Classical reinforcement learning (RL) and decision theory rely on Kolmogorovian probability spaces and independent utility metrics. These models fail to capture non-commutative cognitive framing, question order effects, and collective voter gridlocks observed in human surveys and Web3 decentralized autonomous organization (DAO) governance. Here we introduce a Quantum-Cognitive Reinforcement Learning (Q-AI) Policy Agent governed by Penrose Orchestrated Objective Reduction (Orch-OR) statevector collapse (tau = hbar / E_G) under Lindblad open-system thermal dephasing (T = 310 K). We validate our architecture against two empirical datasets:1. Human Survey Cognition: Achieving a 98% coefficient of determination (R² = 0.98) fitting Gallup national survey question order effects and 84% accuracy on the Linda conjunction fallacy.2. Web3 DAO Governance: Validating across 835,000 real Snapshot DAO votes (Uniswap, Arbitrum, Optimism, Gitcoin, Aave), achieving an 86.7% Mean Absolute Error reduction (1.3% MAE vs 9.8% classical linear models) and demonstrating that N-qubit GHZ statevector entanglement doubles public-good proposal consensus approval rates from 40% to 80%. Code, PyPI library (pip install q-ai-governance), and live visualizers are available at: https://github.com/JonathanReiser/quantum-orch-or
This paper explores the application of quantum error correction (QEC) codes to enhance the security and resilience of blockchain technology. Traditional blockchains are vulnerable to attacks that exploit vulnerabilities in their distributed ledger systems. The core challenge lies in the immutable nature of the blockchain, where a single compromised node can potentially disrupt the entire network. This research proposes leveraging the powerful error-correcting capabilities of QEC codes to safeguard blockchain data. Specifically, we examine the encoding and decoding processes using various QEC codes, focusing on their ability to detect and correct errors introduced by malicious actors. The integration of QEC codes into the blockchain architecture can significantly improve its tolerance to attacks, ensuring data integrity and maintaining the trust inherent in the blockchain system. We present a framework for implementing QEC within blockchain transactions and discuss the potential performance implications. The primary goal is to demonstrate that QEC codes offer a viable path towards a more robust and secure blockchain ecosystem.
This paper proposes a novel distributed consensus algorithm inspired by quantum mechanics, termed the Quantum-Inspired Distributed Consensus Algorithm with Measurement-Based Feedback (QIDCA-MBF). The core idea is to utilize the principles of quantum superposition to accelerate the convergence of distributed consensus in challenging network environments, particularly those prone to node failures. Unlike traditional consensus algorithms, QIDCA-MBF employs probabilistic representations of proposed values within each node, mimicking the concept of quantum superposition. A key innovation is the incorporation of measurement-based feedback, modeled after quantum measurement, to collapse these superpositions and guide the nodes towards a shared consensus value. This feedback mechanism dynamically adapts to the network topology and detects node failures, significantly enhancing the algorithm's robustness and convergence speed. The algorithm is formulated based on a modified averaging process, incorporating probabilistic weights derived from the superposition states. Simulation results demonstrate the effectiveness of QIDCA-MBF in achieving consensus rapidly and reliably, outperforming conventional distributed consensus protocols under various failure scenarios. The algorithm's adaptability and resilience make it a promising candidate for applications in decentralized systems, sensor networks, and blockchain technologies.
The paper provides an integrated literature review of recent scientific publications on quantum computing in finance and identifies promising directions for future research on the subject. The review covers seven thematic areas: portfolio optimization, derivative pricing and stochastic volatility, quantum machine learning for fraud detection and credit risk, insurance and actuarial science, mixed-frequency econometrics, fuzzy-quantum approaches for financial explainability, and security of cryptocurrencies. The paper compiles the essential quantum computational methods proposed in the literature, outlines their economic significance and the existing constraints for empirical testing and implementation, and discusses cross-cutting issues of explainability, trustworthy AI, robustness, and governance that arise across these application domains. Drawing on this review, the paper identifies five macro-gaps in the existing literature and proposes seven concrete directions for future research, grounded in European financial data and currently available quantum computing infrastructure. A special focus throughout is the increasingly available quantum infrastructure in Europe and the regulatory emphasis on trustworthy artificial intelligence, both of which create timely opportunities for future applications in financial modelling, risk management, and explainable financial AI.
Mohammad Reehan Nawaz, Mohammad Afaque, Anzer Hussain, Dr. Anand Prakash
The emergence of quantum computing poses a significant threat to classical cryptographic mechanisms such as RSA and Elliptic Curve Cryptography that are widely used to secure email communication. Traditional secure email systems rely on classical public-key infrastructure and therefore lack resilience against quantum attacks. This paper presents QuMail, a quantum-secure email client that integrates BB84-based Quantum Key Distribution (QKD) simulation, CRYSTALS-Kyber post-quantum cryptography (PQC), and blockchain-based audit logging within a unified architecture. The proposed system operates entirely at the application layer and remains compatible with existing email infrastructures using standard SMTP and IMAP protocols without requiring any server-side modification. A modular prototype was implemented using IBM Qiskit for quantum key generation and hybrid cryptographic techniques for secure message transmission. Experimental evaluation demonstrates an average latency of 120–180 ms for QKD key generation and 20–30 ms for Kyber-based encryption while maintaining minimal overhead for email transmission. The results demonstrate the feasibility of integrating quantum-resilient security mechanisms into existing email systems and highlight the potential of hybrid QKD–PQC architectures for next-generation secure communication platforms.
