arXiv subjects

Oleksandr Kyriienko

Publications and source records attributed to Oleksandr Kyriienko.

At least 37 records · Page 2Linked to original sources

arXiv2025

Quantum algorithm for solving nonlinear differential equations based on physics-informed effective Hamiltonians

We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such operators in the Chebyshev space, where an effective Hamiltonian is a sum of global differential and data constraints. Once the effective Hamiltonian is formed, solutions of differential equations can be obtained using the ground state preparation techniques (e.g. imaginary-time evolution and quantum singular value transformation), bypassing variational search. Unlike approaches based on discrete grids, the algorithm enables evaluation of solutions beyond fixed grid points and implements constraints in the physics-informed way. Our proposal inherits the best traits from quantum machine learning-based DE solving (compact basis representation, automatic differentiation, nonlinearity) and quantum linear algebra-based approaches (fine-grid encoding, provable speed-up for state preparation), offering a robust strategy for quantum scientific computing in the early fault-tolerant era.

quant-ph↗

arXiv2024

Quantum community detection via deterministic elimination

We propose a quantum algorithm for calculating the structural properties of complex networks and graphs. The corresponding protocol -- deteQt -- is designed to perform large-scale community and botnet detection, where a specific subgraph of a larger graph is identified based on its properties. We construct a workflow relying on ground state preparation of the network modularity matrix or graph Laplacian. The corresponding maximum modularity vector is encoded into a $\log(N)$-qubit register that contains community information. We develop a strategy for ``signing'' this vector via quantum signal processing, such that it closely resembles a hypergraph state, and project it onto a suitable linear combination of such states to detect botnets. As part of the workflow, and of potential independent interest, we present a readout technique that allows filtering out the incorrect solutions deterministically. This can reduce the scaling for the number of samples from exponential to polynomial. The approach serves as a building block for graph analysis with quantum speed up and enables the cybersecurity of large-scale networks.

quant-ph↗

arXiv2024

What can we learn from quantum convolutional neural networks?

Quantum machine learning (QML) shows promise for analyzing quantum data. A notable example is the use of quantum convolutional neural networks (QCNNs), implemented as specific types of quantum circuits, to recognize phases of matter. In this approach, ground states of many-body Hamiltonians are prepared to form a quantum dataset and classified in a supervised manner using only a few labeled examples. However, this type of dataset and model differs fundamentally from typical QML paradigms based on feature maps and parameterized circuits. In this study, we demonstrate how models utilizing quantum data can be interpreted through hidden feature maps, where physical features are implicitly embedded via ground-state feature maps. By analyzing selected examples previously explored with QCNNs, we show that high performance in quantum phase recognition comes from generating a highly effective basis set with sharp features at critical points. The learning process adapts the measurement to create sharp decision boundaries. Our analysis highlights improved generalization when working with quantum data, particularly in the limited-shots regime. Furthermore, translating these insights into the domain of quantum scientific machine learning, we demonstrate that ground-state feature maps can be applied to fluid dynamics problems, expressing shock wave solutions with good generalization and proven trainability.

quant-ph↗

arXiv2024

Ground state-based quantum feature maps

We introduce a quantum data embedding protocol based on the preparation of a ground state of a parameterized Hamiltonian. We analyze the corresponding quantum feature map, recasting it as an adiabatic state preparation procedure with Trotterized evolution. We compare the properties of underlying quantum models with ubiquitous Fourier-type quantum models, and show that ground state embeddings can be described effectively by a spectrum with degree that grows rapidly with the number of qubits, corresponding to a large model capacity. We observe that the spectrum contains massive frequency degeneracies, and the weighting coefficients for the modes are highly structured, thus limiting model expressivity. Our results provide a step towards understanding models based on quantum data, and contribute to fundamental knowledge needed for building efficient quantum machine learning (QML) protocols. As non-trivial embeddings are crucial for designing QML protocols that cannot be simulated classically, our findings guide the search for high-capacity quantum models that can largely outperform classical models.

