arXiv subjects

Vladimir V. Gusev

Publications and source records attributed to Vladimir V. Gusev.

At least 19 recordsLinked to original sources

arXiv2026

Scientific applications of quantum computing: challenges and opportunities

The predictive simulation of molecules and materials has had a broad and significant impact. It nevertheless remains constrained by the cost of accurately treating electronic correlation, excited states, and complex energy landscapes. Quantum computing offers a fundamentally different computational paradigm in which quantum states are encoded and manipulated directly rather than approximated on classical hardware. Here we discuss where this approach may provide a genuine scientific advantage in chemistry, materials science, and biochemistry. Promising directions include the high-accuracy treatment of correlated active spaces, improved excited-state simulations, and accelerated exploration of combinatorial structure spaces. The central challenge is therefore not qubit scaling alone, but demonstrably chemically meaningful gains in predictive reliability. We argue that near-term value is most likely to come from disciplined workflow integration rather than wholesale replacement of classical methods. Noisy physical devices, error-mitigated utility experiments, early fault-tolerant devices, and fully fault-tolerant quantum computers offer different scientific prospects, and claims of usefulness must be tied to the specific regime being discussed. Quantum computing will become scientifically valuable when it demonstrably reduces uncertainty in computed energies, rates, spectra, or materials stability after the full costs of state preparation, measurement, error handling, and coupling to classical simulation are included.

quant-ph↗

arXiv2026

Crystal structure prediction using graph neural combinatorial optimization

Crystalline materials are widely used in technological applications, yet their discovery remains a significant challenge. As their properties are driven by structure, crystal structure prediction (CSP) methods play a central role in computational approaches aiming to accelerate this process. Previously, CSP has been approached from a combinatorial optimization perspective, with the core challenge of allocating atoms on a fine grid of predefined discrete positions within a unit cell while minimizing their interaction energy. Exact mathematical optimization methods provide guaranteed solutions, but they become computationally expensive for large-scale instances, where the atomic configuration space grows rapidly, particularly in the absence of additional symmetry constraints. In this work, we introduce a neural combinatorial optimization approach to the atom allocation challenge and, subsequently, CSP, based on graph neural networks (GNNs), which can effectively sample from the distribution of feasible structures in an unsupervised manner. We leverage expander graphs to construct computational graphs over discrete positions that capture both short- and long-range interactions between atoms, and employ the Gumbel-Sinkhorn approach to enforce the desired stoichiometry of the generated structures. We demonstrate that our method outperforms classical heuristic approaches and is competitive with a commercial optimization solver across a range of chemical compositions. This enables the use of ever-expanding GPU infrastructure to tackle the inherent combinatorial challenges of CSP, paving the way for scaling beyond current capabilities.

cs.LG↗

arXiv2025

Language-Based Bayesian Optimization Research Assistant (BORA)

Many important scientific problems involve multivariate optimization coupled with slow and laborious experimental measurements. These complex, high-dimensional searches can be defined by non-convex optimization landscapes that resemble needle-in-a-haystack surfaces, leading to entrapment in local minima. Contextualizing optimizers with human domain knowledge is a powerful approach to guide searches to localized fruitful regions. However, this approach is susceptible to human confirmation bias and it is also challenging for domain experts to keep track of the rapidly expanding scientific literature. Here, we propose the use of Large Language Models (LLMs) for contextualizing Bayesian optimization (BO) via a hybrid optimization framework that intelligently and economically blends stochastic inference with domain knowledge-based insights from the LLM, which is used to suggest new, better-performing areas of the search space for exploration. Our method fosters user engagement by offering real-time commentary on the optimization progress, explaining the reasoning behind the search strategies. We validate the effectiveness of our approach on synthetic benchmarks with up to 15 independent variables and demonstrate the ability of LLMs to reason in four real-world experimental tasks where context-aware suggestions boost optimization performance substantially.