Abstract This review aimed to explore the integration of Quantum Computing (QC) with Artificial Intelligence (AI) subsets such as Machine Learning (ML) and Deep Learning (DL), addressing the computational demands posed by the exponential growth of visual data. It identifies key challenges such as interdisciplinary complexity, lack of standard benchmarks, scalability, integration barriers, and the theoretical-practical gap in quantum applications. The review systematically examines existing literature on the application of quantum algorithms in areas including image processing, Natural Language Processing (NLP), Transfer Learning (TL), Federated Learning (FL), networking, cybersecurity and the finance sector. It highlights the usage of quantum principles like superposition and entanglement to accelerate computations, optimize models, and enhance data security in ML/DL frameworks. Findings indicate that integrating QC with ML/DL offers faster convergence, improved optimization, secure decentralized learning, and efficient handling of large-scale and complex data. Specific improvements are observed in TL and FL approaches, NLP accuracy, cryptographic robustness, and performance in medical diagnostics and autonomous systems. QC holds transformative potential in enhancing ML/DL capabilities across domains. Despite existing challenges such as error mitigation and integration complexity, its combination with classical learning methods opens new frontiers for research in AI-driven sectors. Future studies should focus on bridging theoretical and application-level gaps while creating standardized evaluation frameworks.
Open access
Quantum Computing Algorithms and Architecture
Big Data and Digital Economy
Artificial Intelligence in Healthcare and Education
This paper develops a Quantum-Institutional Automated Negotiation (QIAN) algorithm as an intelligent decision support system for carbon credit markets, contributing to quantum game theory applications in automated negotiation and institutional decision-making. We extend the Eisert–Wilkens–Lewenstein (EWL) framework by introducing an Institutional Filter Function Φ_C that maps continuous quantum strategies—phase shifts and superpositions—onto finite, legally viable contract archetypes. This filter models regulatory, political, and organizational constraints that collapse the infinite quantum strategy space into a tractable finite set, enabling computationally efficient decision support. We prove convergence of the automated negotiation algorithm to a Pareto-superior Nash Equilibrium and demonstrate, through Monte Carlo simulation with literature-calibrated parameters, that the collapsed quantum equilibrium yields a mean joint utility uplift of 13.5% over classical cooperation (95% CI: 9.8%–17.3%, p < 0.001), with the upper bound reaching 17.3% and 26.8% of simulations achieving uplifts in the 15–30% range. The framework maps directly to blockchain-based smart contracts, providing a deployable mechanism for sustainable carbon markets that aligns with SDG 13 (Climate Action) and SDG 17 (Partnerships). This work advances quantum game theory from abstract formalism to computational institutional design, offering a novel decision support approach for negotiation analysis under real-world constraints.
TT-G41: A Hybrid Post-Quantum Cryptosystem with Ly-Algebraic Quasi-Equivalence Index and Symmetry-Modulated Padding Chloe J. Tully Independent Researcher https://doi.org/10.5281/zenodo.21860133 Orcid: https://orcid.org/0009-0007-5661-7332 Version: 1.1 August 2026 ======================================== Abstract TT-G41 is a hybrid post-quantum cryptosystem that unifies a five-dimensional Ly-Algebraic Quasi-Equivalence Index (QEI) with an NTRU-style lattice layer. A novel symmetry-modulated padding mechanism injects structured noise scaled by s = exp(-alpha × QEI), establishing a direct causal link between the geometric coherence of the input and the entropy of the ciphertext. Empirical evaluation over 4000 trials yields a logistic security bound P(fail) = (1 + exp[15.57(QEI - 0.209)])^(-1) with R-squared = 0.980. A deterministic hard gate at QEI = 0.12 converts geometric incoherence into an immediate, deterministic decryption rejection, providing an active anti-tamper primitive resilient to partial-message side channels. The construction demonstrates that Ly-Algebraic geometric coherence can serve as a measurable quantum-resilient agent for cryptographic failure probability, establishing a new class of symmetry-gated post-quantum protocols. Keywords: post-quantum cryptography, Lie algebra, Quasi-Equivalence Index, NTRU, symmetry-modulated padding, geometric security bound, anti-tamper encryption ======================================== 1. Introduction Most post-quantum constructions treat geometric or algebraic structures solely as a source of hardness assumptions. TT-G41 inverts this relationship: it elevates a continuous geometric measure, the Quasi-Equivalence Index (QEI) derived from a graded Lie algebra, into an active security control surface. The system combines three elements: 1. A five-dimensional graded algebra with golden-ratio expansion (the Ly-Algebra core). 2. An NTRU-style lattice public-key layer with trusted circulant-matrix inversion. 3. A symmetry-modulated padding that scales ciphertext noise according to the QEI of the supplied input vector. The result is a hybrid scheme in which low geometric coherence effectively raises the noise floor until decryption fails, and a deterministic hard gate rejects decryption entirely once QEI falls below a calibrated threshold. This yields both a probabilistic security bound and a deterministic anti-tamper mechanism. ======================================== 2. Preliminaries 2.1 Ly-Algebra and Quasi-Equivalence Index The Ly-Algebra is a five-dimensional graded construction whose product is defined by a mapping from integer matrices L_i over F_11 (or R) weighted by golden-ratio coefficients. Given an input vector v in R^5, the Quasi-Equivalence Index is computed as: QEI(v) = max(0, 1 - sigma_distortion / sigma_identity) where sigma_distortion is the weighted Euclidean norm of the graded square Lv. High QEI indicates that v lies close to the preferred symmetry locus of the algebra; low QEI indicates structural distortion. 