quant-ph↗

arXiv2024

Addressing the Readout Problem in Quantum Differential Equation Algorithms with Quantum Scientific Machine Learning

Quantum differential equation solvers aim to prepare solutions as $n$-qubit quantum states over a fine grid of $O(2^n)$ points, surpassing the linear scaling of classical solvers. However, unlike classically stored vectors of solutions, the readout of exact quantum states poses a bottleneck due to the complexity of tomography. Here, we show that the readout problem can be addressed with quantum learning tools where we focus on distilling the relevant features. Treating outputs of quantum differential equation solvers as quantum data, we demonstrate that low-dimensional output can be extracted using a measurement operator adapted to detect relevant features. We apply this quantum scientific machine learning approach to classify solutions for shock wave detection and turbulence modeling in scenarios where data samples come directly from quantum differential equation solvers. We show that the basis chosen for performing analysis greatly impacts classification accuracy. Our work opens up the area of research where quantum machine learning for quantum datasets is inherently required.

quant-ph↗

arXiv2024

Can Geometric Quantum Machine Learning Lead to Advantage in Barcode Classification?

We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries that allows for the classification of similar and dissimilar pairs based on global correlations, and enables generalization from just a few samples. Unlike GQML algorithms developed to date, we propose to focus on symmetry-aware measurement adaptation that outperforms unitary parametrizations. We compare GQML for similarity testing against classical deep neural networks and convolutional neural networks with Siamese architectures. We show that quantum networks largely outperform their classical counterparts. We explain this difference in performance by analyzing correlated distributions used for composing our dataset. We relate the similarity testing with problems that showcase a proven maximal separation between the BQP complexity class and the polynomial hierarchy. While the ability to achieve advantage largely depends on how data are loaded, we discuss how similar problems can benefit from quantum machine learning.

quant-ph↗

arXiv2024

Room-temperature polariton condensate in a two-dimensional hybrid perovskite

Layered 2D halide perovskites are chemically synthesized realizations of quantum well stacks with giant exciton oscillator strengths, tunable emission spectra and very large exciton binding energies. While these features render 2D halide perovskites a promising platform for room-temperature polaritonics, bosonic condensation and polariton lasing in 2D perovskites have so far remained elusive at ambient conditions. Here, we demonstrate room-temperature cavity exciton-polariton condensation in mechanically exfoliated crystals of the 2D Ruddlesden-Popper iodide perovskite $(BA)_{2}(MA)_{2}Pb_{3}I_{10}$ in an open optical microcavity. We observe a polariton condensation threshold of $P_{th}=6.76 fJ$ per pulse and detect a strong non-linear response. Interferometric measurements confirm the spontaneous emergence of spatial coherence across the condensate with an associated first-order autocorrelation reaching $g^{(1)}\approx 0.6$. Our results lay the foundation for a new class of room-temperature polariton lasers based on 2D halide perovskites with great potential for hetero-integration with other van-der-Waals materials and combination with photonic crystals or waveguides.

physics.optics↗

arXiv2024

Femtosecond switching of strong light-matter interactions in microcavities with two-dimensional semiconductors

Ultrafast all-optical logic devices based on nonlinear light-matter interactions hold the promise to overcome the speed limitations of conventional electronic devices. Strong coupling of excitons and photons inside an optical resonator enhances such interactions and generates new polariton states which give access to unique nonlinear phenomena, such as Bose-Einstein condensation, used for all-optical ultrafast polariton transistors. However, the pulse energies required to pump such devices range from tens to hundreds of pJ, making them not competitive with electronic transistors. Here we introduce a new paradigm for all-optical switching based on the ultrafast transition from the strong to the weak coupling regime in microcavities embedding atomically thin transition metal dichalcogenides. Employing single and double stacks of hBN-encapsulated MoS$_2$ homobilayers with high optical nonlinearities and fast exciton relaxation times, we observe a collapse of the 55-meV polariton gap and its revival in less than one picosecond, lowering the threshold for optical switching below 4 pJ per pulse, while retaining ultrahigh switching frequencies. As an additional degree of freedom, the switching can be triggered pumping either the intra- or the interlayer excitons of the bilayers at different wavelengths, speeding up the polariton dynamics, owing to unique interspecies excitonic interactions. Our approach will enable the development of compact ultrafast all-optical logical circuits and neural networks, showcasing a new platform for polaritonic information processing based on manipulating the light-matter coupling.

