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ZLT-P50J: The MIPT Gate Problem – A Zero Leap Theory Prediction for Measurement-Induced Phase Transitions in Quantum Arrays

DANNY YUBI DAGOGLIANO

Published Mar 17, 2026• 0 citations
Publisher

Abstract

The quantum array does not forget that it was watched. Zero Leap Theory predicts that Measurement-Induced Phase Transitions (MIPT) in quantum arrays are structural Gate Collapse driven by operator observational load. The critical measurement rate pc is not a fixed universal constant — it is modulated by accumulated measurement history (H) and observation alignment (Φobs). Three falsifiable predictions registered before results: EHS > 0 (Entanglement Hysteresis Loop under cycling) Basis-Dependent Phase Boundary (pc increases with Φobs) Non-Commutativity of QEC (measurement must fully decouple before correction) First pre-registered Grade-A-eligible test of ZLT in a quantum-computational array system. Parallel domain extension to P50H (molecular motors). Domain reduction mapping provided in Appendix A. Keywords: Zero Leap Theory, MIPT Gate Problem, Measurement-Induced Phase Transition, entanglement hysteresis signature EHS, basis-dependent pc, quantum error correction non-commutativity, quantum arrays, superconducting qubits, Rydberg arrays, pre-registered predictions, operator observational load

