Quantum Techniques in Machine Learning

6 Dec 2026, 08:00 → 11 Dec 2026, 17:00 Africa/Johannesburg

Jan Mouton Learning Centre (Stellenbosch University)

Adrián Pérez-Salinas (ETH Zürich - UPM), Amira Abbas, Dean Brand, Francesco Petruccione (NITheCS)

 

 

QTML 2026 brings together the brightest minds in quantum computing and machine learning for five days of cutting-edge research, collaboration, and discovery. Hosted for the first time in Stellenbosch, South Africa, the 10th edition of this flagship conference continues the tradition of excellence established across three continents. 

Through a series of scientific talks and discussions, QTML fosters collaboration and advances research on the interplay between quantum mechanics and machine learning, from foundational theory to real-world applications.

QTML was first hosted in Verona, Italy (2017), then in Durban, South Africa (2018),  Daejeon, South Korea (2019), virtual (2020, hosted by Zapata Computing), virtual (2021, hosted by RIKEN-AIP), Naples (2022), CERN (2023), Melbourne (2024), Singapore (2025).

For more information, please visit our website.

Sunday 6 December

Tutorials: Dominik Hangleiter

12:30 Lunch

Tutorials: Alexander Schmidhuber

15:00 Coffee break

Tutorials: Jonas Helsen

Monday 7 December

08:00 Registration

Open sessions: Welcome session

Invited talk: Maria Schuld

10:30 Coffee break

Contributed talks: Monday 1

1 Quantum machine learning advantages beyond hardness of evaluation

Recent years have seen rigorous proofs of quantum advantages in machine learning, particularly when data is labeled by cryptographic or inherently quantum functions. These results typically rely on the infeasibility of classical polynomial-sized circuits to evaluate the true labeling function. While broad in scope, these results however reveal little about advantages stemming from the actual learning process itself.
This motivates the study of the so-called identification task, where the goal is to ``just'' identify the labeling function behind a dataset, making the learning step the only possible source of advantage. The identification task also has natural applications, which we discuss. Yet, such identification advantages remain poorly understood. So far they have only been proven in cryptographic settings by leveraging random-generatability, the ability to efficiently generate labeled data. However, for quantum functions this property is conjectured not to hold, leaving identification advantages unexplored.
In this work, we provide the first proofs of identification learning advantages for quantum functions under complexity-theoretic assumptions. Our main result relies on a new proof strategy, allowing us to show that for a broad class of quantum identification tasks there exists an exponential quantum advantage unless BQP is in a low level of the polynomial hierarchy.
Along the way we prove a number of more technical results including the aforementioned conjecture that quantum functions are not random generatable, which shows a new proof strategy was necessary. These findings suggest that for many quantum-related learning tasks, the entire learning process—not just final evaluation—gains significant advantages from quantum computation.

Speaker: Riccardo Molteni (Leiden University)

QTML.pdf

2 Efficient Learning of Structured Quantum Circuits via Pauli Dimensionality and Sparsity

We study the problem of efficiently learning an unknown $n$-qubit unitary channel in diamond distance given query access. We present a general framework showing that if Pauli operators remain low-complexity under conjugation by a unitary, then the unitary can be learned efficiently. This framework yields polynomial-time algorithms for a wide range of circuit classes, including $O(\log \log n)$-depth circuits, quantum $O(\log n)$-juntas, near-Clifford circuits, the Clifford hierarchy, fermionic matchgate circuits, and certain compositions thereof. Our results unify and generalize prior work, and yield efficient learning algorithms for more expressive circuit classes than were previously known.

Our framework is powered by new learning algorithms for unitaries whose Pauli spectrum is either supported on a small subgroup or is sparse. If the Pauli spectrum is supported on a subgroup of size $2^k$, we give an $\widetilde{O}(2^k/\epsilon)$-query algorithm and a nearly matching $\Omega(2^k/\epsilon)$ lower bound. For $k = 2n$, we recover the optimal $O(4^n/\epsilon)$-query algorithm of Haah, Kothari, O’Donnell, and Tang [FOCS ’23]. If the Pauli spectrum is supported on $s$ Pauli operators, we give an $O(s^2/\epsilon^2)$-query algorithm and an $\Omega(s/\epsilon)$ lower bound.

