About Me

I'm a theoretical physicist and Assistant Professor at the Faculty of Electronics, Military University of Technology in Warsaw. My work sits between physics and data science — using the structure of quantum mechanics to build and analyse methods for machine learning.

I've taught at several institutions over the years — Kozminski University, Cardinal Stefan Wyszyński University, and WAT — across subjects from programming and real-time analytics to quantum machine learning. I also mentor within the quantum-computing community through QPoland / Quantum AI Foundation.

Before academia I spent years in industry: as a Big Data / MLOps engineer in Credit Risk at PKO BP, and earlier as a data engineer building real-time pipelines with Kafka and Spark. That's part of why I care whether quantum methods actually run, not just whether they work on paper.

Today I'm a Quantum Machine Learning Engineer at finQbit, building quantum models for derivative pricing, and developing Quantum Information Field Theory (QIFT) with Jacob Cybulski (Deakin University) — a framework for when quantum data encodings genuinely beat classical ones, and when they do not. Recent work: The Inverse Born Rule Equivalence (2026) and Option Pricing on NISQ Computers (2026).

My path ran from particle physics (a PhD on neutrino oscillations) through topological analysis of biomolecules (Scientific Reports, 2018) to quantum machine learning. Before any of that, I trained as a musician for a decade — still how I think about structure and improvisation.

Research

Current Research · Quantum Machine Learning

Quantum Information
Field Theory (QIFT)

QIFT is a theoretical program I am developing with Jacob Cybulski, aimed at characterising when quantum data encodings carry information inaccessible to classical models — and when they do not. It grows out of the concrete results below, which stand on their own and set the stage for the broader framework.

The Inverse Born Rule Equivalence

Proves that real-valued amplitude encodings composed with data-independent circuits yield hypothesis classes equivalent to classical inner-product kernels — a precise boundary on where quantum advantage cannot arise.

arXiv:2602.21350 (Theory)

Option Pricing on NISQ Computers (finQbit)

A QNN approach to pricing financial derivatives, benchmarked on real hardware — IBM Fez, IQM Garnet, IonQ Forte, and Rigetti Ankaa-3.

arXiv:2604.19832 (Option Pricing)

Research
Trajectory

2007–2013

Particle Physics & Quantum Field Theory

PhD on neutrino oscillations and non-standard interactions. Work on family symmetries and the mathematical structure of quantum fields.

2014–2019

Topological Data Analysis & Biomolecular Geometry

Developed the genus invariant for biomolecules. Published in Scientific Reports (2018).

2020–2025

Graph Data Science & Community-Aware Features

Focus on large networks and community detection. Papers in Social Network Analysis and Mining (2024).

2025 →

Quantum Machine Learning & QIFT

Bridging theory and industry. Active development of QIFT and deployment of industrial-grade QML at finQbit.

Current
Projects

Independent Research Group · 2024 →

Action in
Quantum Time

A research group with Jacob Cybulski, Natalia Kopec and Thanh Nguyen, applying quantum machine learning to time-series analysis and anomaly detection. Our aim is to detect early warning signs of high-impact events hidden in noisy temporal data — with applications in medical diagnosis, machine condition monitoring and environmental change.

Expressivity vs. Trainability

Rigorous metrics for parametric quantum circuit design — profiling expressivity (frame potentials, KL divergence to the Haar ensemble, effective dimension) against trainability (gradient-variance scaling, Fisher information, Krylov metrics) — to move ansatz design from heuristics toward predictable engineering.

Preprint (Research Square)

Denoising Quantum Autoencoders

Design of quantum autoencoders for denoising and reconstructing time series. Published as Design Considerations for Denoising Quantum Time-Series Autoencoder (ICCS 2024, LNCS vol. 14837) and extended in ongoing joint work on autoencoder architectures for signal and time-series denoising.

Quantum Reservoir Computing

New approaches to implementing quantum reservoir computing models for temporal data, with a publication in preparation. This thread also formed the basis of a Master's thesis I supervised.

Key
Collaborators

Jacob L. Cybulski

Deakin University, Australia

QIFT · QML · Time Series

Rafał Pracht

finQbit

Quantum Finance · QNN · NISQ

Bogumił Kamiński

SGH Warsaw School of Economics

Graph Theory · Decision Analysis

Paweł Prałat

Toronto Metropolitan University

Complex Networks

François Théberge

Tutte Institute

Graph Algorithms

Bartosz Dziewit

University of Silesia

QFT · Family Symmetries

Publications

Encoding Geometry on the Geometric-Quantization Ladder: a placement, a dictionary to canonical quantum gravity, and its failures

Sebastian Zając
•ResearchGate preprint (2026)

Kwantowe sieci neuronowe jako modele do wykrywania fraudow numer badania KAE/S25:1.25

Sebastian Zając
•SGH (2026)

