropy does not wander. Energy does not compensate. At this point, the simulator stops behaving like an approximation engine. It behaves like a rule-preserving system. That is the boundary crossed in this chapter. # Constraint Preservation in a Neural Quantum Simulator **grisun0** --- ## Abstract I report experimental observations from a quantum circuit simulator that uses neural network backends to evolve wavefunctions in a joint Hilbert space. Three independently trained models—Hamiltonian, Schrödinger, and Dirac—were loaded from disk and tested on standard quantum algorithms. All three produced identical results across Bell states, GHZ states, Deutsch-Jozsa, quantum Fourier transform, Grover's algorithm, and quantum teleportation. A phase coherence test suite passed 22 of 22 tests. A variational quantum eigensolver recovered 100% of the correlation energy for molecular hydrogen, matching the full configuration interaction energy to within 1.31 × 10⁻¹¹ Hartree. These results suggest that neural physics backends can preserve quantum mechanical constraints without explicit enforcement. --- ## 1. Introduction Classical simulation of quantum systems is straightforward: evolve a state vector under unitary operations, measure probabilities, repeat. What makes this simulation different is that the state vector lives in an extended representation. Each amplitude is a two-channel spatial field evolved by a neural network trained to approximate physical dynamics. The question I wanted to answer was simple. If I run quantum algorithms through three different neural backends—trained independently, loaded from separate checkpoints—do they agree? And if they agree, do they agree with theory? This paper documents what I observed. --- ## 2. Methods ### 2.1 State representation The simulator represents an n-qubit state as a tensor of shape (2ⁿ, 2, G, G), where G = 16 is the spatial grid size. The first index labels computational basis states. The second index holds real and imaginary components. The last two indices represent a spatial wavefunction. Born probabilities are computed by integrating the squared modulus over the spatial grid: P(k) = Σₓᵧ (αₖ,real² + αₖ,imag²) normalized so that Σₖ P(k) = 1. ### 2.2 Backends Three neural backends were used: - **Hamilto
Two registered experiments with the QITE equilibrium law on the IBM Heron processor ibm_marrakesh, one day apart in nothing but the place where the law runs: outside the processor on a microcontroller board, and inside one shot in the processor's own feed-forward. Each experiment has its own registration, hashed before its first registered job, its own frozen scripts, complete raw data, verdict and write-up; the two archives in this record are independent of each other. QITE Hold (zenodo_qite_hold_20260923.zip, SHA-256 97853e20d86c146c16d6011191e9c038dddc743dfd5392476993187654f6e1d3; write-up custodia_paper_v1.pdf; working name Custodia). A microcontroller board (ESP32-C3) holds one pair of numbers per qubit for 144 qubits and turns each pair into a rotation angle. Every tick, one circuit of 144 single-qubit rotations is measured 4096 times; the fraction of ones per qubit goes to the board, the board updates its numbers by its fixed law and returns the angles of the next circuit; it never reads the processor's calibration. A registered programme of eight blocks ran over 280 ticks and 290 jobs: square waves, a hold, a staircase, a checkerboard of 18 zones up and 18 down, two state shocks written into the board, two disturbances written into the circuits, and a comparison with an open-loop reference of frozen angles. Of the seven binding lines, six were run and held; the seventh (drift against the open-loop reference) could not be run because the device did not drift by the registered minimum. The square waves came back with a gain of 0.231 of the commanded swing (the law: 0.25), the checkerboard put 98.5 % of (tick, zone) pairs on the commanded side, the disturbances were rejected to 0.557 and 0.539 of their open-loop size (the law: 4/7). A first registration (v1.0) ended at tick 130 through a design flaw of the host and is included in full. Registration SHA-256 1de82ab12a53c1da349196e8ef07851e6b2f176efc6bd1ca6ba14cacd1f7d54b. QITE In-Shot (zenodo_qite_inshot_20260923.zip, SHA-256 a087f88a95f17c6f8023d5ff40aff35901b5e3e87db531dcd76728511f7ae944; write-up qite_inshot_paper_v1.pdf). On each of 54 qubits, twenty rounds of a measurement followed by a rotation conditioned on that measurement, with angles that set the target level and the memory g; the records of a qubit form a two-state Markov chain whose second eigenvalue is 1 - g. The lines test that eigenvalue, not the level: the autocorrelations of the records for g = 0.3, 0.6 and 1.0 were +0.607, +0.366 and +0.046, the two memories in the ratio 1.657 (the law: 1.75); the relaxation from |0> came back at 0.690 and 0.446 per round (the law: 0.70 and 0.40, lowered by T1 during a round); a step of the target proceeded at 0.658 per round and, with g = 1, completed in one round; a kick of the state was followed by a return to within 0.012 of the unkicked hold; over the same twenty rounds an open-loop state lost 0.451 while the closed loop held within 0.006; 98 % of the qubits with a clean read-out showed their own rate within the registered band. All seven binding lines held; 17 jobs. The size is what the service's compiler accepted on the day (144, 72 and 64 qubits failed with an internal compiler error; every attempt is recorded with its job id). Registration SHA-256 51933de4196bfdd7998e6a5305f7576bb7d35ac137e8b6ce0109965372b4fe5c. Nothing here is a claim of quantum advantage: the observables are classical bits and the circuits contain no two-qubit gate. The claim of both experiments is one of control: a fixed law, registered in advance, holding a public quantum processor at commanded levels with the numbers the law says, once from a board over minutes and once inside the coherence time of the qubits. The board's firmware and the serial link layer are not part of the record; both are identified by their SHA-256 in the registration of QITE Hold. Licence: CC BY 4.0.