Speaker: Sabee Grewal (IBM Quantum, Columbia University)

qtml-unitary-tomo.pdf

3 Towards robust quantum advantage in sequence learning with a single reliable gate

While most quantum algorithms either offer sampling advantages with zero fault tolerance or computational advantages with universal fault tolerance, early fault-tolerant quantum devices occupy an intermediate regime in which substantial but not fully universal error-corrected computation is possible. This contrast motivates the question of whether quantum-classical separations can be achieved with substantially sub-universal fault-tolerance. We propose a family of such problems based on sequence learning: two long sequences are respectively given to an encoder and a decoder, and the encoder may pass a short representation of its sequence to the decoder. The decoder must then learn to compute a function of the two sequences. We give a quantum algorithm for sequence learning, indexed by a parameter $k$, such that all training can be done efficiently completely classically, and the entire learned circuit uses only a single $k$-qubit phase gate (plus initialization and a final $X$-basis measurement).

Next we construct an explicit distributional problem based on polynomial evaluation, and prove that our quantum algorithm succeeds perfectly using $n$ qubits passed from encoder to decoder. On the other hand, we prove that every classical linear encoder requires $\Omega(n^k)$ bits to achieve constant advantage over random guessing, and conjecture that the same lower bound holds for all classical encoders, giving an $n^k$ memory separation realizable with a single reliable gate. In practice, we find numerically that the quantum model often outperforms natural classical counterparts even on much simpler problems, suggesting that this model may be of more generic utility beyond carefully constructed tasks.

Speaker: Jonathan Lu (Massachusetts Institute of Technology)

hypergraph_QTML.pdf

4 Distributed Quantum Property Testing with Communication Constraints

We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $\rho$, before communicating via a constrained communication channel with a central node, which aims to infer some property of $\rho$. This framework generalizes the classical distributed inference framework (Acharya, Canonne, and Tyagi COLT2019), by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state $\sigma$, decide whether $\rho=\sigma$ or $\|\rho-\sigma\|_1\geq \epsilon$. Additionally, we focus on the case of limited \textit{quantum} communication between distributed nodes and the central node. We show that when each communication channel is limited to only $n_q\leq \log d$ qubits, then the sample complexity of distributed state certification is $\mathcal{O}(\frac{d^2}{2^{n_q}\epsilon^2})$ when public randomness is available to all nodes. Moreover, under the assumption that the channels used by the distributed nodes are \emph{mixedness-preserving}, we prove a matching lower bound. We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an $\Omega(\frac{d^3}{4^{n_q} \epsilon^2})$ lower bound in the \emph{private-coin} setting under the same assumption as above. Our lower bounds leverage a recently introduced quantum analogue of the celebrated Ingster--Suslina method and generalize arguments from the classical setting. Together, our work provides the first characterization of distributed quantum state certification in the regime of limited quantum communication and establishes a general framework for distributed quantum inference with communication constraints.

Speaker: Mr Chirag Wadhwa (University of Edinburgh)

Distributed_quantum_property_testing.pdf

5 Provable and scalable quantum Gaussian processes for quantum learning

Quantum machine learning has become increasingly popular, but despite tremendous efforts, some of its central issues like trainability, scalability, poor local minima, interpretability, and reliable generalization from limited quantum data still remain. This motivates a different organizing principle for quantum learning, where the model is not chosen as a flexible ansatz, but is instead dictated by the structure and symmetries of the underlying quantum process. Here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The corresponding quantum kernel is not a heuristic similarity measure, but the covariance induced by prior knowledge of the process and measurement, injecting a physics-informed inductive bias into the learning model. Our main theoretical result proves that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, yielding the first family in our framework where the unknown unitary acts non-trivially on all qubits. We demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. These results establish quantum Gaussian processes as a principled route toward structured, uncertainty-aware, and scalable quantum learning. This extended abstract summarizes work available as an arXiv preprint: https://arxiv.org/abs/2605.00099