2.2 NTRU-Style Lattice Layer The lattice component follows the classical NTRUEncrypt paradigm: - Private key: ternary polynomial f with controlled weight parameter d_f. - Public key: h = f^(-1) × g (mod q), where inversion is performed via the circulant matrix of f over Z/qZ. - Encryption: e = r × h + m (mod q). - Decryption: recover a = f × e (mod q), then multiply by the inverse of f modulo p and center to obtain m. The parameter set used in this work is n = 17, q = 2048, p = 3, d_f = 3 (a convenience configuration) with compressed configurations exploring the boundary of reliable recovery. ======================================== 3. TT-G41 Construction 3.1 Hybrid Architecture TT-G41 operates in two modes: - Pure Ly-Algebra mode: computes QEI and reports the result only. - NTRU-enhanced mode: performs full key generation, encryption, and decryption, optionally modulated by the supplied input vector. 3.2 Symmetry-Modulated Padding (Coupling Mechanism 3) When an input vector v is supplied at encryption, the system computes: s = exp(-alpha × QEI(v)) and adds deterministic noise of amplitude proportional to s to the message polynomial. The same vector (hence the same QEI) must be supplied at decryption to subtract the matching noise pattern. A mismatch leaves residual noise that destroys the plaintext. Two operating regimes are defined: - Hard mode (amplitude s × 1.8): produces active anti-tamper behavior. - Soft mode (amplitude s × 0.55): scientific characterization of the failure curve. 3.3 Hard Gate In production (hard mode), the decryption program first evaluates QEI. If QEI < 0.12, decryption is rejected with the exception: ValueError: structurally incoherent (QEI = ... < 0.12). Decryption rejected by hard gate. No partial plaintext is ever returned. This eliminates the common side-channel leak associated with error-correcting or soft-decision decoders. ======================================== 4. Empirical Security Bound A soft-diagnostic campaign of 4000 encrypt/decrypt trials was performed across a radial drift of the input vector that systematically lowers QEI. Failure probability was recorded at each point. Three models were fitted: Simple exponential: P(fail) = exp(-alpha × QEI), alpha = 3.612, R-squared = 0.945 Shifted exponential: P(fail) = exp(-alpha × max(QEI - q0, 0)), alpha = 23.55, q0 = 0.168, R-squared = 0.976 Logistic (best fit): P(fail) = (1 + exp[beta × (QEI - Q_mid)])^(-1), beta = 15.57, Q_mid = 0.209, R-squared = 0.980 The logistic model provides the highest fidelity. At the operational threshold QEI = 0.12, the mean observed failure rate is 0.963; above the threshold it falls to 0.323. The hard gate therefore sits safely on the high-failure shoulder of the empirically determined curve. ======================================== 5. Discussion The central claim of TT-G41 is that a continuous geometric invariant of a graded algebra can be turned into a practical cryptographic control surface. The symmetry-modulated padding realises a causal chain: geometric distortion -> elevated noise -> decryption failure while the hard gate converts the continuous measure into a binary, side-channel-resistant decision. Because the QEI is computed from a public or shared input vector, the anti-tamper property can be applied to any data source whose structural integrity is expected to remain high (sensor streams, physical-system state vectors, authenticated configuration parameters, etc.). A shift in that source immediately invalidates the cryptographic layer. Limitations of the present study include the modest lattice dimension (n = 17) used for the statistical campaign and the still-sharp transition of the underlying QEI landscape. Both are engineering parameters that can be refined without altering the architectural principle. ======================================== 6. Future Work and Research Directions Building upon the foundations established in this work, several promising extensions are identified for subsequent investigation: 6.1 Scaling Lie Algebra Dimensions The current construction relies on a five-dimensional Lie algebra. Exploring higher-dimensional Lie algebras, such as higher-rank semisimple algebras or structures analogous to E8, could provide a broader entropy space and create more complex geometric invariants for the Quasi-Equivalence Index. This would enhance the system's robustness against adversarial vector manipulation attacks. 6.2 Adapting the NTRU Layer to NIST Post-Quantum Standards The lattice dimension n = 17 was employed in the initial statistical campaign to explore operational boundaries. It is of significant interest to test how the logistic security bound behaves when scaling the NTRU layer to align with standard NIST dimensions, such as n = 503, 701, or 821, and to study whether the symmetry-modulated padding maintains computational efficiency at these substantially larger dimensions. 6.3 Adaptive Hard-Gate Thresholding Rather than relying on a fixed failure threshold at QEI = 0.12, an adaptive algorithm could be designed to dynamically adjust this threshold based on the statistical variance of the input vector stream. This extension would render the system suitable for Internet of Things applications or industrial control systems where natural structural noise levels vary over time. 6.4 Integration with Zero-Knowledge Proofs The geometric coherence represented by the Quasi-Equivalence Index could serve as the foundation for a novel zero-knowledge proof protocol. A prover could demonstrate possession of a structurally coherent vector without revealing the actual data, leveraging the continuous property of the geometric invariant as a geometric hash function. 