DOI
10.5281/zenodo.19071030

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The quantum array does not forget that it was watched. Zero Leap Theory predicts that Measurement-Induced Phase Transitions (MIPT) in quantum arrays are structural Gate Collapse driven by operator observational load. The critical measurement rate pc is not a fixed universal constant — it is modulated by accumulated measurement history (H) and observation alignment (Φobs). Three falsifiable predictions registered before results: EHS > 0 (Entanglement Hysteresis Loop under cycling) Basis-Dependent Phase Boundary (pc increases with Φobs) Non-Commutativity of QEC (measurement must fully decouple before correction) First pre-registered Grade-A-eligible test of ZLT in a quantum-computational array system. Parallel domain extension to P50H (molecular motors). Domain reduction mapping provided in Appendix A. Keywords: Zero Leap Theory, MIPT Gate Problem, Measurement-Induced Phase Transition, entanglement hysteresis signature EHS, basis-dependent pc, quantum error correction non-commutativity, quantum arrays, superconducting qubits, Rydberg arrays, pre-registered predictions, operator observational load
This paper establishes Zero Leap Theory's first pre-registered, Grade-A-eligible prospective empirical test in a living quantum system. It provides a domain reduction mapping of RNA Polymerase (RNAP) single-molecule biophysics to ZLT quantum gate operators (P50D), and derives three falsifiable, ordinal predictions for quantum nanomotor experiments prior to publication of relevant experimental results. Two new measurable quantities are introduced: the Quantum Hysteresis Index (QHI), a proxy for the accumulated measurement-history operator H; and the Kinetic Asymmetry Signature (KAS), the observable distinguishing ZLT-predicted H-accumulation from standard decoherence. Analytical mapping of published RNAP motifs to canonical ZLT postulates is documented in Appendix A with explicit Grade B retroductive status. No new axioms are introduced; all formal machinery is inherited from ZLT-P50 and ZLT-P50D. V2.0 This paper establishes the first pre-registered prospective empirical test of Zero Leap Theory (ZLT) in a living molecular system under measurement-sensitive quantum-biological conditions. Building on ZLT-P50D (quantum gate operators), ZLT-P0C (non-commutativity of recovery phases), ZLT-P0D (Bath Operator axioms B0–B3), and ZLT-P50I (Structural Law of Intervention), we derive five falsifiable predictions for single-molecule RNA Polymerase (RNAP) experiments prior to publication of relevant results. Predictions P1–P3 concern measurement-history-dependent stall force (QHI > 0), kinetic asymmetry under sequential force ramps (KAS > 0), and non-compensability of measurement-accumulated degradation by NTP increase. Prediction P4 derives from P0C Theorem 4.1: the backtracking recovery sequence V₁⁻ → V₂⁻ is a structural necessity, not a contingent biological choice — reorganization under active load produces strictly worse recovery within the admissible state space of non-collapsed Φ. Prediction P5 derives from P0D Definition 2.1: the optical trapping laser must satisfy Bath Operator axioms B0–B3 during the recovery phase; each axiom violation predicts a specific P50I-class consequence profile (P₁, P₂, or P₃), with explicit dependence on the motor's H state. Appendix A provides retroductive Grade B alignment with published RNAP motifs. Appendix A.6 introduces a mutation-origin taxonomy classifying transcription errors under optical load into P50I consequence classes. Two new experimental proxies are introduced: the Quantum Hysteresis Index (QHI) and the Kinetic Asymmetry Signature (KAS). No new axioms are introduced; all machinery is inherited from P50, P50D, P0C, P0D, and P50I. v2.0 adds Predictions P4 and P5, Appendix A.6, and updated dependencies relative to v1.0. Keywords Zero Leap Theory, RNA Polymerase, molecular motors, quantum biology, single-molecule biophysics, measurement backaction, quantum hysteresis, non-compensability, pre-registration, prospective prediction, ZLT series
This paper reframes quantum scalability as a structural fragility problem: when correlated disturbance propagation exceeds corrective capacity, stability fails even if local error rates look small. ZLT yields a single canonical bifurcation—an index threshold at NFI_QC < 1—that separates regimes where quantum computation remains controllable from regimes where it is structurally non-scalable. Paper 50E integrates the measurement problem, decoherence, and quantum error correction (QEC) into a unified ZLT diagnostic: a Network Fragility Index for quantum systems (NFI_QC) defined from disturbance propagation and control capacity under memory and correlation. The core result is parameter-free in form: stability admits a canonical regime when NFI_QC < 1, and becomes structurally unstable when NFI_QC ≥ 1, regardless of local mitigation tactics. Engineering thresholds (e.g., safety margins such as 0.8 or scale-separation ratios such as 0.1) are explicitly treated as calibrable guardrails, not universal constants. The paper provides a Passive Alignment Protocol (Via Negativa) for reducing fragility by selectively disabling high-cascade pathways and correlation amplifiers rather than increasing intervention force. A falsification pack (EF/QF) is included: the framework is refuted if correlated-error scaling, cascade monotonicity, or predicted regime transitions fail under operational proxies. Supplementary code is provided as an illustrative operational witness for qualitative dependence (not a universal estimator of hardware-specific maxima).
Monitored many-body quantum systems can exhibit a measurement-induced phase transition (MIPT) between entangling and disentangling dynamical phases. Proposed approaches to study the MIPT experimentally typically rely on a classical decoding process, but the complexity of this decoding generally grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome this difficulty in the context of tree-shaped quantum circuits. We construct a hybrid circuit with Haar-random unitary operators, and we show that the MIPT can be detected without postselection using a simple decoding process whose complexity grows linearly with the number of qubits. The tree structure also enables a complete theoretical description of the MIPT and all its critical properties. We experimentally realize the MIPT on a trapped-ion quantum computer and show that the results are precisely described by theory without the need for error mitigation. To overcome the exponential complexity of measurement induced phase transition (MIPT), the authors propose a protocol which can detect MIPT easily on a tree-like quantum circuit. They experimentally realize the MIPT on a trapped-ion quantum computer and show that the results are precisely described by theory without the need for error mitigation.
This paper establishes the Quantum Bifurcation as a direct manifestation of Zero Leap Theory's Idolatry Amplification mechanism in quantum hardware. The central structural claim: increasing code distance (K) without first correcting the decoder's error model (Π) amplifies logical errors rather than suppressing them when the decoder model is violated by correlated burst events — **ΔW(K|Π_decoder < 0) < 0**. More qubits make it worse, not because of engineering imperfection, but because of a structural law. A **formal Domain Reduction Certificate (DRC)** maps the ZLC triple {Π, K, κ} to measurable QEC observables: Π = gate fidelity / decoder model fidelity; K = code distance redundancy; κ = qubit coherence time relative to correction cycle. Google Willow's beyond-break-even results (Λ = 2.14× suppression per code distance step) confirm ZLC convergence when all three conditions are satisfied. The persistent ~1 correlated event/hour floor across all code sizes (d=3 to d=29) confirms Idolatry Amplification when Π_decoder collapses. The **Kenotic Reset Protocol (KRP)** is the structural solution: (1) halt standard decoder on affected cluster; (2) selectively reset affected physical qubits from fresh ancilla states; (3) re-encode logical qubit from healthy surrounding region; (4) resume standard error correction. Steps 2 and 3 cannot be commuted — a direct test of **P0C Non-Commutativity Theorem** in quantum hardware. **Computational corroboration** (stim v1.15 + pymatching, 1D repetition code, d=3/5/7, 100k shots, seed=42): FC1 ✓ standard decoder on correlated burst → ~50% LER (250× baseline), flat across all code distances; FC2 ✓ KRP recovers to ~0.4% LER (~2× overhead, 125× better than standard on burst); PR3 ✓ LER floor perfectly flat confirming K scaling irrelevance when Π_decoder < 0. **FC3 (commuted KRP → ~50% LER) is pre-registered by this publication** as the priority next simulation — direct test of P0C Non-Commutativity in quantum physics. Structural parallel with ZLT-P50M-D (Diabetic Bifurcation, doi:10.5281/zenodo.19487334): both papers apply the same ZLT structural law in different domains and pre-register tests of P0C Non-Commutativity. Together they form the cross-domain universality evidence chain for P_U (Universality Paper). **Supplementary file:** `zlt_krp_simulation.py` — complete simulation script (stim + pymatching).a
FINDING: Measurement-induced phase transitions (MIPT) in quantum systems reveal a sharp entanglement phase boundary driven by the competition between unitary evolution and projective measurements, with critical points often characterized by universal exponents and effective central charges. | MATH: The MIPT is typically studied via the entanglement entropy S=−Tr(ρAln⁡ρA)S = -\text{Tr}(\rho_A \ln \rho_A)S=−Tr(ρA​lnρA​) scaling as S∼c6ln⁡LS \sim \frac{c}{6} \ln LS∼6c​lnL at criticality (for 1+1D conformal field theory), where ccc is the effective central charge. The critical measurement rate pcp_cpc​ separates volume-law (S∝LS \propto LS∝L) from area-law (S∝constS \propto \text{const}S∝const) phases. For Clifford circuits, the transition is in the percolation universality class with c=0c = 0c=0 (or c=ln⁡2c = \ln 2c=ln2 for Haar random circuits). The "1/(2π)" appears in the context of the quantum Zeno effect: for a system measured at rate γ\gammaγ, the effective Hamiltonian is \(H_{\text{eff}} = H - i \frac{\gamma}{2} \sum_m |m\rangle\langle Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com