Speaker: Jonas Jäger

Provable_and_scalable_quantum_Gaussian_processes_for_quantum_learning.pdf

12:40 Lunch

Invited talk: Richard Küng

Contributed talks: Monday 2

6 Covert Quantum Learning: Privately and Verifiably Learning from Quantum Data

Quantum learning from remotely accessed quantum compute and data must address two key challenges: verifying the correctness of data (verifiability) and ensuring the privacy of the learner’s conclusions (covertness). Inspired by the classical covert (verifiable) learning model of Canetti and Karchmer (TCC 2021), we propose the first models of covert verifiable learning in quantum learning theory and realize them without computational hardness assumptions for remote data access scenarios motivated by established quantum data advantages. Namely, we design covert algorithms for:

(1) learning quadratic functions from public quantum examples and private quantum statistical queries;

(2) Pauli shadow tomography and stabilizer state learning from public multi-copy and private single-copy quantum measurements;

(3) verifiably solving Forrelation and Simon's problem from public quantum queries and private classical queries when the adversary is an i.i.d. ancilla-free eavesdropper.

Our models and corresponding algorithms demonstrate that important, large quantum advantages in learning are privately and verifiably achievable even with untrusted, remote data.

Speakers: Abhishek Anand (Caltech), Ari Karchmer (Morgan Stanley), Matthias C Caro (University of Warwick), Saachi Mutreja (Columbia University)

Covert_EA.pdf

7 Cloning is as Hard as Learning for Stabilizer States

The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to fully learn the state. Rather than arbitrary unknown states, modern quantum learning theory often considers structured classes of states and exploits such structure to develop learning algorithms that outperform general-state tomography. This raises the question: How do the sample complexities of learning and cloning relate for such structured classes?
We answer this question for an important class of states. Namely, for $n$-qubit stabilizer states, we show that the optimal sample complexity of cloning is $\Theta(n)$. Thus, also for this structured class of states, cloning is as hard as learning. To prove this result, we use representation-theoretic tools in the recently proposed Abelian State Hidden Subgroup framework and a new structured version of the recently introduced random purification channel to relate stabilizer state cloning to a variant of the sample amplification problem for probability distributions that was recently introduced in classical learning theory. This allows us to obtain our cloning lower bounds by proving new sample amplification lower bounds for classes of distributions with an underlying linear structure. Our results provide a more fine-grained perspective on No-Cloning theorems, opening up connections from foundations to quantum learning theory and quantum cryptography.

Speakers: Nikhil Bansal (Department of Computer Science, University of Warwick), Dr Matthias C. Caro (Department of Computer Science, University of Warwick), Dr Gaurav Mahajan (Department of Computer Science, Yale University)

qtml-ea.pdf

15:10 Coffee break

Contributed talks: Monday 3

8 Learning Arbitrary Lindbladians with Quantum Error Correction

We study ansatz-free Lindbladian learning, the problem of reconstructing the generator of an open quantum system without prior knowledge of its Hamiltonian or dissipator structures. This problem exhibits two distinct information-theoretic precision limits: Hamiltonian components unmasked by dissipation are Heisenberg-limited, while the remaining Lindbladian components are subject to the quadratically worse standard quantum limit. Existing approaches that attain these optimal scalings strongly rely on pre-specified structure of interaction and noise, leaving the ansatz-free setting an open problem. In this work, we present the first standard-quantum-limited algorithm for learning arbitrary sparse Lindbladians. Under an additional physically motivated regularity condition, our framework also learns the Hamiltonian component disjoint from the dissipator at the Heisenberg limit, without prior knowledge of either the Hamiltonian or dissipator supports. Our main technical ingredient is a recursive random stabilizer-code construction that suppresses the strongest Lindbladian terms while preserving sensitivity to weaker unknown ones. These results establish a scalable framework for characterizing open quantum systems, with quantum error correction serving as a key learning primitive.