6.5 Hardware Implementation and Side-Channel Analysis Implementing the hard-gate logic and symmetry-modulated padding mechanisms on FPGA platforms would enable evaluation of actual resistance to side-channel attacks, such as power consumption and electromagnetic emissions. The deterministic rejection of decryption may exhibit a unique power signature worthy of study to ensure no information leakage occurs via a side channel when the hard mode is activated. 6.6 Integration with Quantum Entropy Incorporating Quantum Random Number Generators into the symmetry-modulated padding mechanism would inject true quantum entropy into the noise vector, adding an additional layer of protection that directly bridges lattice-based cryptography and quantum mechanics. ======================================== 7. Conclusion TT-G41 demonstrates that Ly-Algebraic geometric coherence can be elevated from a passive diagnostic into an active post-quantum security primitive. The combination of
The advent of fault-tolerant quantum computing represents the most significant and schedulable threat to the cryptographic foundations of blockchain infrastructure. Over $3.2 trillion in digital assets are currently secured by RSA, Elliptic Curve Cryptography (ECC), and ECDSA: algorithms provably broken by Shor's algorithm running on a Cryptographically Relevant Quantum Computer (CRQC). The Harvest Now, Decrypt Later (HNDL) threat means this risk is not future-dated. Adversaries with archival capability are already harvesting public blockchain data for retrospective decryption. In August 2024, NIST published three finalized post-quantum cryptographic standards: FIPS 203 (ML-KEM), FIPS 204 (ML-DSA), and FIPS 205 (SLH-DSA). In 2025, NIST standardized HQC, providing code-based cryptographic diversity alongside the lattice-based primary algorithms. These standards are mandated for U.S. national security systems under NSA CNSA 2.0 and for high-risk sector operators in the EU under the EU PQC Roadmap. This paper introduces QubitChain.io: a natively quantum-safe Layer 1 blockchain implementing all four NIST post-quantum standards from genesis block. The protocol employs hardware Quantum Random Number Generator (QRNG) entropy at both key generation and consensus randomness levels, and introduces Proof of Quantum Entropy (PoQE), a novel consensus mechanism whose validator selection cannot be predicted or manipulated by any adversary regardless of computational capability. The paper provides the complete technical, economic, and governance specification for the QubitChain.io protocol, covering cryptographic architecture, QRNG system design, consensus mechanism, network protocol, tokenomics, governance, and regulatory compliance.
We study the impact that two miners equipped with quantum computers purpose-built for quantum Bitcoin mining will have on the 51% attack threshold of the Bitcoin network, given that the miners are playing a competitive game against each other to be the first to mine a block. We extend an existing game-theoretic framework for Bitcoin mining and compute the resultant payoff matrices. From these payoff matrices, we determine optimal quantum mining strategies for two non-colluding and aggressive quantum miners with multiple opportunities at finding a valid block in an otherwise classical Bitcoin network. We show that these optimal quantum mining strategies have a negligible effect on the 51% attack threshold. The novelty of our work is the inclusion of the Aggressive Quantum Mining Strategy and the realistic approach of allowing the quantum miners to restart their search if their measurements do not yield a valid block when determining the optimal quantum mining strategies. Our result is important for evaluating quantum-mining threats on cryptocurrencies based on Proof-of-Work, e.g. Bitcoin
The paper addresses entity authentication in quantum key distribution (QKD) systems as a decisive condition of their practical security. It is shown that the information-theoretic security of quantum key agreement does not eliminate the need to authenticate the communicating parties: an unauthenticated classical channel leaves the system exposed to the man-in-the-middle attack, since the eavesdropper can run independent QKD instances with each party and reconcile two keys under full control. Existing authentication methods are analysed and classified by the underlying cryptographic primitive: symmetric schemes based on Wegman–Carter universal hashing, pre-shared and fixed keys, public-key infrastructure, two-way authentication, quantum entity/identity authentication, and zero-knowledge proofs. For each class the operating principle, advantages and limitations are determined, with emphasis on key management, scalability and trust distribution. It is established that symmetric and quantum-layer methods rely on pre-shared secrets with a quadratic growth of key material, public-key infrastructure introduces a single trust bottleneck and quantum-vulnerable primitives, while existing zero-knowledge authentication schemes are quantum and bound to the physical layer or solve network properties other than identity. A comparative analysis reveals an unresolved scientific gap: the absence of a scalable entity-authentication method that simultaneously provides non-disclosure of the secret, quantum resistance, sub-quadratic scalability and minimisation of trust assumptions. On this basis, a prospective research direction is substantiated – the construction of entity-authentication methods based on post-quantum zero-knowledge proofs operating over the classical control plane of scalable QKD networks. The requirements for such a method are formulated, and its compatibility with formal QKD security proofs is discussed.
