arXiv subjects

Oleksandr Kyriienko

Publications and source records attributed to Oleksandr Kyriienko.

At least 19 recordsLinked to original sources

arXiv2026

A QSVT-Based Quantum Jacobi Algorithm for Linear Systems with Application to the Poisson Equation

Many computational fluid dynamics (CFD) algorithms solve partial differential equations by discretization, resulting in large and sparse systems of linear equations. While iterative methods are widely used to solve these systems classically, most existing quantum linear system solvers target the solution through matrix inversion rather than approximating it using an iterative procedure. In this work, we develop a quantum implementation of the Jacobi method based on quantum singular value transformation (QSVT). By reformulating the Jacobi iteration as a polynomial transformation of a block-encoded operator, the algorithm requires only a constant ancilla overhead with respect to the number of iterations while maintaining a circuit depth that scales linearly with the iteration number. We demonstrate the algorithm for one- and two-dimensional Poisson problems, including the pressure Poisson equation arising in Chorin's projection method for the lid-driven cavity flow. The proposed algorithm provides a promising building block for future quantum implementations of multigrid methods and preconditioning techniques, bringing quantum algorithms closer to established CFD solution strategies.

quant-ph↗

arXiv2026

Adaptive Relational Learning on Multi-instance Quantum Data with Photonic Processors

Loading multiple quantum states in parallel into a quantum machine learning (QML) model can unlock learning tasks where key information resides in the \emph{relations} between states rather than in individual states. We introduce an adaptive relational learning framework for such multi-instance quantum data that accesses pairwise and higher-order relations. Our model combines global measurements via SWAP or CYCLE tests for evaluating an $n$-state Bargmann invariant with shallow trainable transformations applied locally to each input state. We demonstrate the approach for continuous-variable (CV) photonic systems, which naturally provide access to quantum data and necessary computing operations. We solve tasks involving hidden relationship detection, geometric phase classification, and sensing in the presence of an unknown shared nuisance interaction. We benchmark the adaptive model against a non-adaptive ``measure-first'' approach based on continuous-variable classical shadows, and show that the cost of shadow estimation grows rapidly with $n$, while our model avoids this dependence. Already for $n=2$, we achieve perfect test accuracy $A=1.0$ with $500$ inference shots, improving average test accuracy over the shadow-based method by $ΔA=0.15$ while using $100$ times fewer shots per data point. Our work opens routes to sensing and quantum-data applications where adaptive photonic QML can access relational features that are costly to recover with non-adaptive, measure-first models.

quant-ph↗

arXiv2026

Learning structural balance of graphs from quantum spectral features

We develop a quantum approach to spectral feature extraction from the density of states (DOS) of a problem-dependent Hamiltonian, and apply it to machine learning on signed graphs. We propose to embed a signed graph as an Ising model instance with positive and negative interactions, and use the standardized moments of the Ising DOS as features for learning. We show that these moments count signed closed walks, are switching-invariant, and are size-free by construction. As a benchmark, we target learning the frustration index, an NP-hard measure of structural balance that can be labeled exactly at moderate size. At zero field, the models can be sampled classically, allowing the quantum extraction procedure to be certified against exact ground truth. We propose DOS-QPE, a phase estimation on a purified maximally mixed probe, which samples the spectral density with orders of magnitude fewer shots than Hadamard test-based trace sampling and feeds the resulting features directly into classically trained models. On $1.4\times10^5$ labeled graphs the exact DOS determines the frustration index, and five moments recover it with a mean error of 0.4, well below one sign flip. Beyond zero field, the underlying trace-estimation problem is DQC1-complete, providing access to spectral features for which no efficient classical sampling method is known. Our work opens routes towards quantum applications in social network balance analysis, spin-glass studies, correlation clustering, and protein-interaction networks.

quant-ph↗

arXiv2026

Charge Tunable Optical Nonlinearity of Moiré Exciton-Polaritons

Transition metal dichalcogenides represent a versatile platform to study strong light-matter interactions based on excitons and electrons in ordered lattices. Twist-engineering of moiré structures further enables the manipulation of the polaritonic nonlinearities via engineering the exciton landscape on the nanoscale. In this work, we demonstrate in-situ control of the optical saturation-based nonlinearity of moiré exciton-polaritons by phase space restriction via charge doping. Strong exciton-photon coupling is established in a gate-controllable MoTe$_2$-MoSe$_2$ heterobilayer, embedded in a spectrally-tunable open cavity. A small gate voltage can effectively lower the necessary polariton density by one order of magnitude to achieve a similar nonlinear saturation effect as in the charge-neutral case. Our microscopic description successfully explains the observed phenomena in the framework of Pauli blocking for the moiré superlattices with charge preoccupation.

