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Room-Temperature Adelic Nuclear-Spin Qubit v2.0: p-adic Compilation, Dynamical Decoupling, and Five Major Discoveries

Rowan Brad Quni-Gudzinas

Published Jul 13, 2026• 0 citations
Publisher

Abstract

v2.0 incorporates 5 major discoveries from the complete research program (Phases 0-5): (D1) Hensel fidelity ceiling at F=0.997 requiring hybrid GRAPE fine-tuning; (D2) DD residual dephasing as dominant error at 66% per 1ms cycle, requiring CPMG-8 + 0.1ms cycle; (D3) N-layer Ostrowski product formula mathematically requires low-error layers; (D4) 50nm NV spacing viable with Stark-shift addressing; (D5) 10-30x capital cost advantage for benchtop quantum sensing, QKD, and educational markets. All 6 prior-session handoff questions resolved.

DOI
10.5281/zenodo.21330959

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Beyond Pure Dephasing: A Quantitative Analysis of Two-Level Error Correction for Multi-Spin Molecular Qubits

Rowan Brad Quni-Gudzinas

Molecular spin systems exhibit a natural hierarchy of decoherence channels: fast pure dephasing (characterized by the transverse relaxation time T₂) and comparatively slow energy relaxation (characterized by T₁). A recent proposal argues that fault-tolerant quantum computing with molecules requires a hybrid two-level encoding: a first-level *dephasing-tolerant unit* (DTU) that suppresses the leading pure-dephasing channel, followed by a second-level multi-qubit code that corrects residual off-diagonal (relaxation-like) errors [1,2]. This paper provides an independent quantitative assessment of that scheme. Using assumed representative parameters (T₂ = 100 μs, T₁ = 10 ms, within ranges reported in the experimental molecular-spin-qubit literature), a projected dephasing suppression factor S = 100 (an assumption, not a value reported in [1]), and a 1 μs correction cycle, we derive an explicit logical error probability of 2.9998 × 10⁻⁸ per cycle (Γ_L = 2.9998 × 10⁻² s⁻¹, six physical spins per logical qubit) for a three-unit repetition code, valid only when S ≫ R, because the repetition code leaves residual dephasing uncorrected; at S = R the uncorrected single-Z channel contributes p_L = 1 − (1 − p_Z)³ ≈ 2.9997 × 10⁻⁴ per cycle (Γ_L ≈ 2.9997 × 10² s⁻¹). We further derive the *hierarchy condition*: the first-level suppression must satisfy S ≥ γ_φ/γ₁; with our parameters the equality S = γ_φ/γ₁ = 100 holds exactly, placing the scheme at the threshold where residual dephasing and relaxation contribute equally in the correctable relaxation channel. A computed comparison with a five-qubit outer code, which also corrects single Z errors (P_fail ≈ 4.5 × 10⁻⁷ per cycle, Γ_L ≈ 0.45 s⁻¹, 10 physical spins), shows the five-qubit code is preferable at S = R. We identify failure modes, falsifiable predictions, and open questions regarding synthesis and correlated noise. ## 1. Introduction Quantum information processing demands physical platforms combining long coherence times wit Full text and updates: papers.qnfo.org/papers/beyond-pure-dephasing-a-quantitative-analysis-of-two-level-error-correction-for-/