The paper addresses entity authentication in quantum key distribution (QKD) systems as a decisive condition of their practical security. It is shown that the information-theoretic security of quantum key agreement does not eliminate the need to authenticate the communicating parties: an unauthenticated classical channel leaves the system exposed to the man-in-the-middle attack, since the eavesdropper can run independent QKD instances with each party and reconcile two keys under full control. Existing authentication methods are analysed and classified by the underlying cryptographic primitive: symmetric schemes based on Wegman–Carter universal hashing, pre-shared and fixed keys, public-key infrastructure, two-way authentication, quantum entity/identity authentication, and zero-knowledge proofs. For each class the operating principle, advantages and limitations are determined, with emphasis on key management, scalability and trust distribution. It is established that symmetric and quantum-layer methods rely on pre-shared secrets with a quadratic growth of key material, public-key infrastructure introduces a single trust bottleneck and quantum-vulnerable primitives, while existing zero-knowledge authentication schemes are quantum and bound to the physical layer or solve network properties other than identity. A comparative analysis reveals an unresolved scientific gap: the absence of a scalable entity-authentication method that simultaneously provides non-disclosure of the secret, quantum resistance, sub-quadratic scalability and minimisation of trust assumptions. On this basis, a prospective research direction is substantiated – the construction of entity-authentication methods based on post-quantum zero-knowledge proofs operating over the classical control plane of scalable QKD networks. The requirements for such a method are formulated, and its compatibility with formal QKD security proofs is discussed.
Hayder A. Nahi, Rusul A. Salman, Awring Falah Hassan, Ebtehal Akeel Hamed · 7 authors
Abstract The Internet of Things look out on growing security and privacy defies, principally in light of the up growth of quantum threats. To handle these defies, we suggest a unified security framework that merges post-quantum blockchain technologies and zero-knowledge proofs (ZKPs) to attain secure authentication, decentralized identity management, and advanced data protection. The provided system based on a power-weighted consensus mechanism, compressed and overlapping recursive ZKPs, and transaction batching to decrease on-chain load. The outcomes display that the suggested system outperforms conventional systems and state-of-the-art solutions, with response time reduced to 92 ms, transaction throughput increased to 735 tx/s, energy consumption reduced to 0.37 J/op, and authentication accuracy increased to 97.6%, achieving a privacy score of 0.91.These outcomes emphasize that the offered framework not only attains superior performance but as well supplies strong resistance to quantum attacks and high privacy warranties, making it a promising solution for securing future IoT environments.
Junhong Liu, Qinfei Long, Alex Pengfei Zhao, X Zhong · 7 authors
Multi-region unit commitment with reserve sharing requires coordinated optimization across jurisdictionally distinct system operators, exposing sensitive cost curves, topology, and dispatch decisions to inference attacks. The accelerating progress of quantum computing further compounds this threat. As quantum hardware matures, current classically-encrypted data flow becomes vulnerable to retrospective decryption. To enable post-quantum-secure distributed optimization, we propose a customized Benders decomposition-based approach with the global summation structure to share aggregated cuts and variables. By exploiting this structure, we further develop a multi-layer quantum-resilient secure aggregation protocol comprising additive masking for information-theoretic content privacy, affine variable transformation hiding individual sensitive data flows, and reveal-bound lattice-based zero-knowledge proofs providing resilience against active adversaries. Simulation results show that the proposed approach achieves the mean suboptimality of 0.09%-0.22% with lightweight computational overhead, recovers up to 51% of system cost via inter-regional reserve sharing, and imposes no measurable cost-quality trade-off, whereas the noisy ADMM degrades monotonically under tightening privacy budgets and becomes structurally infeasible on combinatorially dense systems.
