About Me

I am a theoretical physicist and Assistant Professor in the Faculty of Electronics at the Military University of Technology in Warsaw. I work at the intersection of theoretical physics and data science, using the geometric and information-theoretic structures of quantum mechanics to build and analyse methods for machine learning and data analysis.

Teaching is a large part of what I do. Over the years I have lectured across a range of institutions — SGH Warsaw School of Economics, Kozminski University, Cardinal Stefan Wyszyński University and the Military University of Technology — and across an equally wide range of subjects: from programming and real-time data analytics, through statistics, data mining and financial engineering, to quantum machine learning and quantum technology. I also mentor within the quantum-computing community as part of QPoland / Quantum AI Foundation.

Alongside academia, I have spent years as a practitioner. I worked as a Big Data / MLOps engineer in the Credit Risk department of PKO BP, building production Python tooling for data scientists (Kedro, Pandas, Polars, Spark) on GCP with Airflow, MLflow and Seldon, and earlier as a data analyst and data engineer designing real-time processing pipelines with Kafka, Spark and Flink. That engineering background keeps my research grounded in what actually runs on real systems.

Today I also work as a Quantum Machine Learning Engineer at finQbit, where I develop quantum models for derivative pricing. My research more broadly asks when quantum data encodings genuinely outperform classical methods, and when they do not — a question I explore both theoretically and on real hardware, in work such as The Inverse Born Rule Equivalence (2026) and Option Pricing on Noisy Intermediate-Scale Quantum Computers (2026), the latter with Prof. Jacob Cybulski (Deakin University). This sits within a longer-running program I am developing with Cybulski, Quantum Information Field Theory (QIFT).

My path has taken me from particle physics (a PhD on neutrino oscillations) through topological analysis of biomolecules (Scientific Reports, 2018) and graph-theoretic methods for anomaly detection, to quantum machine learning — with geometric and information-theoretic structure as the thread tying it together. Before all of it I trained for a decade as a musician, which is still how I think about structure, pattern 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.

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.

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.

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

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

Quantum Neural Networks. Application for credit risk assesment

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

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

S.Z, R. Pracht
Arxiv (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.Z. J. L. Cybulski, B. Dziewit, T. Kulpa
Arxiv (2026)

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

J. L. Cybulski, J. Zwoniarski, A. Strąg, S.Z.
QUANTICS - International Conference on Quantum Information, Computing, Communication and Simulation (2026)

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

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

Quantum Modelling of Time Series: Expressivity vs. Trainability

J. L. Cybulski, S.Z.
TBA (2025)

Kwantowe algorytmy hybrydowe jako modele uczenia maszynowego

S.Z, J. L. Cybulski, T. Kulpa
Sztuczna inteligencja w przedsiębiorstwach i gospodarce (AI Spring 2024) (2025)

Design Considerations for Denoising Quantum Time-Series Autoencoder

J. L. Cybulski, S.Z.
24th International Conference on Computational Science (ICCS) (2024)

Classification Supported by Community-Aware Node Features

B. Kaminski, P. Pralat, F. Theberge, S.Z.
Complex Networks & Their Applications XII vol. 4 (2024)

Predicting Properties of Nodes via Community-Aware Features

B. Kaminski, P. Pralat, F. Theberge, S.Z.
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.Z.
OSF Preprints (2022)

Selected machine learning methods used for credit scoring

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

Variable selection methods

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

Metody selekcji zmiennych w modelach skoringowych

K. Przanowski, S.Z.
Oficyna Wydawnicza SGH (2020)

Family Symmetries and Multi Higgs Doublet Models

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

Genus for biomolecules

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

Genus trace reveals the topological complexity and domain structure of biomolecules

S.Z., 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.Z.
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.Z.
Physics of Atomic Nuclei vol. 80 no. 4 (2017)

Texture zeros in neutrino mass matrix

B.Dziewit, J.Holeczek, M.Richter, M.Zralek, S.Z.
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.Z.
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.Z.
Acta Physica Polonica B vol. 44 no. 11 (2013)

Majorana neutrino mass matrix with CP symmetry breaking

B.Dziewit, M.Zralek, S.Z.
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.Z.
Physica Status Solidi B vol. 246 no. 5 (2009)

Neutrino Oscillations in the case of general interactions

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

Commentary

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

S.Z.
My Remarks (2026)

Your Data is not a set

S.Z.
My Remarks (2026)

Classes of Maps as the Primary Object

S.Z.
My Remarks (2026)

Monographs

A portrait of Quantum Technologies in Finance

Editors: O. ZapataThe Quantum Finance Boardroom (2026)

Sztuczna inteligencja w przedsiębiorstwach i gospodarce (AI Spring 2024)

Editors: T. Doligalski, D. KaszyńskiOficyna Wydawnicza SGH (2025)

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

Editors: S. ZajacOficyna 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.ZajacOficyna Wydawnicza SGH (2020)

Education

University of Silesia in Katowice

Doctor of Philosophy17.09.2013

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

Master of Science27.06.2007

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

Bechelor of Science27.06.2005

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

Music School in Rybnik, I and II degree

Musician2004

Advisor: F. Prus
Accordeon class.