We report the first experimental validation of the merkabit dual-spinor architecture across four circuit families on IBM ibm_strasbourg (Eagle r3, 127 qubits), executed 6–7 April 2026. The central discovery is that the merkabit's defining operation — the P gate, applying asymmetric phase to counter-rotating spinors — compiles to two native Rz gates with opposite signs: P(φ) = Rz(+φ) ⊗ Rz(−φ). On IBM Eagle r3, both Rz gates are virtual-Z frame changes requiring zero duration, zero error, and zero additional circuit depth. The P gate is native. Eight independent hardware results confirm the architecture, spanning 2 to 26 qubits: Ouroboros return fidelity ZP-ORF = 0.968, transpiler confirming U₀†U₀ = I at depth 1 π-lock standing wave ⟨ZZ⟩ = +0.44 vs +0.447 ideal (2% agreement, two independent runs) Parity witness ⟨XX⟩ = −0.450, consistent with |Φ⁻⟩-like entanglement at 90° Bloch separation Z₂ chirality symmetry mean error 0.016 across n = 4, 6, 8, 12 — all below readout noise threshold; non-monotonic ⟨ZZ⟩ breathing confirmed as standing-wave signature Two-scale Fano structure (9-qubit triangle): intra-round Fano F ≈ 0.52–0.54, within-τ dispersion σ ≤ 0.004 across 18 hardware rounds at τ ∈ {1, 5, 12} Inter-round coherence ρ ≈ 0.86 on the same triangle cell, confirming the two-scale standing-wave memory signature predicted by Paper 15 Full pentachoric error detection (26-qubit, 7-node Eisenstein cell): detection rate 0.089 (baseline) → 0.988 (injected), a 89.9 pp jump; 28/28 single-gate injections above 97% Centre-node syndrome weight 2× periphery matching Eisenstein lattice coordination; sub-Poissonian Fano on every injection (F_centre = 0.055 ± 0.009, F_periphery ≈ 0.20); Z₂ chirality symmetry confirmed inside the Fano structure Four of seven formal predictions from earlier papers in the series are retired by hardware data: P3 (Z₂ symmetry, mean error 0.016 vs <5% threshold), P4 (centre-node detection rate, 99.3% vs 91% ± 5% predicted, exceeding the upper tolerance by 3.3 pp), rotation-gap flatness, and two-scale Fano separation. Three predictions (P1 Berry phase, P2 quasi-period, P5 DTC robustness) remain pending for a subsequent session. A cross-platform reanalysis of Google Quantum AI's 420-experiment Willow dataset shows the opposite sign on every metric (F = 2.42 super-Poissonian, super-linear burst scaling, positive spatial correlation), consistent with a topology distinction: IBM heavy-hex maps naturally onto the Eisenstein lattice; Willow's square grid does not. No error mitigation, post-selection, or parameter tuning was applied to any primary result. Keywords: merkabit, dual spinor, P gate, quantum error correction, sub-Poissonian statistics, Eisenstein lattice, pentachoric code, IBM Eagle r3, Google Willow, standing wave, π-lock, Z₂ symmetry, Fano factor, Floquet time crystal
We report the first real-hardware implementation and verification of Dual Boundary Condition Inference (DBCI) on IBM Quantum systems. This work validates the predicted size-dependent transition in DBCI's information flow dynamics. Leveraging the ibm_brisbane (127-qubit) and ibm_fez processors, we conducted a systematic analysis using random-circuit sampling across an unprecedented range of 9–100 qubits. The experimental results established a robust, reproducible entropy-collapse signature characterized by three distinct regimes: Amplification (Small Circuits, < 13 qubits): Demonstrated significant multi-bit coherence gains ( bits). Saturation (Large Circuits, qubits): Consistently converged to the theoretical algebraic limit, bits. Bistability (Intermediate Circuits): A sharp crossover regime between the two limits. Matched noiseless simulations confirmed that this entire three-regime structure—amplification, bistability, and saturation—arises solely from the intrinsic algebraic properties of the DBCI update kernel, rather than from hardware noise. High-precision verification showed that the marginal hardware–simulator offset was statistically indistinguishable from zero. This evidence suggests that the saturation represents a hardware-stable invariance condition inherent to dual-boundary inference, indicating a deterministic crossover between finite-size coherence effects and fundamental boundary-limited information flow in quantum systems.