cond-mat.mes-hall↗

arXiv2026

All-optical nonlinear phase modulation in open semiconductor microcavities

We report a significant advancement in ultra low power light-by-light phase modulation using open semiconductor microcavities in the strong light-matter coupling regime. We achieve cross-phase modulation of up to 247$\pm$17 mrad per particle between laser beams attenuated to single-photon average intensities. This breakthrough extends the potential for quantum information processing and nonlinear quantum optics in strongly coupled light-matter systems, setting a new benchmark in the field without relying on atom-like emitters. Our findings suggest promising new avenues for scalable quantum optical technologies.

physics.optics↗

arXiv2026

Quantum Fourier Generative Models Trainable at Large Scale

We propose an algorithmic framework for building and training quantum generative models corresponding to multivariate probability distributions. Our model uses parallel Fourier feature maps for embedding continuous-valued variables combined with a forrelation-type quantum circuit for tuning Fourier coefficients of the quantum model. Crucially, we develop a distinct training strategy where training is enabled at large scale by log-likelihood loss with unbiased Monte Carlo estimator based on Parseval's identity. Unlike prior work that relied on maximal mean discrepancy (MMD) loss, our approach goes beyond matching just low frequency moments, while enabling efficient classical training. Once the model is trained, we use inverse quantum Fourier transforms to map it into a separate sampling circuit in the computational basis. We demonstrate the efficiency of the suggested framework by validating loss estimation at the scale of over 1000 qubits on a single GPU. We show that univariate and bivariate models with highly non-trivial structure can be trained to low total variation distance, while fine-tuned IQP models with MMD loss show poor performance. Comparing to classical baselines represented by normalizing flow and diffusion models, we show that our approach avoids oversmoothing and preserves multi-modal structure of the target. Finally, we have deployed the trained models on superconducting quantum devices, successfully sampling distributions with per-sample execution times of approximately $300\,μ\mathrm{s}$. Our work shows that quantum generative models with the train-on-classical deploy-on-quantum approach can provide both high-quality structure at increased scale and fast sampling access needed for inference.

quant-ph↗

arXiv2026

Generative modelling powered by room-temperature polariton condensates

Generative modelling requires efficient stochastic nonlinear transformations and physical platforms that can naturally realise them. We experimentally demonstrate that nonlinear optical systems operating in the strong light-matter coupling regime can serve as physical transformation layers for conditional generative modelling. Specifically, we develop a workflow in which room-temperature exciton-polariton condensates formed in organic dye microcavities act as a physical stochastic transform within a generative adversarial network and enable conditional digit-to-image translation. By using the nonlinear many-body dynamics and intrinsic stochasticity of polariton condensates, the workflow outperforms baseline approaches based on digitally injected perturbations. We find that polariton-enabled sampling via generative adversarial network (Polariton GAN) yields improved inception score, digit preservation accuracy and structural similarity compared with both digital sampling and laser-based systems. We further show that spatially correlated output variations can naturally regularise adversarial training and enhance output diversity. Our results establish polariton condensation as a new computational resource for generative modelling, opening a pathway towards physics-enhanced machine learning systems.

cond-mat.dis-nn↗

arXiv2026

Continuous-wave all-optical single-photon transistor based on a Rydberg-atom ensemble

Continuous-wave (cw) architectures provide a promising route to interface disparate quantum systems by relaxing the need for precise synchronization. While essential cw components, including microwave single-photon transistors and microwave-optical converters, have been explored, an all-optical cw single-photon transistor has remained a missing piece. We propose a high-efficiency, high-gain implementation using Rydberg atoms, in which a control photon disrupts the transmission of a continuous probe beam via the van der Waals interaction. This device completes the set of components required for cw processing of quantum signals and paves the way for all-optical processing at the quantum level.

quant-ph↗

arXiv2026

Continuous-wave quantum light control via engineered Rydberg-induced dephasing

We analyze several implementations of all-optical single-photon transistors (SPTs) operating in the continuous-wave (cw) regime, as presented in the companion paper [Phys. Rev. A 113, L011701 (2026)]. The devices rely on ensembles of Rydberg atoms interacting via van der Waals interactions. Under electromagnetically induced transparency (EIT), a weak probe field is fully transmitted through the atomic ensemble in the absence of control photons. Exciting a collective Rydberg state with a single control photon breaks the EIT condition, thereby strongly suppressing the probe transmission. We show how collective Rydberg interactions in an atomic ensemble, confined either in an optical cavity or in free space, give rise to two distinct probe-induced dephasing mechanisms. These processes localize the control excitations, extend their lifetimes, and increase the device efficiency. We characterize the SPTs in terms of control-photon absorption probability and probe gain, supported by numerical simulations of realistic one- and three-dimensional ensembles. The proposed cw devices complement previously demonstrated SPTs and broaden the toolbox of quantum light manipulation circuitry.

