arXiv subjects

Vedran Dunjko

Publications and source records attributed to Vedran Dunjko.

At least 19 recordsLinked to original sources

arXiv2026

Cautious optimism for deep parameterized quantum circuits

A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.

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arXiv2026

Provable learning separation for predicting time-evolution of quantum many-body systems

Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations? We address this problem by studying the learnability of quantum many-body dynamics from the perspective of probably approximately correct (PAC)-learning. Concretely, we devise a supervised learning problem where the training set consists of specifications of randomized stabilizer probe states, evolution times sampled uniformly from a polynomially large time interval $[0,T]$, coupled with expectation values of certain observables evaluated on the resulting time-evolved state under an unknown Hamiltonian. For this learning task, we provide an efficient quantum procedure whose training phase learns the underlying Hamiltonian from short-time training samples, and whose deployment phase combines Hamiltonian simulation with the classical shadows protocol to perform inference on a newly given data point. By contrast, the existence of $O(\mathsf{poly}(n))$-time instances ensures classical hardness: by embedding a $\mathsf{BQP}$-complete computation into the polynomially long time-dynamics of a low-intersection variant of the Feynman-Kitaev clock Hamiltonian construction, we show that, for a certain family of input distributions, no randomized classical polynomial-time algorithm can fulfill our learning condition, unless $\mathsf{BQP}\subseteq\mathsf{P/poly}$. Furthermore, we show that the classically hard instance maintains quantum learnability. We also give an interpretation of our results in learning-assisted certified quantum simulation. Taken together, our results demonstrate a rigorous learning separation for a natural ML task based on Hamiltonian evolution, while building connections between quantum learning theory, quantum simulation, and QML.

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arXiv2026

Evidence of Quantum Machine Learning Advantage with Tens of Noisy Qubits

Learning problems involving quantum data are natural candidates for demonstrating an advantage in quantum machine learning. Recent results indicate that, for certain tasks and under noiseless conditions, coherent processing of quantum data outperforms fixed-measurement schemes followed by classical processing. It remained uncertain whether this performance gap persists at a finite scale, and in the presence of noise that is unavoidable with current quantum devices. In this work, we present simulations and analysis of the performance of existing hardware on a learning problem known to exhibit asymptotic advantage, now subjected to noisy quantum data. Comparing coherent quantum processing directly against fixed-measurement schemes, our results demonstrate a clear performance separation at a scale of just 30 to 40 noisy qubits. Already at this scale, the fundamental bottleneck is no longer classical computation but data acquisition; matching the noisy coherent protocol with measure-first strategies would still require months or even years of measurements. By systematically evaluating hardware constraints such as state preparation, gate errors, readout errors, connectivity, and coherence times, we provide evidence that a demonstration of such a strong learning advantage is accessible on near-term devices.

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arXiv2026

Universality of Classically Trainable, Quantum-Deployed Boson-Sampling Generative Models

Recent work on the instantaneous quantum polynomial-time (IQP) quantum-circuit Born machine (QCBM) highlights a promising paradigm for generative modeling: train classically, deploy quantumly. In this setting, the training objective can be evaluated efficiently on a classical computer, while sampling from the resulting model may still be classically intractable. Furthermore, in the IQP-QCBM framework, extending the model family with ancillary qubits has been proven to yield universality. This paper asks whether similar results hold for linear-optical generative models. To this end, we introduce the Boson Sampling Born Machine (BSBM). Our analysis retraces analogous steps as were found for IQP-QCBMs with twists. Using recent results that enable classical approximation of broad classes of expectation values in linear optics, we show that BSBMs can be trained classically for wide families of loss functions. Next, we argue that "basic" BSBMs are not universal generative models, and that universality can be achieved by expanding the model while preserving efficient classical training and sampling hardness. In our approach, we introduce and analyze the role of constant-function postprocessing, generalizing the construction for IQP-QCBMs, which under suitable conditions can lead to universality while preserving the hardness of classically simulating the models. We showcase a family of BSBMs, characterized by a single hyperparameter, that allows for a monotonic increase in expressivity toward universality while retaining the capacity to represent ostensibly hard distributions. Furthermore, we discuss the possible modalities for the efficient classical training, in the sense of efficient estimation of gradients of the loss function.