physics.optics↗

arXiv2024

The topology of data hides in quantum thermal states

We provide a quantum protocol to perform topological data analysis (TDA) via the distillation of quantum thermal states. Recent developments of quantum thermal state preparation algorithms reveal their characteristic scaling defined by properties of dissipative Lindbladians. This contrasts with protocols based on unitary evolution which have a scaling depending on the properties of the combinatorial Laplacian. To leverage quantum thermal state preparation algorithms, we translate quantum TDA from a real-time to an imaginary-time picture, shifting the paradigm from a unitary approach to a dissipative one. Starting from an initial state overlapping with the ground state of the system, one can dissipate its energy via channels unique to the dataset, naturally distilling its information. Therefore calculating Betti numbers translates into a purity estimation. Alternatively, this can be interpreted as the evaluation of the Rényi 2-entropy, Uhlmann fidelity or Hilbert-Schmidt distance relative to thermal states with the embedded topology of simplicial complexes. Our work opens the field of TDA toward a more physical interpretation of the topology of data.

quant-ph↗

arXiv2024

Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids

We develop a quantum simulation-based approach for studying properties of strongly correlated magnetic materials at increasing scale. We consider a paradigmatic example of a quantum spin liquid (QSL) state hosted by the honeycomb Kitaev model, and use a trainable symmetry-guided ansatz for preparing its ground state. Applying the tools of quantum subspace expansion (QSE), Hamiltonian operator approximation, and overlap measurements, we simulate the QSL at zero temperature and finite magnetic field, thus moving outside of the symmetric subspace. Next, we implement a protocol for quantum subspace expansion-based measurement of spin-spin correlation functions. Finally, we perform QSE-based simulation of the dynamical structure factor obtained from Green's functions of the finite field Kitaev model. Our results show that quantum simulators offer an insight to quasiparticle properties of strongly correlated magnets and can become a valuable tool for studying material science.

quant-ph↗

arXiv2024

Multidimensional Quantum Generative Modeling by Quantum Hartley Transform

We develop an approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions. First, we design a differentiable Hartley feature map parametrized by real-valued argument that enables quantum models suitable for solving stochastic differential equations and regression problems. Unlike the naturally complex Fourier encoding, the proposed Hartley feature map circuit leads to quantum states with real-valued amplitudes, introducing an inductive bias and natural regularization. Next, we propose a quantum Hartley transform circuit as a map between computational and Hartley basis. We apply the developed paradigm to generative modeling from solutions of stochastic differential equations, and utilize the quantum Hartley transform for fine sampling from parameterized distributions through an extended register. Finally, we present tools for implementing multivariate quantum generative modeling for both correlated and uncorrelated distributions. As a result, the developed quantum Hartley models offer a distinct quantum approach to generative AI at increasing scale.

quant-ph↗

arXiv2024

Beyond the Buzz: Strategic Paths for Enabling Useful NISQ Applications

There is much debate on whether quantum computing on current NISQ devices, consisting of noisy hundred qubits and requiring a non-negligible usage of classical computing as part of the algorithms, has utility and will ever offer advantages for scientific and industrial applications with respect to traditional computing. In this position paper, we argue that while real-world NISQ quantum applications have yet to surpass their classical counterparts, strategic approaches can be used to facilitate advancements in both industrial and scientific applications. We have identified three key strategies to guide NISQ computing towards practical and useful implementations. Firstly, prioritizing the identification of a "killer app" is a key point. An application demonstrating the distinctive capabilities of NISQ devices can catalyze broader development. We suggest focusing on applications that are inherently quantum, e.g., pointing towards quantum chemistry and material science as promising domains. These fields hold the potential to exhibit benefits, setting benchmarks for other applications to follow. Secondly, integrating AI and deep-learning methods into NISQ computing is a promising approach. Examples such as quantum Physics-Informed Neural Networks and Differentiable Quantum Circuits (DQC) demonstrate the synergy between quantum computing and AI. Lastly, recognizing the interdisciplinary nature of NISQ computing, we advocate for a co-design approach. Achieving synergy between classical and quantum computing necessitates an effort in co-designing quantum applications, algorithms, and programming environments, and the integration of HPC with quantum hardware. The interoperability of these components is crucial for enabling the full potential of NISQ computing.

