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Alexei Kaltchenko

Publications and source records attributed to Alexei Kaltchenko.

10 recordsLinked to original sources
arXiv2026

ChatGPT Solves All Tested Qiskit Homework Assignments

Generative AI creates an assessment challenge in quantum software education: a student can provide a homework notebook to ChatGPT and request a completed submission. This study examined whether introductory Qiskit homework could remain autogradable while requiring students to run, review, and discuss results rather than banning AI. Three packages were tested: seeded basis-state circuits with bit flips and customized measurement mappings; Quantum Fourier Transform followed by inverse-transform recovery; and seeded Deutsch-Jozsa with customized oracle masks. The designs used personalization, simulator execution, JSON submissions, hidden references, circuit metrics, reflections, and optional IBM Quantum execution. For each package, one student-visible instance was tested in 50 separate ChatGPT sessions, yielding 150 sessions overall. Every final artifact was executed and passed its grader. Nine sessions were fully archived; none required operator code changes or correction of quantum logic. Under the study's operational definition, each tested instance had zero observed ChatGPT-resiliency. Seeds changed parameters rather than task structure, expected results remained derivable from visible assignment logic, scaffolding exposed key solution steps, and hidden grading verified output consistency without establishing independent authorship or understanding. Because one instance was repeated for each package, the results do not establish solvability for every seed or possible Qiskit assessment. The tested personalized, execution-oriented take-home designs therefore did not prevent successful completion under a minimally engaged-student workflow. Correct artifacts should be complemented by direct assessment through supervised modification, oral defense, prediction, and transfer tasks.

cs.CY↗
arXiv2025

Entropy Heat-Mapping: Localizing GPT-Based OCR Errors with Sliding-Window Shannon Analysis

Vision-language models such as OpenAI GPT-4o can transcribe mathematical documents directly from images, yet their token-level confidence signals are seldom used to pinpoint local recognition mistakes. We present an entropy-heat-mapping proof-of-concept that turns per-token Shannon entropy into a visual ''uncertainty landscape''. By scanning the entropy sequence with a fixed-length sliding window, we obtain hotspots that are likely to contain OCR errors such as missing symbols, mismatched braces, or garbled prose. Using a small, curated set of scanned research pages rendered at several resolutions, we compare the highlighted hotspots with the actual transcription errors produced by GPT-4o. Our analysis shows that the vast majority of true errors are indeed concentrated inside the high-entropy regions. This study demonstrates--in a minimally engineered setting--that sliding-window entropy can serve as a practical, lightweight aid for post-editing GPT-based OCR. All code and annotation guidelines are released to encourage replication and further research.

cs.CV↗
arXiv2024

Assessing GPT Model Uncertainty in Mathematical OCR Tasks via Entropy Analysis

This paper investigates the uncertainty of Generative Pre-trained Transformer (GPT) models in extracting mathematical equations from images of varying resolutions and converting them into LaTeX code. We employ concepts of entropy and mutual information to examine the recognition process and assess the model's uncertainty in this Optical Character Recognition (OCR) task. By analyzing the conditional entropy of the output token sequences, we provide both theoretical insights and practical measurements of the GPT model's performance given different image qualities. Our experimental results, obtained using a Python implementation available on GitHub, demonstrate a clear relationship between image resolution and GPT model uncertainty. Higher-resolution images lead to lower entropy values, indicating reduced uncertainty and improved accuracy in the recognized LaTeX code. Conversely, lower-resolution images result in increased entropy, reflecting higher uncertainty and a higher likelihood of recognition errors. These findings highlight the practical importance of considering image quality in GPT-based mathematical OCR applications and demonstrate how entropy analysis, grounded in information-theoretic concepts, can effectively quantify model uncertainty in real-world tasks.

cs.IT↗
arXiv2021

Kolmogorov complexity of unitary transformations in quantum computing

We introduce a notion of Kolmogorov complexity of unitary transformation, which can (roughly) be understood as the least possible amount of information required to fully describe and reconstruct a given finite unitary transformation. In the context of quantum computing, it corresponds to the least possible amount of data to define and describe a quantum circuit or quantum computer program. Our Kolmogorov complexity of unitary transformation is built upon Kolmogorov "qubit complexity" of Berthiaume, W. Van Dam and S. Laplante via mapping from unitary transformations to positive operators, which are subsequently "purified". We discuss the optimality of our notion of Kolmogorov complexity in a broad sense and obtain a simple complexity bound.

quant-ph↗
arXiv2021

Classical Complexity of Unitary Transformations

We discuss a classical complexity of finite-dimensional unitary transformations, which can been seen as a computable approximation of classical descriptional complexity of a unitary transformation acting on a set of qubits.

quant-ph↗
arXiv2012

Nearest-neighbor Entropy Estimators with Weak Metrics

A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak metrics, a new nearest-neighbor entropy estimator is constructed and has a parameter with which the estimator is optimized to reduce its bias. It is shown that estimator's variance is upper-bounded by a nearly optimal Cramer-Rao lower bound.

cs.IT↗
arXiv2008

Quantum Data Compression and Relative Entropy Revisited

B. Schumacher and M. Westmoreland have established a quantum analog of a well-known classical information theory result on a role of relative entropy as a measure of non-optimality in (classical) data compression. In this paper, we provide an alternative, simple and constructive proof of this result by constructing quantum compression codes (schemes) from classical data compression codes. Moreover, as the quantum data compression/coding task can be effectively reduced to a (quasi-)classical one, we show that relevant results from classical information theory and data compression become applicable and therefore can be extended to the quantum domain.

quant-ph↗
arXiv2004

Algorithms for Estimating Information Distance with Application to Bioinformatics and Linguistics

After reviewing unnormalized and normalized information distances based on incomputable notions of Kolmogorov complexity, we discuss how Kolmogorov complexity can be approximated by data compression algorithms. We argue that optimal algorithms for data compression with side information can be successfully used to approximate the normalized distance. Next, we discuss an alternative information distance, which is based on relative entropy rate (also known as Kullback-Leibler divergence), and compression-based algorithms for its estimation. Based on available biological and linguistic data, we arrive to unexpected conclusion that in Bioinformatics and Computational Linguistics this alternative distance is more relevant and important than the ones based on Kolmogorov complexity.

cs.CC↗
arXiv2003

Universal Compression of Ergodic Quantum Sources

For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic quantum sources with von Neumann entropy rates less than $r$. We prove that, for any $r>0$, there exists a blind, source-independent block compression scheme which compresses every source from $F(r)$ to $r n$ qubits per input block length $n$ with arbitrarily high fidelity for all large $n$. As our second result,we show that the stationarity and the ergodicity of a quantum source $\{ρ_m \}_{m=1}^{\infty}$ are preserved by any trace-preserving completely positive linear map of the tensor product form ${\cal E}^{\otimes m}$, where a copy of ${\cal E}$ acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.

quant-ph↗