cs.LG↗

arXiv2025

MACS: Multi-Agent Reinforcement Learning for Optimization of Crystal Structures

Geometry optimization of atomic structures is a common and crucial task in computational chemistry and materials design. Following the learning to optimize paradigm, we propose a new multi-agent reinforcement learning method called Multi-Agent Crystal Structure optimization (MACS) to address periodic crystal structure optimization. MACS treats geometry optimization as a partially observable Markov game in which atoms are agents that adjust their positions to collectively discover a stable configuration. We train MACS across various compositions of reported crystalline materials to obtain a policy that successfully optimizes structures from the training compositions as well as structures of larger sizes and unseen compositions, confirming its excellent scalability and zero-shot transferability. We benchmark our approach against a broad range of state-of-the-art optimization methods and demonstrate that MACS optimizes periodic crystal structures significantly faster, with fewer energy calculations, and the lowest failure rate.

cs.LG↗

arXiv2024

Establishing Deep InfoMax as an effective self-supervised learning methodology in materials informatics

The scarcity of property labels remains a key challenge in materials informatics, whereas materials data without property labels are abundant in comparison. By pretraining supervised property prediction models on self-supervised tasks that depend only on the "intrinsic information" available in any Crystallographic Information File (CIF), there is potential to leverage the large amount of crystal data without property labels to improve property prediction results on small datasets. We apply Deep InfoMax as a self-supervised machine learning framework for materials informatics that explicitly maximises the mutual information between a point set (or graph) representation of a crystal and a vector representation suitable for downstream learning. This allows the pretraining of supervised models on large materials datasets without the need for property labels and without requiring the model to reconstruct the crystal from a representation vector. We investigate the benefits of Deep InfoMax pretraining implemented on the Site-Net architecture to improve the performance of downstream property prediction models with small amounts (<10^3) of data, a situation relevant to experimentally measured materials property databases. Using a property label masking methodology, where we perform self-supervised learning on larger supervised datasets and then train supervised models on a small subset of the labels, we isolate Deep InfoMax pretraining from the effects of distributional shift. We demonstrate performance improvements in the contexts of representation learning and transfer learning on the tasks of band gap and formation energy prediction. Having established the effectiveness of Deep InfoMax pretraining in a controlled environment, our findings provide a foundation for extending the approach to address practical challenges in materials informatics.

cs.LG↗

arXiv2024

Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations

Virtual sensing techniques allow for inferring signals at new unmonitored locations by exploiting spatio-temporal measurements coming from physical sensors at different locations. However, as the sensor coverage becomes sparse due to costs or other constraints, physical proximity cannot be used to support interpolation. In this paper, we overcome this challenge by leveraging dependencies between the target variable and a set of correlated variables (covariates) that can frequently be associated with each location of interest. From this viewpoint, covariates provide partial observability, and the problem consists of inferring values for unobserved channels by exploiting observations at other locations to learn how such variables can correlate. We introduce a novel graph-based methodology to exploit such relationships and design a graph deep learning architecture, named GgNet, implementing the framework. The proposed approach relies on propagating information over a nested graph structure that is used to learn dependencies between variables as well as locations. GgNet is extensively evaluated under different virtual sensing scenarios, demonstrating higher reconstruction accuracy compared to the state-of-the-art.

cs.LG↗

arXiv2024

HypBO: Accelerating Black-Box Scientific Experiments Using Experts' Hypotheses

Robotics and automation offer massive accelerations for solving intractable, multivariate scientific problems such as materials discovery, but the available search spaces can be dauntingly large. Bayesian optimization (BO) has emerged as a popular sample-efficient optimization engine, thriving in tasks where no analytic form of the target function/property is known. Here, we exploit expert human knowledge in the form of hypotheses to direct Bayesian searches more quickly to promising regions of chemical space. Previous methods have used underlying distributions derived from existing experimental measurements, which is unfeasible for new, unexplored scientific tasks. Also, such distributions cannot capture intricate hypotheses. Our proposed method, which we call HypBO, uses expert human hypotheses to generate improved seed samples. Unpromising seeds are automatically discounted, while promising seeds are used to augment the surrogate model data, thus achieving better-informed sampling. This process continues in a global versus local search fashion, organized in a bilevel optimization framework. We validate the performance of our method on a range of synthetic functions and demonstrate its practical utility on a real chemical design task where the use of expert hypotheses accelerates the search performance significantly.