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arXiv2026

Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines

Instantaneous quantum polynomial quantum circuit Born machines (IQP-QCBMs) have been proposed as quantum generative models with a classically tractable training objective based on the maximum mean discrepancy (MMD) and a potential quantum advantage motivated by sampling-complexity arguments, making them an exciting model worth deeper investigation. While recent works have further proven the universality of a (slightly generalized) model, the next immediate question pertains to its trainability, i.e., whether it suffers from the exponentially vanishing loss gradients, known as the barren plateau issue, preventing effective use, and how regimes of trainability overlap with regimes of possible quantum advantage. Here, we provide significant strides in these directions. To study the trainability at initialization, we analytically derive closed-form expressions for the variances of the partial derivatives of the MMD loss function and provide general upper and lower bounds. With uniform initialization, we show that barren plateaus depend on the generator set and the spectrum of the chosen kernel. We identify regimes in which low-weight-biased kernels avoid exponential gradient suppression in structured topologies. Also, we prove that a small-variance Gaussian initialization ensures polynomial scaling for the gradient under mild conditions. As for the potential quantum advantage, we further argue, based on previous complexity-theoretic arguments, that sparse IQP families can output a probability distribution family that is classically intractable, and that this distribution remains trainable at initialization at least at lower-weight frequencies.

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arXiv2026

Machine learning with minimal use of quantum computers: Provable advantages in Learning Under Quantum Privileged Information (LUQPI)

Quantum machine learning (QML) is often listed as a promising candidate for useful applications of quantum computers, in part due to numerous proofs of possible quantum advantages. A central question is how small a role quantum computers can play while still enabling provable learning advantages over classical methods. We study an especially restricted setting in which a quantum computer is used only as a feature extractor: it acts independently on individual data points, without access to labels or global dataset information, is available only to augment the training set, and is not available at deployment. Training and deployment are therefore carried out by fully classical learners on a dataset augmented with quantum-generated features. We formalize this model by adapting the classical framework of Learning Under Privileged Information (LUPI) to the quantum case, which we call Learning Under Quantum Privileged Information (LUQPI). Within this framework, we show that even such minimally involved quantum feature extraction, available only during training, can yield exponential quantum-classical separations for suitable concept classes and data distributions under reasonable computational assumptions. We further situate LUQPI within a taxonomy of related quantum and classical learning settings and show how standard classical machinery, most notably the SVM+ algorithm, can exploit quantum-augmented data. Finally, we present numerical experiments in a physically motivated many-body setting, where privileged quantum features are expectation values of observables on ground states, and observe consistent performance gains for LUQPI-style models over strong classical baselines.

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arXiv2025

Universality and kernel-adaptive training for classically trained, quantum-deployed generative models

The instantaneous quantum polynomial (IQP) quantum circuit Born machine (QCBM) has been proposed as a promising quantum generative model over bitstrings. Recent works have shown that the training of IQP-QCBM is classically tractable w.r.t. the so-called Gaussian kernel maximum mean discrepancy (MMD) loss function, while maintaining the potential of a quantum advantage for sampling itself. Nonetheless, the model has a number of aspects where improvements would be important for more general utility: (1) the basic model is known to be not universal - i.e. it is not capable of representing arbitrary distributions, and it was not known whether it is possible to achieve universality by adding hidden (ancillary) qubits; (2) a fixed Gaussian kernel used in the MMD loss can cause training issues, e.g., vanishing gradients. In this paper, we resolve the first question and make decisive strides on the second. We prove that for an $n$-qubit IQP generator, adding $n + 1$ hidden qubits makes the model universal. For the latter, we propose a kernel-adaptive training method, where the kernel is adversarially trained. We show that in the kernel-adaptive method, the convergence of the MMD value implies weak convergence in distribution of the generator. We also analytically analyze the limitations of the MMD-based training method. Finally, we verify the performance benefits on the dataset crafted to spotlight improvements by the suggested method. The results show that kernel-adaptive training outperforms a fixed Gaussian kernel in total variation distance, and the gap increases with the dataset dimensionality. These modifications and analyses shed light on the limits and potential of these new quantum generative methods, which could offer the first truly scalable insights in the comparative capacities of classical versus quantum models, even without access to scalable quantum computers.

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arXiv2025

Computational complexity of the homology problem with orientable filtration: MA-completeness

We show the existence of an MA-complete homology problem for a certain subclass of simplicial complexes. The problem is defined through a new concept of orientability of simplicial complexes that we call a "uniform orientable filtration", which is related to sign-problem freeness in homology. The containment in MA is achieved through the design of new, higher-order random walks on simplicial complexes associated with the filtration. For the MA-hardness, we design a new gadget with which we can reduce from an MA-hard stoquastic satisfiability problem. Therefore, our result provides the first natural MA-complete problem for higher-order random walks on simplicial complexes, combining the concepts of topology, persistent homology, and quantum computing.