Speaker: Mr Petr Ivashkov (ETH Zürich)

Extended_Abstract_QTML_2026.pdf

9 Learning scalable entanglement distribution policies

A quantum internet must distribute entanglement across imperfect repeaters, where the order in which each node waits, swaps, or purifies its links sets how fast and how reliably it is delivered. Choosing that order is a sequential decision problem: the dominant "swap-as-soon-as-possible'' (swap-asap) heuristic is optimal only for perfect hardware, and learned policies so far are tied to a single fixed network, leaving scalability open. We parameterise the per-node policy with a size-agnostic graph neural network (GraphSAGE) trained by Double-DQN, so one set of weights acts on a chain of any length. Trained on small imperfect chains ($N=4$-$10$), it transfers without retraining to larger ones ($N=10$-$15$) outperforming hand-crafted heuristics, with the advantage growing at the unseen sizes and vanishing only where swap-asap is already optimal.

Speaker: Christos Chalkias (Leiden University)

QRN_GNN_EA.pdf

Open sessions: Poster session

Tuesday 8 December

08:00 Registration

Invited talk: Ryan Babbush

Contributed talks: Tuesday 1

10 Decoded Quantum Interferometry is Obstructed by Topological Structure

We study the performance of Decoded Quantum Interferometry (DQI) on typical instances of MAX-$k$-XOR-SAT. We prove that if the decoding step of DQI corrects up to the maximum threshold of the best known computationally efficient decoders (e.g. belief propagation), then DQI is obstructed by a topological feature of the near-optimal space of solutions known as the overlap gap property (OGP). We then show that, for sufficiently large constant $k$, MAX-$k$-XOR-SAT exhibits an OGP. As the OGP is widely conjectured to exactly characterize the asymptotic performance of state-of-the-art classical algorithms, this result suggests that DQI has no quantum advantage on MAX-$k$-XOR-SAT instances exhibiting an OGP using the best known efficient classical LDPC decoders. We also give numerical evidence supporting this conjecture by showing that approximate message passing (AMP)—a classical algorithm conjectured to saturate the OGP threshold—outperforms DQI on a related ensemble of MAX-$k$-XOR-SAT instances. Finally, we prove that depth-$1$ QAOA outperforms DQI at sufficiently large $k$ under the same decoding threshold assumption.

Our result follows by showing that DQI is approximately Lipschitz under the quantum Wasserstein metric over many standard ensembles of codes. We then prove that MAX-$k$-XOR-SAT exhibits both an OGP and a related topological obstruction known as the chaos property; this is the first known OGP threshold for MAX-$k$-XOR-SAT at fixed, sufficiently large $k$, which may be of independent interest. Finally, we prove that both of these topological properties inhibit approximately Lipschitz algorithms such as DQI from optimizing MAX-$k$-XOR-SAT to large approximation ratio with any constant probability.

Speakers: Eric Anschuetz (Caltech), Jonathan Lu (Massachusetts Institute of Technology)

OGP_QTML.pdf

11 Canonical quantization of neurons

Canonical quantization provides a systematic procedure for constructing
quantum models from classical Hamiltonians. Here, we apply this principle to a fundamental computational primitive of machine learning: the neuron. Specifically, by viewing a neuron as a composition of an energy function and an activation function, we quantize this model by replacing the energy function with a quantum Hamiltonian and applying the activation function to it through matrix functional calculus. This results in an activation observable that can be measured on an input quantum state. We investigate the use of these quantized neurons for function approximation, where the objective is to learn an unknown observable from labeled quantum data. For this purpose, we develop hybrid quantum–classical algorithms for training and evaluation, including procedures for measuring the activation observable and estimating gradients of the squared loss error. Our algorithms for gradient estimation rely on basic primitives like classical random sampling, the Hadamard test, and Hamiltonian simulation, and those for measuring an activation observable rely on quantum algorithms known as the power of one qumode and Schrödingerization. Numerical experiments demonstrate that our quantized neurons exhibit enhanced expressive capabilities relative to corresponding classical neurons on representative learning tasks. Our work establishes canonical quantization as a principled framework for constructing quantum machine learning primitives and provides a foundation for developing neural architectures tailored to quantum data.

