- Introduction (p. 1)
- Part I. Mathematical Foundations of Complex Spectral Surrogate Modeling (p. 15)
- I.1. Hermitian Geometry of Complex Estimation (p. 15)
- I.2. Regularization and Spectral Models of Quantum Dynamics (p. 89)
- I.3. Identifiability and Numerical Verification (p. 132)
- I.4. Statistical Optimality and Sequential Updating (p. 183)
- I.5. CSSF(QA) for BESS Placement in a Minimal Power Grid (p. 219)
- Part II. Theorems of Complex-Spectral Surrogate Modeling (p. 319)
- II.1. The Aizenberg Theorem on Complex-Phase Correction and Hermitian Batch Estimation (p. 319)
- II.2. The Aizenberg Theorem on Complex Toric Recovery of Quantum Variational Landscapes (p. 338)
- Part III. Exponential Spaces and Complex Spectral Approximation (p. 358)
- III.1. The Exponential as the Structural Law of Continuous Transformations (p. 360)
- III.2. Exponential Mapping, Compact Groups, and Duality (p. 368)
- III.3. Hermitian Geometry as the Intrinsic Geometry of Exponential Systems (p. 375)
- III.4. Exponential Systems, Discretization, and Frame Theory (p. 383)
- III.5. Sampling, Interpolation, and High-Dimensional Exponential Spaces (p. 390)
- III.6. Regularization as Spectral Functional Calculus (p. 398)
- III.7. Positive-Definite Functions, Kernels, and Probabilistic Structure (p. 405)
- III.8. Noncommutative Extension and Retrospective Foundation of the Aizenberg Theorems (p. 412)
- Part III Conclusion (p. 420)
- Part III Bibliography (p. 421)
- Part IV. Physically Informed Quantum-Spectral Placement of BESS (p. 422)
- IV.1. Strategic Decision Object: Placement, Scale, and a Unified Objective Function (p. 422)
- IV.2. Physical Features and the Neural-Spectral Layer: From the AC Field to CSNN-T (p. 526)
- IV.3. Physically Informed QUBO: Singleton Value, Interactions, and Strict Constraints (p. 598)
- IV.4. Continuous QA, Digital Product Formulas, and the Physical Image of MA-QAOA (p. 694)
- IV.5. Toric-Hardware Dictionary, Hardware Residual, and Active QPU Learning (p. 785)
- IV.6. Exact BESS Spectrum, LSF-Weighted Mixer, and Graph-Localized Dictionary (p. 932)
- IV.7. Active Scientific Control of QPU Data, Physically Admissible QUBO Optimization, and Adaptive Reinforcement of CSSF(QA) (p. 1012)
- IV.8. Certifiable CSSF(QA) Superiority, Paired Statistical Evidence, and Multi-Axis OOD Generalizability (p. 1061)
- IV.9. Reproducible Experimental Environment, the case300 Evidence Corpus, and a Unified Mathematical Formulation of CSSF(QA) (p. 1149)
- IV.10. Experimental Verification of QA Response, Physical Superiority of BESS Placement, and Statistical Certification of the CSSF(QA) Effect (p. 1237)
- IV.11. Closed Evidentiary Loop, Quantum-Portfolio Geometry, and Multitask Certification of CSSF(QA) (p. 1341)
- IV.12. Resource Complexity, Fundamental Limits, and the Proven Scientific Contribution of CSSF(QA) (p. 1406)
Quantum Annealing Trigonometrization
via Aizenberg MVN Theory: Applications to BESS Placement
This book is 100% completeLast updated on 2026-10-27
A research monograph connecting quantum annealing, Aizenberg MVN theory and complex spectral surrogate models, with detailed applications to battery energy storage placement in power grids.
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Quantum Annealing Trigonometrization develops a complex-spectral framework for modeling the response of quantum annealers and applying it to battery energy storage system (BESS) placement in power grids.
Starting from Aizenberg multi-valued neuron (MVN) theory, the monograph represents annealing control through accumulated operator angles, complex phases and harmonics. It connects continuous quantum annealing, QAOA-like phase coordinates, Hermitian least-squares estimation and regularized spectral reconstruction.
The book is organized into four parts:
I. Mathematical foundations of complex spectral surrogate modeling, including identifiability, regularization, numerical verification, statistical optimality and sequential updating.
II. Theorems of complex-spectral surrogate modeling, addressing complex-phase correction, Hermitian batch estimation and toric recovery of quantum variational landscapes.
III. Exponential spaces and complex spectral approximation, including group structure, frame theory, sampling, kernels and spectral functional calculus.
IV. Physically informed quantum-spectral placement of BESS, bringing together AC power-grid features, QUBO formulations, hardware residuals, active QPU learning, experimental design and statistical certification within CSSF(QA).
The emphasis is on reconstructing measured response, selecting informative hardware experiments, testing transfer across related problems and rejecting surrogate models that fail independent validation.
Written for researchers and advanced practitioners in quantum optimization, complex-valued neural networks and power systems, this English-language monograph brings the mathematics of spectral approximation into a detailed engineering setting.
Companion code and experiments: CSSF(QA)This book is accompanied by the public Quantum Annealing Trigonometrization Framework repository. It implements CSSF(QA), connecting the monograph's complex-Hermitian spectral models to quantum-annealing control, D-Wave QPU experiments, and physically validated BESS placement on the IEEE 300-bus system.
Readers will find an adapted case300 notebook associated with the monograph, a separate GPU/SQA validation programme, and technical setup and Colab guidance. The repository provides a practical bridge from the book's theory to code and computational experiments. It documents the real-QPU case300 protocol and GPU/SQA framework validation separately.
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Serhii Barskyi
Serhii Barskyi is a data scientist specializing in spectral methods, Fourier-based machine learning, and quantum optimization, with applications to smart grid energy systems planning and BESS placement. He is the author of Quantum Annealing Trigonometrization via Aizenberg MVN Theory: Applications to BESS Placement.
He teaches a structured, year-long programme in quantum optimization and data science and mentors learners on Preply. His teaching covers Aizenberg MVN/MLMVN networks, QAOA, D-Wave quantum annealing, QUBO/BQM, Ocean SDK, Pegasus embedding, and hybrid solvers. He connects least squares, SVD, the Moore-Penrose pseudoinverse, and harmonic analysis with practical Python and AI projects, helping learners build and present DeepTech portfolios. His technical toolkit also includes Qiskit and Django REST.
He has more than nine years of experience in DeepTech startup development and international business incubators. His experience includes Technovation Challenge semifinal appearances in 2017 and 2021, the Social Impact Award final in 2021, and Global Industry Challenge finals in 2025 and 2026.
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