quant-ph↗

arXiv2024

Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics

We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on a quantum register that utilizes a linear combination of unitaries (LCU) approach to store the trajectory information. Second, we extend quantum methods to Gauss-Seidel iterative methods. Additionally, we propose a quantum-suitable resolvent decomposition based on the Woodbury identity. From a technical perspective, we develop and utilize tools for the block encoding of specific matrices as well as their multiplication. We benchmark the approach on paradigmatic fluid dynamics problems. Our results stress that instead of inverting large matrices, one can program quantum computers to perform multigrid-type computations and leverage corresponding advances in scientific computing.

quant-ph↗

arXiv2024

Microscopic theory of nonlinear phase space filling in polaritonic lattices

We develop a full microscopic theory for a nonlinear phase space filling (NPSF) in strongly coupled two-dimensional polaritonic lattices. Ubiquitous in polaritonic experiments, the theoretical description of NPSF, remains limited to perturbative treatment and homogeneous samples. In this study, we go beyond the existing theoretical description and discover the broad scope of regimes where NPSF crucially modifies the optical response. Studying the quantum effects of non-bosonicity, cooperative light-matter coupling, and Coulomb blockade, we reveal several regimes for observing the nonlinear Rabi splitting quench due to the phase space filling. Unlike prior studies, we derive nonlinear Rabi frequency scaling all the way to the saturation limit and show that the presence of a lattice potential leads to qualitatively distinct nonlinearity. We concentrate on three regimes of NPSF: 1) planar; 2) fractured; and 3) ultralocalized. In planar saturation, the Rabi frequency decreases exponentially as a function of exciton density. For the fractured case, where excitons form a lattice with sites exceeding the exciton size, we discover fast NPSF at low occupation in the lattice. This is followed by slower NPSF as the medium becomes fully saturated. This behavior is particularly pronounced in the presence of Coulomb (or Rydberg) blockade, where regions of fast and slow NPSF depend on the strength of repulsion. For the ultralocalized NPSF, we observe the square-root saturation typical to the collection of two-level systems. Our findings can help describing recent observations of strong nonlinearity in heterobilayers of transition metal dichalcogenides where Moir{é} lattices emerge naturally [Nature \textbf{591}, 61 (2021)]. The theory also opens the prospects for engineering strongly nonlinear responses of polaritonic lattices with patterned samples, driving polaritonics into the quantum regime.

cond-mat.mes-hall↗

arXiv2024

Nonlinear Rydberg exciton-polaritons in Cu$_2$O microcavities

Rydberg excitons (analogues of Rydberg atoms in condensed matter systems) are highly excited bound electron-hole states with large Bohr radii. The interaction between them as well as exciton coupling to light may lead to strong optical nonlinearity, with applications in sensing and quantum information processing. Here, we achieve strong effective photon-photon interactions (Kerr-like optical nonlinearity) via the Rydberg blockade phenomenon and the hybridisation of excitons and photons forming polaritons in a Cu$_2$O-filled microresonators. Under pulsed resonant excitation polariton resonance frequencies are renormalised due to the reduction of the photon-exciton coupling with increasing exciton density. Theoretical analysis shows that the Rydberg blockade plays a major role in the experimentally observed scaling of the polariton nonlinearity coefficient as $\propto n^{4.4 \pm 1.8}$ for principal quantum numbers up to n = 7. Such high principal quantum numbers studied in a polariton system for the first time are essential for realisation of high Rydberg optical nonlinearities, which paves the way towards quantum optical applications and fundamental studies of strongly-correlated photonic (polaritonic) states in a solid state system.