Speaker: Mark Wilde (Cornell University)

fermi_dirac_machines_as_quantizations_of_neurons (8).pdf

10:30 Coffee break

Contributed talks: Tuesday 2

12 Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians

Topological data analysis (TDA) is a machine learning technique that uses topology to extract patterns from data and has shown the potential to exhibit quantum advantage. A key concept in TDA is persistent homology, which measures the robustness of topological information at different lengthscales. In this paper, we introduce and study the problem of normalized persistence, a practically motivated and easily interpretable version of persistent homology that counts the fraction of holes that persist at different lengthscales. We prove that a variant of normalized persistence is $\mathsf{DQC}_1$-hard and contained in $\mathsf{BQP}$, giving evidence of an exponential quantum speedup
for TDA under the standard assumption that $\mathsf{DQC}_1 \not\subseteq \mathsf{BPP}$. These are the first $\mathsf{DQC}_1$-hardness results that are directly applicable to TDA instances.
We also find a close connection between normalized persistence and the
complexity of estimating spectral quantities in the low-energy subspace of local Hamiltonians. We study a family of such problems, including a low-energy normalized subtrace and spectral density. We show that these are $\mathsf{DQC}_1$-hard for $O(1)$-local Hamiltonians, strengthening previous results that required log-local interactions. We also introduce a variant of $\mathsf{DQC}_1$ with perfect completeness ($\mathsf{SDQC}_1$) to characterize the hardness of problems normalized by an exact kernel. This includes normalized persistence for $O(1)$-local Hamiltonians, which we show is $\mathsf{SDQC}_1$-hard.

Speakers: Dominic Lowe (Imperial College London), Ryu Hayakawa (Kyoto University)

Normalized Persistence (Extended Abstract).pdf

13 Quantum principal component analysis without eigenvector recovery

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-k projection. These steps can be computationally costly in high-dimensional and quantum-data settings, sensitive to small eigengaps, and unnecessary when downstream tasks only require principal-subspace scores. Such score-based objectives are important in applications such as anomaly detection, spectral-energy profiling, and other postselection tasks. To address these needs, we introduce a measurement-based soft PCA framework that replaces the hard top-k projector with an entropy-regularized Fermi--Dirac filter. This filter is the unique optimizer of an entropy-regularized variational formulation of PCA and converges to the classical PCA projector in the zero-temperature limit.

This filter has a direct interpretation as a quantum measurement, which naturally suggests a quantum approach. For centered covariance operators represented by quantum feature states, a single fixed circuit, together with threshold calibration, accesses all optimal filters for different rank budgets or retained-variance levels without rank-dependent circuit updates or eigenvector recovery. For new inputs, the same calibrated quantum circuit yields soft principal subspace scores, spectral energy profiles, and postselected filtered states. The required centering of both training and test data is performed coherently inside the quantum protocol, which is particularly important for quantum data where no classical feature vectors or centered Gram matrix are directly available. By reframing PCA as a calibrated measurement task, this framework bypasses the need for iterative eigenvector extraction and achieves a dimension-independent sample complexity $O(\eta^{-2})$ for normalized fractional-rank or retained variance scoring at additive accuracy $\eta$.