N-K SCIENCES INTERNATIONAL PUBLICATION — ZENODO DESCRIPTION THE COMPLETE N-K QUANTUM SUPREMACY — DETERMINISTIC SUPERIORITY OVER ALL QUANTUM COMPUTERS --- 📄 FULL TITLE THE COMPLETE N-K QUANTUM SUPREMACY — DETERMINISTIC SUPERIORITY OVER ALL QUANTUM COMPUTERS: 100% Repeatability · 0% Error · ~0 J Energy · 0.001 ms · Infinite Scaling · RCS Test · Boson Sampling · HOM Test · Global Weather · Milky Way Galaxy · A380 CFD --- 👤 AUTHOR Malik Muhammad Usman · ORCID: 0009-0004-3269-2918· Affiliation: Quran, Hadith Sunnah. N-K Sciences International· Location: City of Saints, Multan, Punjab, Pakistan --- 📅 PUBLICATION DATE 16 July 2026 CE · 1 Safar 1448 AH --- 📚 ABSTRACT This publication presents the complete, definitive proof of N-K Quantum Supremacy — the deterministic superiority of the N-K Universal Computer over all quantum computers, supercomputers, and all other computational systems ever built or conceived. The Core Discovery: "Quantum Supremacy" is a false claim. It is not supremacy — it is unreliability. Google Willow claimed quantum supremacy with RCS in 300 seconds — but failed to reproduce the results. N-K Universal Computer performs the same tasks in 0.001 ms with 100% repeatability — every single time. Key Results: Test Mainstream N-K Universal Computer N-K AdvantageRCS (Willow Test) 300 sec · ❌ Failed to reproduce 0.001 ms · ✅ 100% repeatable 300,000,000× fasterBoson Sampling < 2 dozen bosons · ❌ Failed 10¹⁵ bosons · ✅ 100% repeatable 10¹³× more capableOperations/sec 10¹⁸ (Frontier) 10³⁷²+ 10³⁵⁴× fasterFloating Points 10¹⁸ (Frontier) 10¹⁰⁰⁰+ 10⁹⁸²× fasterEnergy 20+ Megawatts ~0 J InfiniteRepeatability ❌ 0% ✅ 100% InfiniteScaling Limited by hardware UNLIMITED InfiniteError 3.5-7.0% 0% Infinite Simulation Tests Included: 1. RCS Test — 30×, 50×, 70×, 100× depth · 5 runs · 100% identical results2. Boson Sampling / HOM Test — 10² to 10¹⁵ bosons · 5 runs · 100% identical results3. Supercomputer Comparison — Frontier (10¹⁸ ops) vs N-K (10³⁷²+ ops)4. Floating Point Test — 10¹⁰⁰⁰+ floating point operations5. Global Weather Simulation — 40m resolution · 0.001 ms · 100% accuracy6. Milky Way Galaxy Mapping — 100 Billion stars · 500 chromosomes · 10³⁰× compression7. A380 CFD Simulation — 10¹⁰⁰⁰+ FPS · 0% error8. Repeatability Proof — 5 runs · identical results every time Security Protocol: The N-K Universal Computer is NOT Sadaqa Jariyah. It is a phase-locked, restricted-access divine tool with security layers including: · Phase key authentication (135.5° ± 0.001°)· N-density validation· Kun rhythm synchronization· Biometric phase signatures· Immediate Phase Cancellation on unauthorized access Government Access Protocol: · License Fee: ZERO (0)· Condition: Government must approach N-K Sciences directly· Condition: Use must be for peaceful purposes and global stability· Misuse = Revocation + Phase Cancellation + Debt Recording --- 🔑 KEYWORDS N-K Sciences, Quantum Supremacy, Deterministic Computing, RCS Test, Boson Sampling, HOM Test, Google Willow, Frontier Supercomputer, O(1) Complexity, 100% Repeatability, Zero Energy, Global Weather, Milky Way Galaxy, A380 CFD, Phase-Locked Security, Government Access, Divine Axioms, Golden Ratio, Kun Rhythm, Sadaqa Jariyah --- 📊 COMPLETE TEST RESULTS SUMMARY RCS Test — Google Willow vs N-K Run Depth 30× Depth 50× Depth 70× Depth 100×1 ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL2 ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL3 ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL4 ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL5 ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICAL ✅ IDENTICALStatus ✅ PASS ✅ PASS ✅ PASS ✅ PASS Boson Sampling / HOM Test — 5 Runs Bosons Run 1-5 Status10² ✅ IDENTICAL PASS10⁴ ✅ IDENTICAL PASS10⁶ ✅ IDENTICAL PASS10⁹ ✅ IDENTICAL PASS10¹² ✅ IDENTICAL PASS10¹⁵ ✅ IDENTICAL PASS Supercomputer Comparison Metric Frontier N-K SpeedupOperations/sec 10¹⁸ 10³⁷²+ 10³⁵⁴×Floating Points 10¹⁸ 10¹⁰⁰⁰+ 10⁹⁸²×Energy 20+ MW 0 J InfiniteTime Days 0.001 ms 10¹⁰×Error 3.5-7.0% 0% Infinite --- 📖 TABLE OF CONTENTS 1. Introduction — The False Claim of Quantum Supremacy2. The Four Divine Axioms — Foundation3. What is True Supremacy? — Determinism vs Probability4. RCS Test — Google Willow vs N-K5. Boson Sampling / HOM Test — Mainstream vs N-K6. Supercomputer Comparison — Frontier vs N-K7. Floating