cond-mat.mes-hall↗

arXiv2024

Geometric quantum machine learning of BQP$^A$ protocols and latent graph classifiers

Geometric quantum machine learning (GQML) aims to embed problem symmetries for learning efficient solving protocols. However, the question remains if (G)QML can be routinely used for constructing protocols with an exponential separation from classical analogs. In this Letter we consider Simon's problem for learning properties of Boolean functions, and show that this can be related to an unsupervised circuit classification problem. Using the workflow of geometric QML, we learn from first principles Simon's algorithm, thus discovering an example of BQP$^A\neq$BPP protocol with respect to some dataset (oracle $A$). Our key findings include the development of an equivariant feature map for embedding Boolean functions, based on twirling with respect to identified bitflip and permutational symmetries, and measurement based on invariant observables with a sampling advantage. The proposed workflow points to the importance of data embeddings and classical post-processing, while keeping the variational circuit as a trivial identity operator. Next, developing the intuition for the function learning, we visualize instances as directed computational hypergraphs, and observe that the GQML protocol can access their global topological features for distinguishing bijective and surjective functions. Finally, we discuss the prospects for learning other BQP$^A$-type protocols, and conjecture that this depends on the ability of simplifying embeddings-based oracles $A$ applied as a linear combination of unitaries.

quant-ph↗

arXiv2023

Quantum topological data analysis via the estimation of the density of states

We develop a quantum topological data analysis (QTDA) protocol based on the estimation of the density of states (DOS) of the combinatorial Laplacian. Computing topological features of graphs and simplicial complexes is crucial for analyzing datasets and building explainable AI solutions. This task becomes computationally hard for simplicial complexes with over sixty vertices and high-degree topological features due to a combinatorial scaling. We propose to approach the task by embedding underlying hypergraphs as effective quantum Hamiltonians and evaluating their density of states from the time evolution. Specifically, we compose propagators as quantum circuits using the Cartan decomposition of effective Hamiltonians and sample overlaps of time-evolved states using multi-fidelity protocols. Next, we develop various post-processing routines and implement a Fourier-like transform to recover the rank (and kernel) of Hamiltonians. This enables us to estimate the Betti numbers, revealing the topological features of simplicial complexes. We test our protocol on noiseless and noisy quantum simulators and run examples on IBM quantum processors. We observe the resilience of the proposed QTDA approach to real-hardware noise even in the absence of error mitigation, showing the promise to near-term device implementations and highlighting the utility of global DOS-based estimators.

quant-ph↗

arXiv2023

Protocols for classically training quantum generative models on probability distributions

Quantum Generative Modelling (QGM) relies on preparing quantum states and generating samples from these states as hidden - or known - probability distributions. As distributions from some classes of quantum states (circuits) are inherently hard to sample classically, QGM represents an excellent testbed for quantum supremacy experiments. Furthermore, generative tasks are increasingly relevant for industrial machine learning applications, and thus QGM is a strong candidate for demonstrating a practical quantum advantage. However, this requires that quantum circuits are trained to represent industrially relevant distributions, and the corresponding training stage has an extensive training cost for current quantum hardware in practice. In this work, we propose protocols for classical training of QGMs based on circuits of the specific type that admit an efficient gradient computation, while remaining hard to sample. In particular, we consider Instantaneous Quantum Polynomial (IQP) circuits and their extensions. Showing their classical simulability in terms of the time complexity, sparsity and anti-concentration properties, we develop a classically tractable way of simulating their output probability distributions, allowing classical training to a target probability distribution. The corresponding quantum sampling from IQPs can be performed efficiently, unlike when using classical sampling. We numerically demonstrate the end-to-end training of IQP circuits using probability distributions for up to 30 qubits on a regular desktop computer. When applied to industrially relevant distributions this combination of classical training with quantum sampling represents an avenue for reaching advantage in the NISQ era.

quant-ph↗