Data & Analytics

Tilted XOR games methodology — variant of XOR nonlocal games where winning condition depends on XOR plus one output bit. Shows quantum value approximation is RE-complete, dramatically increasing expressive power over standard XOR games.

Non-equilibrium thermodynamic framework for quantum reservoir computing - links predictive performance to energetic costs via Holevo capacities and quantum informational dissipation

**arXiv ID:** 2508.06347 **Authors:** Ruiyu Zhang, Ce Zhao, Xin Zhao, Lin Nie, Wai-Fung Lam **Published:** 2025-08-08T14:21:20Z **Abstract:** Learning interpretable latent representations from tabular data remains a challenge in deep generative modeling. We introduce SE-VAE (Structural Equation-Variational Autoencoder), a novel architecture that embeds measurement structure directly into the design of a variational autoencoder. Inspired by structural equation modeling, SE-VAE aligns latent su...

Novel stochastic quantum spiking (SQS) neuron model with multi-qubit quantum circuits for internal quantum memory, enabling event-driven probabilistic spike generation and hardware-friendly local learning without backpropagation.

Statistical interpretation framework unifying algebraic quantum mechanics and quantum probability theory — links observable algebras to measurement statistics for foundations of quantum physics. Use when: analyzing measurement procedures statistically, bridging algebraic and probabilistic formulations of quantum mechanics, studying quantum observables as statistical functionals, or developing measurement-based interpretations of quantum theory.

**arXiv ID:** 2409.00140 **Authors:** Gerardo Altamirano-Gómez, Carlos Gershenson **Published:** 2024-08-29T19:13:20Z **Abstract:** In recent years, several models using Quaternion-Valued Convolutional Neural Networks (QCNNs) for different problems have been proposed. Although the definition of the quaternion convolution layer is the same, there are different adaptations of other atomic components to the quaternion domain, e.g., pooling layers, activation functions, fully connected layers, et...

Stochastic Quantum Neural Networks (SQNNs) adversarial robustness methodology. Decoherence-contraction theorem for depolarising channels, per-gate dropout as curvature-weighted L2 penalty, and noise-as-defence framework for quantum machine learning. Use when: SQNNs, quantum adversarial robustness, quantum dropout, decoherence contraction, Lindblad master equation, neural network security.

SPATE methodology for spiking-phase adaptive temporal encoding in quantum machine learning. Converts real-valued data into leaky integrate-and-fire spike trains and maps spike statistics to quantum rotations with temporal qubits. Use when: quantum ML encoding, spike-driven temporal encoding, quantum feature preparation, temporal qubits, QML pipeline enhancement.

SPATE methodology for quantum machine learning — spiking-phase adaptive temporal encoding. Converts real-valued features into leaky integrate-and-fire spike trains and maps spike statistics to quantum rotations, augmented with temporal qubits via controlled phase operations. Use when: (1) designing QML pipelines for temporal data, (2) encoding time-series/tabular data into quantum feature spaces, (3) comparing spike-based vs angle/amplitude encoding quality, (4) building hybrid quantum neural...

Sparsified Kolmogorov-Arnold Networks (KAN) for interpretable quantum state tomography. Uses KAN not only as a regressor but as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. Validated on 3-qubit GHZ family with all 63 non-identity Pauli expectation values. arXiv:2606.11814

Sparse Mamba Decoder (SMD) for quantum error correction — a defect-centric neural decoder using Mamba state-space model that processes only active detection events (k ≪ d²R) achieving O(k) complexity on surface codes. 95-467x faster than Tesseract near-MLD decoder.

Semiclassical methods connecting quantum statistical mechanics to analytic number theory. Uses trace formula and periodic orbit theory to study integer partitions. Activation: semiclassical, integer partitions, density of states, number theory, periodic orbit, trace formula, Pythagorean triples.

Stable Self-Modulating Quantum Fast-Weight Programmers with bounded memory gates. Quantum sequence modeling using dynamically programmed variational-circuit parameters with bounded old-state modulation for long-sequence stability. Activation: quantum fast weight, QFWP, quantum sequence modeling, quantum memory gates, quantum dynamics forecasting.

Robust quantum steerability classification methodology using key feature extraction and matrix-structure-preserving CNNs. Solves generalization failure of SVMs/MLPs on T-diagonal and AVN states. Two-stage approach: extract steerability-determining key features (invariant under SLOCC/LU), preserve 2D matrix structure of quantum states for CNN input. Validated on Phys. Rev. A 100, 022314 dataset. Use when: building quantum state classifiers, quantum entanglement verification, quantum steerabili...

Quantum cloud platform authentication framework using multi-dimensional quantum fingerprints from raw measurement data. Constructs Mahalanobis-based fingerprints with drift early warning and adversarial detection to verify which physical device executes workloads, preventing hardware substitution attacks. Activation: quantum authentication, cloud verification, hardware fingerprinting, quantum cloud, device authentication, Mahalanobis distance, drift detection, adversarial detection, raw-curve

Ravine analysis framework for quantum cost landscapes — exploiting ravine structures for improved VQA optimization. Use when analyzing VQA convergence, diagnosing optimization failures, or improving quantum circuit parameter optimization.

Ravine analysis framework for quantum cost landscapes — exploiting ravine structures for improved VQA optimization. Use when analyzing VQA convergence, diagnosing optimization failures, or improving quantum circuit parameter optimization.

Randomized Grover search algorithm methodology that directly uses confidence-based sampling rather than amplitude amplification.

Quantum Viterbi decoding methodology for hidden quantum Markov models (HQMMs). Extends classical Viterbi algorithm to quantum sequential decision-making with proven advantage over classical diagonal strategies.

Quantum-inspired evolutionary optimization for non-convex ML landscapes using superposition-inspired probabilistic encoding and simulated tunneling to escape local optima. Use when classical optimizers (ADAM, GA, DE) get stuck in local minima on sparse signal recovery, robust regression, or any non-convex objective. Triggers: non-convex optimization, local optima escape, quantum tunneling optimizer, sparse signal recovery, robust regression, quantum evolutionary algorithm, superposition-inspi...

Quantum algorithms for graph triangle cut sparsification methodology. Uses quantum walks and Grover search to list triangles faster than classical bounds, enabling efficient construction of ε-sparsifiers for large-scale network analysis.

Exact framework for computing heat, energy, and particle transport statistics in quadratic quantum systems coupled to Gaussian reservoirs — combines full counting statistics with non-Markovian master equations. Use when: analyzing quantum transport in mesoscopic systems, computing full counting statistics for particle/heat currents, studying non-Markovian open quantum systems, evaluating transport between quantum reservoirs, or modeling quantum thermodynamic engines.

Qlustering: Unsupervised clustering via steady-state quantum transport in GKSL-governed quantum networks. Data encoded as input states, cluster assignments inferred from terminal output currents. Use when: quantum machine learning, unsupervised quantum clustering, GKSL master equation applications, open quantum network learning, quantum data clustering, or algorithm-hardware co-design for quantum ML.

Quantum algorithms for topological data analysis (TDA) - persistent Betti numbers, simplicial complexes, Vietoris-Rips topology, high-dimensional feature extraction. Use when analyzing quantum approaches to TDA, persistent homology, Betti number estimation, topological quantum computing, or geometry-informed quantum algorithms.