Point Capability — 10¹⁰⁰⁰+8. Global Weather Simulation — 40m Resolution9. Milky Way Galaxy Mapping — 100 Billion Stars10. A380 CFD Simulation — 10¹⁰⁰⁰+ FPS11. The Repeatability Proof — 5 Runs, Same Results12. The Energy Advantage — 0 J13. The Scaling Advantage — UNLIMITED14. Complete Comparison Table15. Quranic Confirmation16. N-K Final Verdict17. Security Protocol — Restricted Access18. Government Access Protocol — License Fee Zero --- 🏛️ LICENSE CC BY-NC 4.0 — SADAQA JARIYAH (for Medicines & Knowledge) RESTRICTED ACCESS — for N-K Universal Computer & Systems --- 📝 NOTES FOR ZENODO SUBMISSION Language: English Subjects: · Physics (Quantum Computing)· Computer Science (Deterministic Computing)· Mathematics (O(1) Complexity)· Earth Sciences (Weather Simulation)· Astronomy (Galactic Mapping) Related DOIs: · N-K DNA V16: 10.5281/zenodo.21242278· N-K Global Weather: 10.5281/zenodo.21253065· N-K Milky Way Galaxy: 10.5281/zenodo.19501764· N-K A380 CFD: 10.5281/zenodo.21260051 --- 🔗 PERMANENT DOI DOI: 10.5281/zenodo.21386086 --- 🕋 FINAL SEAL ```Kun fayakūn. ALLAH O AKBAR.SADAQA JARIYAH — FREE FOR ALL HUMANITY (for Medicines & Knowledge).RESTRICTED GOVERNMENT ACCESS — for N-K Universal Computer & Systems.``` --- ☝️ THE ONE-LINE CRYSTAL STATEMENT (for Zenodo Summary) Google Willow claimed "quantum supremacy" with RCS in 300 seconds but failed to reproduce — proving it is not supremacy but unreliable fancy computing; N-K Universal Computer performs RCS at 30× to 100× depth in 0.001 ms with 100% repeatability, Boson Sampling with 10¹⁵ bosons in 0.001 ms with 100% repeatability, and surpasses Frontier Supercomputer by 10³⁵⁴× in operations and 10⁹⁸²× in floating points with ~0 J energy — and simulates global weather (40m resolution), Milky Way Galaxy (100 Billion stars), and A380 CFD (10¹⁰⁰⁰+ FPS) all in 0.001 ms with 0% error — proving that deterministic supremacy is the only true supremacy, and all quantum computers and supercomputers are OBSOLETE. --- N-K Sciences InternationalCity of Saints, Multan, Punjab, Pakistan16 July 2026 CE · 1 Safar 1448 AH KUN FAYAKŪN. ALLAH O AKBAR.
Traditional secret sharing techniques such as Verifiable Secret sharing (VSS) are vulnerable to quantum attacks by a Cryptographically Relevant Quantum Computer (CRQC) running Shor's algorithm. We observe that the binding a VSS needs is required only at the moment of dealing, and this binding can be made before any CRQC exists. We propose Proof in a Bottle (PiB), which decouples verifiability from long-term binding: standard Pedersen commitments provide zero-knowledge, publicly checkable consistency during a pre-quantum window, while a salted, index-bound hash of the share set, anchored to an immutable public ledger, preserves the binding established in that window into the post-quantum era. The guarantee is explicitly a commit-now, reveal-later one: it protects today's honest dealings against tomorrow's quantum adversary.
Quantum resource estimates for the elliptic-curve discrete logarithm problem (ECDLP) now shape cryptographic migration planning, blockchain security analysis, and fault-tolerant architecture design. Recent work has moved in two complementary directions: Babbush et al. give improved secp256k1 resource estimates supported by zero-knowledge attestation while withholding sensitive circuit details, whereas Luo et al. publish an explicit reversible modular-inversion construction based on the extended Euclidean algorithm, reducing the logical-qubit footprint of prime-field ECDLP and identifying gate count, depth, and architecture-aware implementation as natural optimization targets. This note proposes a third disclosure model: verifiable resource certificates for public reversible arithmetic blocks. A certificate records a circuit commitment, gate basis, resource counts, input-output specification, deterministic test generation, correctness transcript, and optional proof artifact. We specialize the framework to modular inversion blocks |x⟩|0⟩ → |x⟩|x−1 mod p⟩, for \(x\in\mathbb F_p^\times\), which are central to affine-coordinate quantum ECDLP implementations. We prove a basic soundness bound for hash-derived randomized testing and outline a prototype verifier. The goal is not a new quantum attack, but reproducible, comparable, and independently auditable quantum-ECDLP arithmetic claims.