Speaker: Yewei Yuan (Shanghai Jiao Tong University)

abstract.pdf

arxiv_attach.pdf

14 On the Query Complexity of Quantum Mean Estimation for Multivariate Heavy-Tailed Distributions

We study quantum mean estimation for multivariate heavy-tailed distributions. Specifically, we consider random vectors whose $p$-th central moment is bounded for some $p\in(1,2]$; this includes the bounded-variance case when $p=2$, while allowing infinite variance when $p<2$. We first propose a quantum heavy-tailed mean estimator ($\texttt{QHTME}$), for estimating the mean of random variables under this heavy-tailed assumption. In the low-dimensional regime, $\texttt{QHTME}$ achieves a lower query complexity than the optimal classical heavy-tailed mean estimator while recovering the known bounded-variance quantum query complexity when $p=2$. We further develop an unbiased quantum mean estimator, denoted by $\texttt{QUHTME}$, by combining $\texttt{QHTME}$ with a generalized multi-level Monte Carlo technique. On the quantum lower bound side, we show that, when the dimension $d$ is small and can be treated as a constant, our quantum mean estimators are optimal up to logarithmic factors. We also establish a dimension-dependent lower bound in the low-dimensional regime by introducing a new hard primitive based on bit-string recovery and search problems. Finally, we show that these quantum heavy-tailed mean estimators lead to provable quantum speedups for stochastic optimization with heavy-tailed stochastic gradient noise, suggesting a route toward quantum advantages for machine-learning-relevant optimization problems in the heavy-tailed setting.

Speaker: Bin Luo (The Chinese University of Hong Kong)

QTML_On_the_Query_Complexity_of_Quantum_Mean_Estimation_For_Multivariate_Heavy_Tailed_Distributions (1).pdf

15 An unbounded quantum memory advantage for reinforcement learning world models

World models allow reinforcement-learning agents to evaluate actions in simulation before acting. For planning, however, reproducing typical simulated trajectories is not enough: the model must sample futures conditioned on a specified history and candidate action. This distinction is critical in safety settings, where a rare history, such as a pedestrian suddenly entering the road, can determine whether an otherwise successful policy acts catastrophically. Here we investigate whether quantum memory can improve such conditional world modeling. We formulate quantum world models as finite-dimensional conditional quantum simulators for planning, and introduce a quantum bisimulation distance that turns errors between memory states into guarantees on values and action-values. We then construct a controlled task in which the rare histories relevant for control have conditional futures that cannot be represented exactly by any finite classical world model. Consequently, every finite classical world model incurs an action-value error bounded below by a constant independent of its number of memory states. In contrast, a single qutrit samples the required conditional futures exactly, yielding zero planning error for every policy and for optimal control. Our results show that finite quantum memory can provide exact conditional simulators for reinforcement-learning tasks beyond the reach of finite classical memory.

Speakers: Dr Hailan Ma (Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore and Centre for Quantum Technologies), Dr Josep Lumbreras (Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University and Centre for Quantum Technologies, Singapore)

longabstractqmtl_v3.pdf

16 Representation theory for passive linear optics: anti-concentration, barren plateaus and classical simulability

Photonic quantum systems are a promising platform for near-term quantum technologies, combining low noise, high-fidelity linear-optical operations, and scalability to large numbers of optical modes. In this work, we develop the first general framework for computing second moments of particle-number-preserving bosonic observables under Haar-random passive linear-optical transformations. Exploiting representation-theoretic tools for the unitary group, we derive closed-form expressions valid for arbitrary number of photons and modes. We identify a class of observables, which we call generalised parity operators, that can evade concentration while seemingly remaining beyond the reach of currently known simulation techniques, suggesting a regime in which trainability and classical hardness may coexist. Moreover, we further establish anti-concentration of Boson Sampling output probabilities in the experimentally relevant regime, resolving an open conjecture and taking a step closer to a rigorous proof of the hardness of boson sampling.