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arXiv2025

Quantum generative modeling for financial time series with temporal correlations

Quantum generative adversarial networks (QGANs) have been investigated as a method for generating synthetic data with the goal of augmenting training data sets for neural networks. This is especially relevant for financial time series, since we only ever observe one realization of the process, namely the historical evolution of the market, which is further limited by data availability and the age of the market. However, for classical generative adversarial networks it has been shown that generated data may (often) not exhibit desired properties (also called stylized facts), such as matching a certain distribution or showing specific temporal correlations. Here, we investigate whether quantum correlations in quantum inspired models of QGANs can help in the generation of financial time series. We train QGANs, composed of a quantum generator and a classical discriminator, and investigate two approaches for simulating the quantum generator: a full simulation of the quantum circuits, and an approximate simulation using tensor network methods. We tested how the choice of hyperparameters, such as the circuit depth and bond dimensions, influenced the quality of the generated time series. The QGAN that we trained generate synthetic financial time series that not only match the target distribution but also exhibit the desired temporal correlations, with the quality of each property depending on the hyperparameters and simulation method.

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arXiv2025

Quantum Advantage in Learning Quantum Dynamics via Fourier coefficient extraction

One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised learning version of this problem, where we are given random examples of the inputs to the dynamics as classical data, paired with the expectation values of some observable after the time evolution, as corresponding output labels. The task is to replicate the corresponding input-output function. We prove that this task can yield provable exponential classical-quantum learning advantages under common complexity assumptions in natural settings. To design our quantum learning algorithms, we introduce a new method, which we term \textit{\subroutine}~algorithm for parametrized circuit functions, and which may be of independent interest. Furthermore, we discuss the limitations of generalizing our method to arbitrary quantum dynamics while maintaining provable guarantees. We explain that significant generalizations are impossible under certain complexity-theoretic assumptions, but nonetheless, we provide a heuristic kernel method, where we trade-off provable correctness for broader applicability.

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arXiv2025

Quantum computing and artificial intelligence: status and perspectives

This white paper discusses and explores the various points of intersection between quantum computing and artificial intelligence (AI). It describes how quantum computing could support the development of innovative AI solutions. It also examines use cases of classical AI that can empower research and development in quantum technologies, with a focus on quantum computing and quantum sensing. The purpose of this white paper is to provide a long-term research agenda aimed at addressing foundational questions about how AI and quantum computing interact and benefit one another. It concludes with a set of recommendations and challenges, including how to orchestrate the proposed theoretical work, align quantum AI developments with quantum hardware roadmaps, estimate both classical and quantum resources - especially with the goal of mitigating and optimizing energy consumption - advance this emerging hybrid software engineering discipline, and enhance European industrial competitiveness while considering societal implications.

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arXiv2025

Quantum machine learning advantages beyond hardness of evaluation

The most general examples of quantum learning advantages involve data labeled by cryptographic or intrinsically quantum functions, where classical learners are limited by the infeasibility of evaluating the labeling functions using polynomial-sized classical circuits. While broad in scope, such results reveal little about advantages arising from the learning process itself. In cryptographic settings, further insight is possible via random-generatability - the ability to classically generate labeled data - enabling hardness proofs for identification tasks, where the goal is to identify the labeling function from a dataset, even when evaluation is classically intractable. These tasks are particularly relevant in quantum contexts, including Hamiltonian learning and identifying physically meaningful order parameters. However, for quantum functions, random-generatability is conjectured not to hold, leaving no known identification advantages in genuinely quantum regimes. In this work, we give the first proofs of quantum identification learning advantages under standard complexity assumptions. We confirm that quantum-hard functions are not random-generatable unless BQP is contained in the second level of the polynomial hierarchy, ruling out cryptographic-style data generation strategies. We then introduce a new approach: we show that verifiable identification - solving the identification task for valid datasets while rejecting invalid ones - is classically hard for quantum labeling functions unless BQP is in the polynomial hierarchy. Finally, we show that, for a broad class of tasks, solving the identification problem implies verifiable identification in the polynomial hierarchy. This yields our main result: a natural class of quantum identification tasks solvable by quantum learners but hard for classical learners unless BQP is in the polynomial hierarchy.

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arXiv2025

Note on the Universality of Parameterized IQP Circuits with Hidden Units for Generating Probability Distributions

In a series of recent works, an interesting quantum generative model based on parameterized instantaneous polynomial quantum (IQP) circuits has emerged as they can be trained efficiently classically using any loss function that depends only on the expectation values of observables of the model. The model is proven not to be universal for generating arbitrary distributions, but it is suspected that marginals can be - much like Boltzmann machines achieve universality by utilizing hidden (traced-out in quantum jargon) layers. In this short note, we provide two simple proofs of this fact. The first is near-trivial and asymptotic, and the second shows universality can be achieved with a reasonable number of additional qubits.