quant-ph↗

arXiv2025

Exciton-polariton condensate in the van der Waals magnet CrSBr

Van der Waals magnets are an emergent material class of paramount interest for fundamental studies in coupling light with matter excitations, which are uniquely linked to their underlying magnetic properties. Among these materials, the semiconducting magnet CrSBr is possibly a first playground where we can study simultaneously the interaction of photons, magnons, and excitons at the quantum level. Here we demonstrate a coherent macroscopic quantum phase, the bosonic condensation of exciton-polaritons, emerging in a CrSBr flake embedded in a fully tunable cryogenic open optical cavity. The Bose condensate is characterized by a highly non-linear threshold-like behavior, and coherence manifests distinctly via its first and second order quantum correlations. We find that the condensate's non-linearity is highly susceptible to the magnetic order in CrSBr. Specially, it can encounter a sign change from attractive to repulsive interactions when the intrinsic antiferromagnetic order transforms to the forced ferromagnetic order. Our findings open a route towards magnetically controllable quantum fluids of light, and optomagnonic devices where spin magnetism is coupled to on-chip Bose-Einstein condensates.

cond-mat.mtrl-sci↗

arXiv2025

Photonics-Enhanced Graph Convolutional Networks

Photonics can offer a hardware-native route for machine learning (ML). However, efficient deployment of photonics-enhanced ML requires hybrid workflows that integrate optical processing with conventional CPU/GPU based neural network architectures. Here, we propose such a workflow that combines photonic positional embeddings (PEs) with advanced graph ML models. We introduce a photonics-based method that augments graph convolutional networks (GCNs) with PEs derived from light propagation on synthetic frequency lattices whose couplings match the input graph. We simulate propagation and readout to obtain internode intensity correlation matrices, which are used as PEs in GCNs to provide global structural information. Evaluated on Long Range Graph Benchmark molecular datasets, the method outperforms baseline GCNs with Laplacian based PEs, achieving $6.3\%$ lower mean absolute error for regression and $2.3\%$ higher average precision for classification tasks using a two-layer GCN as a baseline. When implemented in high repetition rate photonic hardware, correlation measurements can enable fast feature generation by bypassing digital simulation of PEs. Our results show that photonic PEs improve GCN performance and support optical acceleration of graph ML.

physics.optics↗

arXiv2025

Quantum Chebyshev Probabilistic Models for Fragmentation Functions

Quantum generative modeling is emerging as a powerful tool for advancing data analysis in high-energy physics, where complex multivariate distributions are common. However, efficiently learning and sampling these distributions remains challenging. We propose a quantum protocol for a bivariate probabilistic model based on shifted Chebyshev polynomials, trained as a circuit-based representation of two correlated variables, with sampling performed via quantum Chebyshev transforms. As a key application we study fragmentation functions (FFs) of charged pions and kaons from single-inclusive hadron production in electron-positron annihilation. We learn the joint distribution of momentum fraction $z$ and energy scale $Q$, and infer their correlations from the entanglement structure. Building on the generalization capabilities of the quantum model and extended register architecture, we perform fine-grid multivariate sampling for FF dataset augmentation. Our results highlight the growing potential of quantum generative modeling to advance data analysis and scientific discovery in high-energy physics.

quant-ph↗

arXiv2025

Spectroscopy on a single nonlinear mode recognizes quantum states

Characterising optical quantum states is essential for the development of quantum technologies. While traditional approaches to perform full quantum state tomography are often experimentally demanding, neuromorphic architectures may provide an effective alternative. In this work, we demonstrate how a quantum nonlinear driven-dissipative mode is sufficient to act as a quantum reservoir. By analyzing the occupations at different frequencies in the emission spectrum, a linear regression suffices in many cases to recognize the relevant parameters of incident squeezed states. Beyond highlighting the general potential of this approach under continuous driving, we illustrate its effectiveness in an explicit nontrivial example where the source is a degenerate optical parametric oscillator (OPO), coupled to a nonlinear polariton microcavity.

quant-ph↗

arXiv2025

From quantum feature maps to quantum reservoir computing: perspectives and applications