cs.LG↗

arXiv2022

Site-Net: Using global self-attention and real-space supercells to capture long-range interactions in crystal structures

Site-Net is a transformer architecture that models the periodic crystal structures of inorganic materials as a labelled point set of atoms and relies entirely on global self-attention and geometric information to guide learning. Site-Net processes standard crystallographic information files to generate a large real-space supercell, and the importance of interactions between all atomic sites is flexibly learned by the model for the prediction task presented. The attention mechanism is probed to reveal Site-Net can learn long-range interactions in crystal structures, and that specific attention heads become specialized to deal with primarily short- or long-range interactions. We perform a preliminary hyperparameter search and train Site-Net using a single graphics processing unit (GPU), and show Site-Net achieves state-of-the-art performance on a standard band gap regression task.

cond-mat.mtrl-sci↗

arXiv2021

Combinatorial Algorithms for Multidimensional Necklaces

A necklace is an equivalence class of words of length $n$ over an alphabet under the cyclic shift (rotation) operation. As a classical object, there have been many algorithmic results for key operations on necklaces, including counting, generating, ranking, and unranking. This paper generalises the concept of necklaces to the multidimensional setting. We define multidimensional necklaces as an equivalence classes over multidimensional words under the multidimensional cyclic shift operation. Alongside this definition, we generalise several problems from the one dimensional setting to the multidimensional setting for multidimensional necklaces with size $(n_1,n_2,...,n_d)$ over an alphabet of size $q$ including: providing closed form equations for counting the number of necklaces; an $O(n_1 \cdot n_2 \cdot ... \cdot n_d)$ time algorithm for transforming some necklace $w$ to the next necklace in the ordering; an $O((n_1 \cdot n_2 \cdot ... \cdot n_d)^5)$ time algorithm to rank necklaces (determine the number of necklaces smaller than $w$ in the set of necklaces); an $O((n_1\cdot n_2 \cdot ... \cdot n_d)^{6(d + 1)} \cdot \log^d(q))$ time algorithm to unrank multidimensional necklace (determine the $i^{th}$ necklace in the set of necklaces). Our results on counting, ranking, and unranking are further extended to the fixed content setting, where every necklace has the same Parikh vector, in other words every necklace shares the same number of occurrences of each symbol. Finally, we study the $k$-centre problem for necklaces both in the single and multidimensional settings. We provide strong approximation algorithms for solving this problem in both the one dimensional and multidimensional settings.

math.CO↗

arXiv2021

Ranking Bracelets in Polynomial Time

The main result of the paper is the first polynomial-time algorithm for ranking bracelets. The time-complexity of the algorithm is O(k^2 n^4), where k is the size of the alphabet and n is the length of the considered bracelets. The key part of the algorithm is to compute the rank of any word with respect to the set of bracelets by finding three other ranks: the rank over all necklaces, the rank over palindromic necklaces, and the rank over enclosing apalindromic necklaces. The last two concepts are introduced in this paper. These ranks are key components to our algorithm in order to decompose the problem into parts. Additionally, this ranking procedure is used to build a polynomial-time unranking algorithm.

math.CO↗

arXiv2020

The K-Centre Problem for Necklaces

In graph theory, the objective of the k-centre problem is to find a set of $k$ vertices for which the largest distance of any vertex to its closest vertex in the $k$-set is minimised. In this paper, we introduce the $k$-centre problem for sets of necklaces, i.e. the equivalence classes of words under the cyclic shift. This can be seen as the k-centre problem on the complete weighted graph where every necklace is represented by a vertex, and each edge has a weight given by the overlap distance between any pair of necklaces. Similar to the graph case, the goal is to choose $k$ necklaces such that the distance from any word in the language and its nearest centre is minimised. However, in a case of k-centre problem for languages the size of associated graph maybe exponential in relation to the description of the language, i.e., the length of the words l and the size of the alphabet q. We derive several approximation algorithms for the $k$-centre problem on necklaces, with logarithmic approximation factor in the context of l and k, and within a constant factor for a more restricted case.