Quantum Modelling of Time Series: Expressivity vs. Trainability

J. L. Cybulski, S. Zając
•Communications in Computer and Information Science (2026)

The Hermitian inner product selects the time axis, the Born rule measures it

Sebastian Zając
•Arxiv preprint (2026)

Quantum Neural Networks. Application for credit risk assesment

S. Zając, K. Kuba
•Quantum Technologies in Finance book (2026)

Option Pricing on Noisy Intermediate-Scale Quantum Computers: A Quantum Neural Network Approach

S. Zając, R. Pracht
•Arxiv preprint (2026)

The Inverse Born Rule Equivalence. On the Informational Limits of Real-Valued Amplitude Encodings and the Measurement of Quantum Advantage in Data Embeddings

S. Zając . J. L. Cybulski, B. Dziewit, T. Kulpa
•Arxiv preprint (2026)

Co-Evolutionary Asymmetry vs. Modular Design: Optimization Trade-Offs in Quantum Denoising Autoencoders.

J. L. Cybulski, J. Zwoniarski, A. Strąg, S. Zając
•Communications in Computer and Information Science (2026)

RSCUcaller: R Package for analyzing differences in relative synonymous codon usage

M.Mazdziarz, S. Zając., Ł. Paukszto, J. Sawicki
•BMC Bioinformatics vol. 26 no. 141 (2025)

Predicting Properties of Nodes via Community-Aware Features

B. Kaminski, P. Pralat, F. Theberge, S. Zając
•Social Network Analysis and Mining vol. 14 (2024)

Incorporating Gravity into the Path Integral of Quantum Mechanics Using the Thermodynamics of Spacetime

G. Biehle, C. Ellgen, B. Sabra, S. Zając
•OSF Preprints (2022)

Selected machine learning methods used for credit scoring

M. Wrzosek, D. Kaszynski, K. Przanowski, S.Zając
•Oficyna Wydawnicza SGH (2020)

Variable selection methods

K. Przanowski, S. Zając, D. Kaszynski, L. Opinski
•Oficyna Wydawnicza SGH (2020)

Metody selekcji zmiennych w modelach skoringowych

K. Przanowski, S. Zając
•Oficyna Wydawnicza SGH (2020)

Family Symmetries and Multi Higgs Doublet Models

B. Dziewit, J. Holeczek, S. Zając, M. Zralek
•Symmetry vol. 12(1) no. 156 (2020)

Genus for biomolecules

P. Rubach, S. Zając , B. Jastrzebski, J. I. Sulkowska, P. Sulkowski
•Nucleic Acids Research (2019)

Genus trace reveals the topological complexity and domain structure of biomolecules

S. Zając, C. Geary , E. A. Andersen, P. Dabrowski-Tumanski, J. Sulkowska, P. Sulkowski
•Nature Scientific Reports vol. 8 (2018)

Lepton Masses and Mixing in Two-Higgs-Doublet Model

P. Chaber, B. Dziewit, J. Holeczek, M. Richter, M. Zralek, S. Zając
•Physical Review D vol. 98 (2018)

The discrete family symmetries as the possible solution to the flavour problem

B. Dziewit, J. Holeczek, M. Richter, M. Zralek, S. Zając
•Physics of Atomic Nuclei vol. 80 no. 4 (2017)

Texture zeros in neutrino mass matrix

B. Dziewit, J. Holeczek, M. Richter, M. Zralek, S. Zając
•Physics of Atomic Nuclei vol. 80 no. 2 (2017)

The Flavour Problem and the Family Symmetry Beyond the Standard Model

B. Dziewit, J. Holeczek, M. Richter, M. Zralek, S.Zając
•Acta Physica Polonica B vol. 46 no. 11 (2015)

Attempts at Explaining Neutrino Masses and Mixings Using Finite Horizontal Symmetry Groups

B. Dziewit, M. Zralek, S. Zając
•Acta Physica Polonica B vol. 44 no. 11 (2013)

Majorana neutrino mass matrix with CP symmetry breaking

B. Dziewit, M. Zralek, S. Zając
•Acta Physica Polonica B vol. 42 no. 11 (2011)

The method of the likelihood and the Fisher information in the construction of physical models.

E. W. Piotrowski, J. Sladkowski, J. Syska, S.Zając
•Physica Status Solidi B vol. 246 no. 5 (2009)

Neutrino Oscillations in the case of general interactions

J. Syska, M. Zralek, S. Zając
•Acta Physica Polonica B vol. 38 no. 11 (2007)

Commentary

The friendship paradox isn't a paradox—it's a quantum phenomenon.