We explore the interplay between two emerging paradigms: reservoir computing and quantum computing. We observe how quantum systems featuring beyond-classical correlations and vast computational spaces can serve as non-trivial, experimentally viable reservoirs for typical tasks in machine learning. With a focus on neutral atom quantum processing units, we describe and exemplify a novel quantum reservoir computing (QRC) workflow. We conclude exploratively discussing the main challenges ahead, whilst arguing how QRC can offer a natural candidate to push forward reservoir computing applications.

quant-ph↗

arXiv2025

Advantage for Discrete Variational Quantum Algorithms in Circuit Recompilation

The relative power of quantum algorithms, using an adaptive access to quantum devices, versus classical post-processing methods that rely only on an initial quantum data set, remains the subject of active debate. Here, we present evidence for an exponential separation between adaptive and non-adaptive strategies in a quantum circuit recompilation task. Our construction features compilation problems with loss landscapes for discrete optimization that are unimodal yet non-separable, a structure known in classical optimization to confer exponential advantages to adaptive search. Numerical experiments show that optimization can efficiently uncover hidden circuit structure operating in the regime of volume-law entanglement and high-magic, while non-adaptive approaches are seemingly limited to exhaustive search requiring exponential resources. These results indicate that adaptive access to quantum hardware provides a fundamental advantage.

quant-ph↗

arXiv2025

Electrically tunable and enhanced nonlinearity of moiré exciton-polaritons in transition metal dichalcogenide bilayers

We develop a microscopic theory for nonlinear optical response of moiré exciton-polaritons in bilayers of transition metal dichalcogenides (TMDs). Our theory allows to study the tunnel-coupled intralayer and interlayer excitonic modes for a wide range of twist angles ($θ$), external electric field, and light-matter coupling, providing insights into the hybridization regime inaccessible before. Specifically, we account for the Umklapp scattering processes of two exciton-polaritons responsible for enhanced nonlinearity, and show that it is crucial for describing interactions at strong hybridization. We reveal a regime of attractive nonlinearity for moiré polaritons, stemming from the anisotropic Coulomb interactions, which can explain some of experimental features of optical response in TMD bilayers. Furthermore, within our theory we demonstrate that the attractive nonlinearity can be tuned into repulsive by applying an external electric field. Our findings show that nonlinear moiré polaritons offer a controllable platform nonlinear polaritonic devices.

cond-mat.mes-hall↗

arXiv2025

Polaritonic Machine Learning for Graph-based Data Analysis

Photonic and polaritonic systems offer a fast and efficient platform for accelerating machine learning (ML) through physics-based computing. To gain a computational advantage, however, polaritonic systems must: (1) exploit features that specifically favor nonlinear optical processing; (2) address problems that are computationally hard and depend on these features; (3) integrate photonic processing within broader ML pipelines. In this letter, we propose a polaritonic machine learning approach for solving graph-based data problems. We demonstrate how lattices of condensates can efficiently embed relational and topological information from point cloud datasets. This information is then incorporated into a pattern recognition workflow based on convolutional neural networks (CNNs), leading to significantly improved learning performance compared to physics-agnostic methods. Our extensive benchmarking shows that photonic machine learning achieves over 90\% accuracy for Betti number classification and clique detection tasks - a substantial improvement over the 35\% accuracy of bare CNNs. Our study introduces a distinct way of using photonic systems as fast tools for feature engineering, while building on top of high-performing digital machine learning.

cond-mat.dis-nn↗

arXiv2025

Vortex Detection from Quantum Data

Quantum solutions to differential equations represent quantum data -- states that contain relevant information about the system's behavior, yet are difficult to analyze. We propose a toolbox for reading out information from such data, where customized quantum circuits enable efficient extraction of flow properties. We concentrate on the process referred to as quantum vortex detection (QVD), where specialized operators are developed for pooling relevant features related to vorticity. Specifically, we propose approaches based on sliding windows and quantum Fourier analysis that provide a separation between patches of the flow field with vortex-type profiles. First, we show how contour-shaped windows can be applied, trained, and analyzed sequentially, providing a clear signal to flag the location of vortices in the flow. Second, we develop a parallel window extraction technique, such that signals from different contour positions are coherently processed to avoid looping over the entire solution mesh. We show that Fourier features can be extracted from the flow field, leading to classification of datasets with vortex-free solutions against those exhibiting Lamb-Oseen vortices. Our work exemplifies a successful case of efficiently extracting value from quantum data and points to the need for developing appropriate quantum data analysis tools that can be trained on them.

quant-ph↗