•Oct 5, 2026•0 citations
v2.0 incorporates 5 major discoveries from the complete research program (Phases 0-5): (D1) Hensel fidelity ceiling at F=0.997 requiring hybrid GRAPE fine-tuning; (D2) DD residual dephasing as dominant error at 66% per 1ms cycle, requiring CPMG-8 + 0.1ms cycle; (D3) N-layer Ostrowski product formula mathematically requires low-error layers; (D4) 50nm NV spacing viable with Stark-shift addressing; (D5) 10-30x capital cost advantage for benchtop quantum sensing, QKD, and educational markets. All 6 prior-session handoff questions resolved.
v3.0 — Red-Team Fixes Edition. Incorporates all 5 red-team gap fixes: (G1) Mediator array architecture — 10nm gate pairs + 50nm spectator qubits with DD switching resolves the 2-qubit entanglement gap; (G2) DD model recalibrated with 50% pulse error penalty for conservative T2 estimates; (G3) Full adelic pipeline specification for end-to-end integration; (G4) Buffer dissemination confirmed with D1 tracking; (G5) NV-13C near-term validation pathway added parallel to Posner long-term synthesis. All claims retested. 4 skill updates queued (buffer-integration v4.1, publication-publisher v3.5, literature-search v2.1, infrastructure-audit). 6 Kaizen patterns captured, 5 self-improvements identified.
The nitrogen-vacancy (NV) centre in diamond is the only solid-state qubit that operates at room temperature, yet its viability for fault-tolerant quantum computing has been dismissed on the grounds that decoherence times are too short. Here we show, through a calibrated twelve-channel decoherence model spanning 1.3 K to 600 K (60+ experimental anchors, R² = 0.953), that single- and two-qubit gate error rates fall below the surface code threshold of 1% at 295 K for bulk ultra-pure diamond under dynamical decoupling with N ≥ 2048 pi-pulses. The key enabler is the recently demonstrated T₂ = 2T₁ limit (4.34 ms at room temperature), achieved by filtering the spin-lattice Han noise channel above 1 MHz via high-order CPMG. The model now includes ¹³C nuclear spectral diffusion (dominant in ultra-pure bulk at high B-field, validated against Wrachtrup QV=8 at -5.4%) and a magnetic-field-dependent T₁ correction. For standard-grade bulk diamond, we identify a Peltier-cooled sweet spot at 200–270 K that brings all gates below threshold at a cooling cost of ~200 EUR. We further show that the XZZX surface code, exploiting the strongly Z-biased noise of NV circuits (effective bias η_eff ≈ 834 from idle-dominated architecture), reduces the physical qubit overhead by more than 95% compared to the standard surface code. Combined with soft-information decoding using analog photoluminescence counts, this establishes a concrete path from the current QV=8 (Wrachtrup 2026) to QV > 1000. Decoherence is no longer the bottleneck for NV-based quantum computing at room temperature. UK Patent Applications GB2606382.6 and GB2606639.9 cover methods described herein.
Molecular spin systems exhibit a natural hierarchy of decoherence channels: fast pure dephasing (characterized by the transverse relaxation time T₂) and comparatively slow energy relaxation (characterized by T₁). A recent proposal argues that fault-tolerant quantum computing with molecules requires a hybrid two-level encoding: a first-level *dephasing-tolerant unit* (DTU) that suppresses the leading pure-dephasing channel, followed by a second-level multi-qubit code that corrects residual off-diagonal (relaxation-like) errors [1,2]. This paper provides an independent quantitative assessment of that scheme. Using assumed representative parameters (T₂ = 100 μs, T₁ = 10 ms, within ranges reported in the experimental molecular-spin-qubit literature), a projected dephasing suppression factor S = 100 (an assumption, not a value reported in [1]), and a 1 μs correction cycle, we derive an explicit logical error probability of 2.9998 × 10⁻⁸ per cycle (Γ_L = 2.9998 × 10⁻² s⁻¹, six physical spins per logical qubit) for a three-unit repetition code, valid only when S ≫ R, because the repetition code leaves residual dephasing uncorrected; at S = R the uncorrected single-Z channel contributes p_L = 1 − (1 − p_Z)³ ≈ 2.9997 × 10⁻⁴ per cycle (Γ_L ≈ 2.9997 × 10² s⁻¹). We further derive the *hierarchy condition*: the first-level suppression must satisfy S ≥ γ_φ/γ₁; with our parameters the equality S = γ_φ/γ₁ = 100 holds exactly, placing the scheme at the threshold where residual dephasing and relaxation contribute equally in the correctable relaxation channel. A computed comparison with a five-qubit outer code, which also corrects single Z errors (P_fail ≈ 4.5 × 10⁻⁷ per cycle, Γ_L ≈ 0.45 s⁻¹, 10 physical spins), shows the five-qubit code is preferable at S = R. We identify failure modes, falsifiable predictions, and open questions regarding synthesis and correlated noise. ## 1. Introduction Quantum information processing demands physical platforms combining long coherence times wit Full text and updates: papers.qnfo.org/papers/beyond-pure-dephasing-a-quantitative-analysis-of-two-level-error-correction-for-/