arXiv subjects

Ivan Zelinka

Publications and source records attributed to Ivan Zelinka.

15 recordsLinked to original sources

arXiv2026

Optimization Landscape Geometry in VQE for Frustrated Quantum Spin Models

We benchmark eight classical optimizers for exact-statevector VQE calculations on a controlled hierarchy of frustrated spin models, ranging from a diagonal Ising glass to transverse-field Ising and anisotropic Heisenberg models. The benchmark includes local, stochastic-gradient, evolutionary, covariance-adaptation, and swarm-based optimization methods under matched function-evaluation budgets. To understand their performance beyond final energies, we characterize the underlying Hamiltonian--ansatz landscapes in terms of local minima, gradients, curvature, and ground-state reachability. We use simple variational circuits, from an $R_y$ product-state ansatz for the diagonal model to shallow $R_y$--CNOT hardware-efficient circuits for the noncommuting models, and study how increasing circuit depth changes their expressivity, reachability, and optimization geometry. We find that optimizer performance changes substantially across the model hierarchy and is closely connected to landscape structure, while the variational gap represents a separate source of error. These results show how classical optimization, variational expressivity, and landscape geometry jointly determine VQE performance for frustrated spin models.

quant-ph↗

arXiv2026

Linear Proposal Operators and Stochastic Search Geometry in SOMA and Differential Evolution

Swarm and evolutionary algorithms are usually analyzed as complete procedural systems in which nonlinear selection, replacement, and adaptation obscure simpler structure within candidate generation. This paper introduces an operator--selection factorization that separates objective-independent variation from boundary repair and fitness-dependent selection, and uses it to study the proposal geometry of the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE). The canonical SOMA proposal is shown to be affine in the search space and exactly linear in an augmented migrant--leader state. In leader-relative coordinates, the resulting operator provides a direct interpretation of interpolation, projection, overshooting, and coordinate masking. Under Bernoulli perturbation masks, we derive closed-form expressions for the proposal mean, covariance, expected squared step length, expected squared distance from the leader, active dimensionality, and coordinate coverage. For canonical DE/rand/1/bin, we derive the finite-population moments of differential mutation and characterize the additional covariance and coordinate dependence induced by forced-coordinate binomial crossover. Exact enumeration and Monte Carlo experiments verify the analytical identities and quantify the effects of mask conditioning, boundary repair, and fitness-based selection. The analysis further motivates geometry-controlled and rotation-aware SOMA variants, together with an adaptive population-reducing extension of iSOMA. Experiments on the complete noiseless BBOB benchmark show that these operator-guided variants substantially improve upon canonical SOMA and are competitive with established DE methods in several dimension--budget regimes. The results demonstrate how proposal-level operator analysis can support both the interpretation and design of population-based optimizers.

cs.NE↗

arXiv2026

Quantum Machine Learning for Colorectal Cancer Data: Anastomotic Leak Classification and Risk Factors

This study evaluates colorectal risk factors and compares classical models against Quantum Neural Networks (QNNs) for anastomotic leak prediction. Analyzing clinical data with 14\% leak prevalence, we tested ZZFeatureMap encodings with RealAmplitudes and EfficientSU2 ansatze under simulated noise. $F_β$-optimized quantum configurations yielded significantly higher sensitivity (83.3\%) than classical baselines (66.7\%). This demonstrates that quantum feature spaces better prioritize minority class identification, which is critical for low-prevalence clinical risk prediction. Our work explores various optimizers under noisy conditions, highlighting key trade-offs and future directions for hardware deployment.

cs.LG↗

arXiv2026

A Longitudinal Analysis of the CEC Single-Objective Competitions (2010-2024) and Implications for Variational Quantum Optimization

This paper provides a historical analysis of the IEEE CEC Single Objective Optimization competition results (2010-2024). We analyze how benchmark functions shaped winning algorithms, identifying the 2014 introduction of dense rotation matrices as a key performance filter. This design choice introduced parameter non-separability, reduced effectiveness of coordinate-dependent methods (PSO, GA), and established the dominance of Differential Evolution variants capable of preserving the rotational invariance of their difference vectors, specifically L-SHADE. Post-2020 analysis reveals a shift towards high complexity hybrid optimizers that combine different mechanisms (e.g., Eigenvector Crossover, Societal Sharing, Reinforcement Learning) to maximize ranking stability. We conclude by identifying structural similarities between these modern benchmarks and Variational Quantum Algorithm landscapes, suggesting that evolved CEC solvers possess the specific adaptive capabilities required for quantum control.

quant-ph↗

arXiv2025

From Classical to Hybrid: A Practical Framework for Quantum-Enhanced Learning

This work addresses the challenge of enabling practitioners without quantum expertise to transition from classical to hybrid quantum-classical machine learning workflows. We propose a three-stage framework: starting with a classical self-training model, then introducing a minimal hybrid quantum variant, and finally applying diagnostic feedback via QMetric to refine the hybrid architecture. In experiments on the Iris dataset, the refined hybrid model improved accuracy from 0.31 in the classical approach to 0.87 in the quantum approach. These results suggest that even modest quantum components, when guided by proper diagnostics, can enhance class separation and representation capacity in hybrid learning, offering a practical pathway for classical machine learning practitioners to leverage quantum-enhanced methods.