cs.DS↗

arXiv2017

Sets of Stochastic Matrices with Converging Products: Bounds and Complexity

An SIA matrix is a stochastic matrix whose sequence of powers converges to a rank-one matrix. This convergence is desirable in various applications making use of stochastic matrices, such as consensus, distributed optimization and Markov chains. We study the shortest SIA products of sets of matrices. We observe that the shortest SIA product of a set of matrices is usually very short and we provide a first upper bound on the length of the shortest SIA product (if one exists) of any set of stochastic matrices. We also provide an algorithm that decides the existence of an SIA product. When particularized to automata, the problem becomes that of finding periodic synchronizing words, and we develop the consequences of our results in relation with the celebrated Cerny conjecture in automata theory. We also investigate links with the related notions of positive-column, Sarymsakov, and scrambling matrices.

cs.DM↗

arXiv2016

Primitive sets of nonnegative matrices and synchronizing automata

A set of nonnegative matrices $\mathcal{M}=\{M_1, M_2, \ldots, M_k\}$ is called primitive if there exist indices $i_1, i_2, \ldots, i_m$ such that $M_{i_1} M_{i_2} \ldots M_{i_m}$ is positive (i.e. has all its entries $>0$). The length of the shortest such product is called the exponent of $\mathcal{M}$. The concept of primitive sets of matrices comes up in a number of problems within control theory, non-homogeneous Markov chains, automata theory etc. Recently, connections between synchronizing automata and primitive sets of matrices were established. In the present paper, we significantly strengthen these links by providing equivalence results, both in terms of combinatorial characterization, and computational aspects. We study the maximal exponent among all primitive sets of $n \times n$ matrices, which we denote by $\exp(n)$. We prove that $\lim_{n\rightarrow\infty} \tfrac{\log \exp(n)}{n} = \tfrac{\log 3}{3}$, and moreover, we establish that this bound leads to a resolution of the Černý problem for carefully synchronizing automata. We also study the set of matrices with no zero rows and columns, denoted by $\mathcal{NZ}$, due to its intriguing connections to the Černý conjecture and the recent generalization of Perron-Frobenius theory for this class. We characterize computational complexity of different problems related to the exponent of $\mathcal{NZ}$ matrix sets, and present a quadratic bound on the exponents of sets belonging to a special subclass. Namely, we show that the exponent of a set of matrices having total support is bounded by $2n^2 -5n +5$.

cs.FL↗

arXiv2015

Synchronizing automata and principal eigenvectors of the underlying digraphs

A coloring of a digraph with a fixed out-degree k is a distribution of k labels over the edges resulting in a deterministic finite automaton. An automaton is called synchronizing if there exists a word which sends all states of the automaton to a single state. In the present paper we study connections between spectral and synchronizing properties of digraphs. We show that if a coloring of a digraph is not synchronizing, then the stationary distribution of an associated Markov chain has a partition of coordinates into blocks of equal sum. Moreover, if there exists such a partition, then there exists a non-synchronizing automaton with such stationary distribution. We extend these results to bound the number of non-synchronizing colorings for digraphs with particular eigenvectors. We also demonstrate that the length of the shortest synchronizing word of any coloring is at most $w^2 - 3w + 3$, where $w$ is the sum of the coordinates of the integer principal eigenvector of the digraph.

cs.FL↗

arXiv2015

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.

cs.FL↗

arXiv2014

Synchronizing automata with random inputs

We study the problem of synchronization of automata with random inputs. We present a series of automata such that the expected number of steps until synchronization is exponential in the number of states. At the same time, we show that the expected number of letters to synchronize any pair of the famous Cerny automata is at most cubic in the number of states.

cs.FL↗

arXiv2014

Reset thresholds of automata with two cycle lengths

We present several series of synchronizing automata with multiple parameters, generalizing previously known results. Let p and q be two arbitrary co-prime positive integers, q > p. We describe reset thresholds of the colorings of primitive digraphs with exactly one cycle of length p and one cycle of length q. Also, we study reset thresholds of the colorings of primitive digraphs with exactly one cycle of length q and two cycles of length p.

cs.FL↗

arXiv2013

Finitely generated ideal languages and synchronizing automata

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.

cs.FL↗