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