Sebastian Zając
•My Remarks (2026)

Your Data is not a set

Sebastian Zając
•My Remarks (2026)

Classes of Maps as the Primary Object

Sebastian Zając
•My Remarks (2026)

Monographs

A portrait of Quantum Technologies in Finance

Editors: O. Zapata•The Quantum Finance Boardroom (2026)

Sztuczna inteligencja w przedsiębiorstwach i gospodarce (AI Spring 2024)

Editors: T. Doligalski, D. Kaszyński•Oficyna Wydawnicza SGH (2025)

Modelowanie dla biznesu. Analityka w czasie rzeczywistym - narzędzia informatyczne i biznesowe

Editors: S. Zajac•Oficyna Wydawnicza SGH (2022)

The Credit scoring in the context of interpretable machine learning. Theory and Practice.

Editors: D. Kaszyński, B. Kamiński, T. Szapiro.•Oficyna Wydawnicza SGH (2020)

Modelowanie dla biznesu. Metody machine learning, modele portfela Consumer Finance, modele rekurencyjne analizy przeżycia, modele skoringowe

Editors: K. Przanowski, S. Zając•Oficyna Wydawnicza SGH (2020)

Education

University of Silesia in Katowice

Doctor of Philosophy•17.09.2013

Advisor: prof. dr hab Marek Zrałek
Accelerator neutrino oscillations and their non-standard interactions (PL) View

Master of Science•27.06.2007

Advisor: dr hab. Jerzy Król
Some geometrical and topological methods in classical and quantum field theory (PL). View

Bechelor of Science•27.06.2005

Advisor: dr hab. Jacek Syska
Time Series analysis with ARMA and ARIMA processes. Application in SAS. (PL) View

Karol and Antoni Szafranek Music School in Rybnik, I and II degree

Musician•2004

Advisor: F. Prus
Accordeon class.

About Me

Research

Quantum InformationField Theory (QIFT)

The Inverse Born Rule Equivalence

Option Pricing on NISQ Computers (finQbit)

ResearchTrajectory

CurrentProjects

Action inQuantum Time

Expressivity vs. Trainability

Denoising Quantum Autoencoders

Quantum Reservoir Computing

KeyCollaborators

Publications

Encoding Geometry on the Geometric-Quantization Ladder: a placement, a dictionary to canonical quantum gravity, and its failures

Kwantowe sieci neuronowe jako modele do wykrywania fraudow numer badania KAE/S25:1.25

Quantum Modelling of Time Series: Expressivity vs. Trainability

The Hermitian inner product selects the time axis, the Born rule measures it

Quantum Neural Networks. Application for credit risk assesment

Option Pricing on Noisy Intermediate-Scale Quantum Computers: A Quantum Neural Network Approach

The Inverse Born Rule Equivalence. On the Informational Limits of Real-Valued Amplitude Encodings and the Measurement of Quantum Advantage in Data Embeddings

Co-Evolutionary Asymmetry vs. Modular Design: Optimization Trade-Offs in Quantum Denoising Autoencoders.

RSCUcaller: R Package for analyzing differences in relative synonymous codon usage

Kwantowe algorytmy hybrydowe jako modele uczenia maszynowego

Design Considerations for Denoising Quantum Time-Series Autoencoder

Classification Supported by Community-Aware Node Features

Predicting Properties of Nodes via Community-Aware Features

Incorporating Gravity into the Path Integral of Quantum Mechanics Using the Thermodynamics of Spacetime

Selected machine learning methods used for credit scoring

Variable selection methods

Metody selekcji zmiennych w modelach skoringowych

Family Symmetries and Multi Higgs Doublet Models

Genus for biomolecules

Genus trace reveals the topological complexity and domain structure of biomolecules

Lepton Masses and Mixing in Two-Higgs-Doublet Model

The discrete family symmetries as the possible solution to the flavour problem

Texture zeros in neutrino mass matrix

The Flavour Problem and the Family Symmetry Beyond the Standard Model

Attempts at Explaining Neutrino Masses and Mixings Using Finite Horizontal Symmetry Groups

Majorana neutrino mass matrix with CP symmetry breaking

The method of the likelihood and the Fisher information in the construction of physical models.

Neutrino Oscillations in the case of general interactions

Commentary

The friendship paradox isn't a paradox—it's a quantum phenomenon.

Your Data is not a set

Classes of Maps as the Primary Object

Monographs

A portrait of Quantum Technologies in Finance

Sztuczna inteligencja w przedsiębiorstwach i gospodarce (AI Spring 2024)

Modelowanie dla biznesu. Analityka w czasie rzeczywistym - narzędzia informatyczne i biznesowe

The Credit scoring in the context of interpretable machine learning. Theory and Practice.

Modelowanie dla biznesu. Metody machine learning, modele portfela Consumer Finance, modele rekurencyjne analizy przeżycia, modele skoringowe

Education

University of Silesia in Katowice

Karol and Antoni Szafranek Music School in Rybnik, I and II degree

Quantum Information
Field Theory (QIFT)

Research
Trajectory

Current
Projects

Action in
Quantum Time

Key
Collaborators