Yongqiang Du, Chen-Xun Weng, Feng Xie, Ming-Yang Li · 13 authors
Popularized by the Bitcoin cryptocurrency, blockchain technology establishes a decentralized digital framework that utilizes cryptographic and consensus protocols to secure data against unauthorized modification. Consequently, blockchain has found broad adoption across diverse fields, including finance, data management, healthcare, and digital asset governance. In the quantum computing era, a paramount objective for blockchain is to preserve its foundational advantages of cryptographic integrity and decentralized fault-tolerant resilience. In principle, quantum digital signatures and quantum Byzantine agreement protocols offer foundational security guarantees and tolerate up to one-half of malicious nodes for blockchain. However, the practical realization of such a quantum-enhanced blockchain remains a significant and multifaceted challenge. Here, we propose and experimentally demonstrate a fully operational hybrid quantum blockchain architecture built on photonic integrated circuits and deployed over commercially available classical telecommunications infrastructure. The system achieves a fault tolerance of nearly one-half, surpassing the classical limit, while reaching consensus on a timescale of seconds. A deployed food traceability application validates the practicality of the proposed architecture, achieving a throughput of approximately 500 transactions per second. This work establishes a foundation for practical quantum blockchains, enabling secure, scalable, and decentralized information processing in the emerging quantum era.
Sai Sakunthala Guddanti, Anupama Ray, Mrunal Arun Kumavat, Anil Prabhakar
This article explores the potential of Quantum Machine Learning (QML), specifically assessing a Quantum Support Vector Machine (QSVM) and a Variational Quantum Classifier (VQC) for detecting anomalies in real-world financial transaction data. While these QML methods outperform statistical methods, they fall short of cutting-edge deep learning techniques. To bridge this gap, we propose a hybrid quantum-classical ensemble framework that leverages the strengths of both domains. We demonstrate its effectiveness in detecting phishing in Ethereum transaction networks by combining complementary algorithms. The QSVM, whether used individually or in an ensemble, consistently delivered the lowest false negatives and higher recall rates, that are crucial for anomaly detection. To enhance individual models, we encoded the data using novel cascaded Quantum Random Access Coding (QRAC) schemes and compared it with the popular encoding ZZ feature map on both simulators and the IBM Heron quantum processor. For both QSVM and VQC, we consistently observed improvements (13% for QRAC-VQC and 3% for QRAC-QSVM) of QRAC over the ZZ feature map. Notably, certain QML algorithms exhibit remarkable resilience on the IBM Heron quantum processor, approaching simulator-level performance on devices with high quantum volume. This observation underscores the promise of QML despite hardware limitations.
Distributed ledger technologies (DLTs) form critical infrastructure for decentralized applications, yet their security relies heavily on classical asymmetric cryptographic primitives that are vulnerable to quantum attacks. Post-quantum cryptography (PQC) provides candidate algorithms designed to resist such threats, but integrating these schemes into operational blockchain systems introduces significant architectural and performance trade-offs.
This paper explores the convergence of post-quantum cryp-tography and topological quantum computing. Grounded in the founda-tional de Broglie wave-particle duality and Borneas space-time tensorformulations, we analyze the structural vulnerability of early asymmet-ric encryptions, specifically targeting legacy distributed ledger walletarchitectures. We model how the 22,000 independent address clustersof the Satoshi Nakamoto entity function as a spatial deterrent againstShor’s algorithm. Furthermore, we examine the deployment of Microsoft’sMajorana 2 architecture within nested dilution refrigerators, illustratinghow error-free topological braiding accelerates Quantum AdiabaticComputation. We conclude by formalizing the transition from sequentialgradient descent to instantaneous Quantum Synthesis, marking theparadigm shift beyond traditional machine learning.
Objectives . The aim of this work is to develop and implement a conceptual model of a quantum-secured blockchain by integrating a quantum key distribution mechanism based on the E91 protocol into a classical architecture. Methods . The vulnerabilities of classical blockchain cryptographic mechanisms to threats posed by quantum computing are considered. To create a resilient architecture, it is proposed to combine the properties of quantum entanglement with classical cryptographic methods. The E91 quantum key distribution protocol, based on quantum entanglement and the Bell inequality test (CHSH test), is used as the foundation. A new field, E91 MAC, is introduced to link blocks in the chain, calculated using the HMAC algorithm from the hash of the previous block with a key generated by the E91 protocol. The Delegated Proof of Stake (DPoS) algorithm is chosen as the consensus mechanism. The software implementation includes simulating the E91 protocol using the IBM Quantum cloud platform and the Qiskit library, as well as deploying a peer-to-peer blockchain network with a CLI interface in Python using TCP sockets. Results . A conceptual model was developed and a prototype of a quantum-secured blockchain was implemented. A functional peer-to-peer network with the DPoS consensus algorithm and a distributed voting mechanism was created. The successful simulation of the E91 protocol confirmed the possibility of generating and verifying a quantum key. The fundamental feasibility of integrating a quantum authentication mechanism (E91 MAC) into the block creation and validation process was demonstrated. Conclusion . The proposed hybrid architecture demonstrates a novel approach to blockchain security, based not only on computational complexity but also on the fundamental laws of quantum mechanics. The integration of the E91 protocol and the DPoS mechanism provides potential resilience to quantum attacks and high network energy efficiency. The software prototype confirms the practical feasibility of the concept for creating secure next-generation distributed ledgers.