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arXiv2025

Weighted Approximate Quantum Natural Gradient for Variational Quantum Eigensolver

The variational quantum eigensolver (VQE) is one of the most prominent algorithms using near-term quantum devices, designed to find the ground state of a Hamiltonian. In VQE, a classical optimizer iteratively updates the parameters in the quantum circuit. Among various optimization methods, the quantum natural gradient descent (QNG) stands out as a promising optimization approach for VQE. However, standard QNG only leverages the quantum Fisher information of the entire system and treats each subsystem equally in the optimization process, without accounting for the different weights and contributions of each subsystem corresponding to each local term in the Hamiltonian. To address this limitation, we propose a Weighted Approximate Quantum Natural Gradient (WA-QNG) method tailored for $k$-local Hamiltonians. In this paper, we theoretically analyze the potential advantages of WA-QNG compared to QNG from three distinct perspectives and reveal its connection with the Gauss-Newton method. We also show it outperforms the standard quantum natural gradient descent in the numerical simulations for seeking the ground state of the Hamiltonian.

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arXiv2025

Detecting underdetermination in parameterized quantum circuits

A central question in machine learning is how reliable the predictions of a trained model are. Reliability includes the identification of instances for which a model is likely not to be trusted based on an analysis of the learning system itself. Such unreliability for an input may arise from the model family providing a variety of hypotheses consistent with the training data, which can vastly disagree in their predictions on that particular input point. This is called the underdetermination problem, and it is important to develop methods to detect it. With the emergence of quantum machine learning (QML) as a prospective alternative to classical methods for certain learning problems, the question arises to what extent they are subject to underdetermination and whether similar techniques as those developed for classical models can be employed for its detection. In this work, we first provide an overview of concepts from Safe AI and reliability, which in particular received little attention in QML. We then explore the use of a method based on local second-order information for the detection of underdetermination in parameterized quantum circuits through numerical experiments. We further demonstrate that the approach is robust to certain levels of shot noise. Our work contributes to the body of literature on Safe Quantum AI, which is an emerging field of growing importance.

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arXiv2025

Double descent in quantum kernel methods

The double descent phenomenon challenges traditional statistical learning theory by revealing scenarios where larger models do not necessarily lead to reduced performance on unseen data. While this counterintuitive behavior has been observed in a variety of classical machine learning models, particularly modern neural network architectures, it remains elusive within the context of quantum machine learning. In this work, we analytically demonstrate that linear regression models in quantum feature spaces can exhibit double descent behavior by drawing on insights from classical linear regression and random matrix theory. Additionally, our numerical experiments on quantum kernel methods across different real-world datasets and system sizes further confirm the existence of a test error peak, a characteristic feature of double descent. Our findings provide evidence that quantum models can operate in the modern, overparameterized regime without experiencing overfitting, potentially opening pathways to improved learning performance beyond traditional statistical learning theory.

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arXiv2024

Variational Quantum Generative Modeling by Sampling Expectation Values of Tunable Observables

Expectation Value Samplers (EVSs) are quantum generative models that can learn high-dimensional continuous distributions by measuring the expectation values of parameterized quantum circuits. However, these models can demand impractical quantum resources for good performance. We investigate how observable choices affect EVS performance and propose an Observable-Tunable Expectation Value Sampler (OT-EVS), which achieves greater expressivity than standard EVS. By restricting the selectable observables, it is possible to use the classical shadows measurement scheme to reduce the sample complexity of our algorithm. In addition, we propose an adversarial training method adapted to the needs of OT-EVS. This training prioritizes classical updates of observables, minimizing the more costly updates of quantum circuit parameters. Numerical experiments, using an original simulation technique for correlated shot noise, confirm our model's expressivity and sample efficiency advantages compared to previous designs. We envision our proposal to encourage the exploration of continuous generative models running with few quantum resources.

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arXiv2024

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard

Determining whether an abstract simplicial complex, a discrete object often approximating a manifold, contains multi-dimensional holes is a task deeply connected to quantum mechanics and proven to be QMA1-hard by Crichigno and Kohler. This task can be expressed in linear algebraic terms, equivalent to testing the non-triviality of the kernel of an operator known as the Combinatorial Laplacian. In this work, we explore the similarities between abstract simplicial complexes and signed or unsigned graphs, using them to map the spectral properties of the Combinatorial Laplacian to those of signed and unsigned graph Laplacians. We prove that our transformations preserve efficient sparse access to these Laplacian operators. Consequently, we show that key spectral properties, such as testing the presence of balanced components in signed graphs and the bipartite components in unsigned graphs, are QMA1-hard. These properties play a paramount role in network science. The hardness of the bipartite test is relevant in quantum Hamiltonian complexity, as another example of testing properties related to the eigenspace of a stoquastic Hamiltonians are quantumly hard in the sparse input model for the graph.

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