quant-ph↗

arXiv2025

Reliable Optimization Under Noise in Quantum Variational Algorithms

The optimization of Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise, which distorts the cost landscape, creates false variational minima, and induces statistical bias called winner's curse. We investigate this phenomenon by benchmarking eight classical optimizers spanning gradient-based, gradient-free, and metaheuristic methods on quantum chemistry Hamiltonians H$_2$, H$_4$ chain, LiH (in both full and active spaces) using the truncated Variational Hamiltonian Ansatz. We analyze difficulties of gradient-based methods (e.g., SLSQP, BFGS) in noisy regimes, where they diverge or stagnate. We show that the bias of estimator can be corrected by tracking the \textit{population mean}, rather than the biased best individual when using population based optimizer. Our findings, which are shown to generalize to hardware-efficient circuits and condensed matter models, identify adaptive metaheuristics (specifically CMA-ES and iL-SHADE) as the most effective and resilient strategies. We conclude by presenting a set of practical guidelines for reliable VQE optimization under noise, centering on the co-design of physically motivated ansatz and the use of adaptive optimizers.

quant-ph↗

arXiv2025

Optimization Strategies for Variational Quantum Algorithms in Noisy Landscapes

Variational Quantum Algorithms (VQAs) are a leading approach for near-term quantum computing but face major optimization challenges from noise, barren plateaus, and complex energy landscapes. We benchmarked more than fifty metaheuristic algorithms for the Variational Quantum Eigensolver (VQE) using a three-phase procedure: initial screening on the Ising model, scaling tests up to nine qubits, and convergence on a 192-parameter Hubbard model. Landscape visualizations revealed that smooth convex basins in noiseless settings become distorted and rugged under finite-shot sampling, explaining the failure of gradient-based local methods. Across models, CMA-ES and iL-SHADE consistently achieved the best performance, while Simulated Annealing (Cauchy), Harmony Search, and Symbiotic Organisms Search also showed robustness. In contrast, widely used optimizers such as PSO, GA, and standard DE variants degraded sharply with noise. These results identify a small set of resilient algorithms for noisy VQE and provide guidance for optimization strategies on near-term quantum devices.

quant-ph↗

arXiv2025

Quantum Machine Learning for Predicting Anastomotic Leak: A Clinical Study

Anastomotic leak (AL) is a life-threatening complication following colorectal surgery, and its accurate prediction remains a significant clinical challenge. This study explores the potential of Quantum Neural Networks (QNNs) for AL prediction, presenting a rigorous benchmark against hyperparameter-tuned classical models including logistic regression, multilayer perceptrons, and boosting algorithms. Using a clinical dataset of 200 patients and four key predictors identified through statistical analysis, we evaluated QNNs with ZZFeatureMap encoding and EfficientSU2 and RealAmplitudes ansätze simulated under realistic hardware noise models. Our framework emphasizes robustness, with performance metrics averaged over 10 independent optimization runs using multiple algorithms. The EfficientSU2-BFGS combination achieved the highest mean AUC of $0.7966 \pm 0.0237$, while RealAmplitudes with CMA-ES excelled in Average Precision ($0.5041 \pm 0.1214$), critical for imbalanced medical datasets. We establish a direct link between optimizer convergence and model efficacy, where effective variational parameter optimization translates to improved classification metrics. Interpretability analysis suggests QNNs may capture complex, non-linear feature relationships not evident in classical linear models. This work highlights QNNs' potential as screening tools while underscoring the need for model selection based on specific clinical goals, pending validation on larger datasets.

quant-ph↗

arXiv2025

Quantum Neural Networks for Propensity Score Estimation and Survival Analysis in Observational Biomedical Studies

This study investigates the application of quantum neural networks (QNNs) for propensity score estimation to address selection bias in comparing survival outcomes between laparoscopic and open surgical techniques in a cohort of 1177 colorectal carcinoma patients treated at University Hospital Ostrava (2001-2009). Using a dataset with 77 variables, including patient demographics and tumor characteristics, we developed QNN-based propensity score models focusing on four key covariates (Age, Sex, Stage, BMI). The QNN architecture employed a linear ZFeatureMap for data encoding, a SummedPaulis operator for predictions, and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for robust, gradient-free optimization in noisy quantum environments. Variance regularization was integrated to mitigate quantum measurement noise, with simulations conducted under exact, sampling (1024 shots), and noisy hardware (FakeManhattanV2) conditions. QNNs, particularly with simulated hardware noise, outperformed classical logistic regression and gradient boosted machines in small samples (AUC up to 0.750 for n=100), with noise modeling enhancing predictive stability. Propensity score matching and weighting, optimized via genetic matching and matching weights, achieved covariate balance with standardized mean differences of 0.0849 and 0.0869, respectively. Survival analyses using Kaplan-Meier estimation, Cox proportional hazards, and Aalen additive regression revealed no significant survival differences post-adjustment (p-values 0.287-0.851), indicating confounding bias in unadjusted outcomes. These results highlight QNNs' potential, enhanced by CMA-ES and noise-aware strategies, to improve causal inference in biomedical research, particularly for small-sample, high-dimensional datasets.

quant-ph↗

arXiv2025

Phase transitions in swarm optimization algorithms

physics.comp-ph↗

arXiv2025

Perturbations and Phase Transitions in Swarm Optimization Algorithms

Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that swarm optimization algorithms also exhibit transitions from chaos, analogous to a motion of gas molecules, when particles explore solution space disorderly, to order, when particles follow a leader, similar to molecules propagating along diffusion gradients in liquid solutions of reagents. We analyze these `phase-like' transitions in swarm optimization algorithms using recurrence quantification analysis and Lempel-Ziv complexity estimation. We demonstrate that converging iterations of the optimization algorithms are statistically different from non-converging ones in a view of applied chaos, complexity and predictability estimating indicators. An identification of a key factor responsible for the intensity of their phase transition is the main contribution of this paper. We examined an optimization as a process with three variable factors -- an algorithm, number generator and optimization function. More than 9.000 executions of the optimization algorithm revealed that the nature of an applied algorithm itself is the main source of the phase transitions. Some of the algorithms exhibit larger transition-shifting behavior while others perform rather transition-steady computing. These findings might be important for future extensions of these algorithms.

physics.comp-ph↗

arXiv2023

From Malware Samples to Fractal Images: A New Paradigm for Classification. (Version 2.0, Previous version paper name: Have you ever seen malware?)

To date, a large number of research papers have been written on the classification of malware, its identification, classification into different families and the distinction between malware and goodware. These works have been based on captured malware samples and have attempted to analyse malware and goodware using various techniques, including techniques from the field of artificial intelligence. For example, neural networks have played a significant role in these classification methods. Some of this work also deals with analysing malware using its visualisation. These works usually convert malware samples capturing the structure of malware into image structures, which are then the object of image processing. In this paper, we propose a very unconventional and novel approach to malware visualisation based on dynamic behaviour analysis, with the idea that the images, which are visually very interesting, are then used to classify malware concerning goodware. Our approach opens an extensive topic for future discussion and provides many new directions for research in malware analysis and classification, as discussed in conclusion. The results of the presented experiments are based on a database of 6 589 997 goodware, 827 853 potentially unwanted applications and 4 174 203 malware samples provided by ESET and selected experimental data (images, generating polynomial formulas and software generating images) are available on GitHub for interested readers. Thus, this paper is not a comprehensive compact study that reports the results obtained from comparative experiments but rather attempts to show a new direction in the field of visualisation with possible applications in malware analysis.

cs.CR↗

arXiv2023

Forecasting and stabilizing chaotic regimes in two macroeconomic models via artificial intelligence technologies and control methods

One of the key tasks in the economy is forecasting the economic agents' expectations of the future values of economic variables using mathematical models. The behavior of mathematical models can be irregular, including chaotic, which reduces their predictive power. In this paper, we study the regimes of behavior of two economic models and identify irregular dynamics in them. Using these models as an example, we demonstrate the effectiveness of evolutionary algorithms and the continuous deep Q-learning method in combination with Pyragas control method for deriving a control action that stabilizes unstable periodic trajectories and suppresses chaotic dynamics. We compare qualitative and quantitative characteristics of the model's dynamics before and after applying control and verify the obtained results by numerical simulation. Proposed approach can improve the reliability of forecasting and tuning of the economic mechanism to achieve maximum decision-making efficiency.

math.OC↗

arXiv2022

Computing with Modular Robots

Propagating patterns are used to transfer and process information in chemical and physical prototypes of unconventional computing devices. Logical values are represented by fronts of traveling diffusive, trigger or phase waves. We apply this concept of pattern based computation to develop experimental prototypes of computing circuits implemented in small modular robots. In the experimental prototypes the modular robots Cubelets are concatenated into channels and junction. The structures developed by Cubelets propagate signals in parallel and asynchronously. The approach is illustrated with a working circuit of a one-bit full adder. Complementarily a formalization of these constructions are developed across Sleptsov nets. Finally, a perspective to swarm dynamics is discussed.

cs.RO↗

arXiv2020

On patterns and dynamics of Rule 22 cellular automaton

Rule 22 elementary cellular automaton (ECA) has a 3--cell neighborhood, binary cell states, where a cell takes state `1' if there is exactly one neighbor, including the cell itself, in state `1'. In Boolean terms the cell-state transition is a XOR function of three cell states. In physico--chemical terms the rule might be seen as describing propagation of self-inhibiting quantities/species. Space-time dynamics of Rule 22 demonstrates non-trivial patterns and quasi-chaotic behavior. We characterize the phenomena observed in this rule using mean field theory, attractors, de Bruijn diagrams, subset diagrams, filters, fractals and memory.

nlin.CG↗