Speaker: Hela Mhiri (LIP6, EPFL)

extended-abstract-qtml.pdf

12:40 Lunch

Invited talk: Robin Kothari

Contributed talks: Tuesday 3

17 Private training in quantum machine learning

With the emergence of machine learning (ML) models trained on large datasets containing potentially sensitive data, a major question in AI safety is how to make learning private with respect to the training data. Similar to classical machine learning, quantum machine learning (QML) models are not devoid of privacy vulnerabilities. Differential privacy (DP) is a standard tool for training ML models on sensitive data, but its impact in QML remains poorly understood. In this work we study private training in hybrid variational QML models using a classical private DP-SGD optimizer applied to pipelines with classical inputs and outputs. We analyze the interplay between gradient clipping and calibrated noise addition in DP-SGD, and its impact on optimization and accuracy for noisy and noiseless quantum models. We first explain why quantum noise does not provide a satisfactory replacement for the calibrated noise in DP-SGD for ensuring privacy. We then show how the deterministic bounds on gradient norms for a wide class of quantum models translate into explicit control of the detrimental clipping bias introduced by DP-SGD. Finally, we formulate a numerical comparison protocol under fixed clipping threshold and privacy budget and evaluate it on synthetic and image-classification tasks for equivalent quantum and classical models. Our results suggest that quantum models can retain higher accuracy in private-training regimes where the formal privacy guarantee is ensured by a classical DP-SGD mechanism.

Speaker: Tigran Sedrakyan (LIP6)

extended_abstract.pdf

main.pdf

15:10 Coffee break

Open sessions: Discussion on Generative AI

Open sessions: Poster session

Wednesday 9 December

08:00 Registration

Invited talk: Gorka Muñoz-Gil

Contributed talks: Wednesday 1

18 Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions

Quantum convolutional neural networks (QCNNs) are quantum circuits for characterizing complex quantum states. They have been proposed for recognizing quantum phases of matter at low sampling cost and have been designed for condensed matter systems in one dimension. Here we construct a QCNN that can perform phase recognition in two dimensions and correctly identify the phase transition from a Toric Code phase with $\mathbb{Z}_2$-topological order to the paramagnetic phase. The network also exhibits a noise threshold up to which the topological order is recognized. Furthermore, it captures correlations between all stabilizer elements of the Toric Code, which cannot be accessed by direct measurements. This increases the threshold for errors leading to such correlations and allows for correctly identifying the topological phase in the presence of strong correlated errors. Our work generalizes phase recognition with QCNNs to higher spatial dimensions and intrinsic topological order, where exploration and characterization via classical numerics become challenging.

Speaker: Leon C. Sander (Friedrich-Alexander-Universität Erlangen-Nürnberg)

extAbstract_Sander.pdf

19 Automated near-term quantum algorithm discovery for molecular ground states

Abstract submission for a talk.

Speaker: Konstantinos Meichanetzidis (Quantinuum)

Quantinuum_Hiverge_QTMLAbstract (5).pdf

20 Hybrid quantum-classical neural network for sample-efficient recognition of topological phases

With increasing maturity of quantum computers, standard methods for characterizing global properties of their output quantum states via direct measurements and classical post-processing are becoming increasingly impractical due to large measurement costs. Here, we introduce, numerically benchmark and experimentally realize a hybrid quantum-classical neural network, consisting of a shallow parameterized quantum circuit followed by measurements and a classical neural network. The parameterized quantum circuit performs a nonlocal transformation of the measurement basis, which is jointly trained with the classical neural network to maximize the statistical distance between data obtained by measuring different quantum states. Using supervised learning, we demonstrate that the hybrid neural network distinguishes the topological phase of the surface code from both a symmetry-enriched topological phase and random product states. Compared with a classical neural network trained on randomized Pauli measurements, the hybrid neural network reduces both training and inference sample complexities for recognizing topological phases by approximately one order of magnitude. Enabled by its shallow quantum circuit, we demonstrate training of the hybrid neural network on a superconducting quantum processor with quantum hardware in the loop. These results establish the hybrid neural network as a promising framework for sample-efficient characterization of complex quantum states on current and near-term quantum hardware.

Speaker: Markus K. Hoffmann (Friedrich-Alexander Universität Erlangen-Nürnberg)

HNN_QTML2026_Extended_Abstract.pdf

10:40 Coffee break

Contributed talks: Wednesday 2

21 Learning to Reconstruct Wigner Functions in Phase Space

Wigner function learning is a central tool for characterizing continuous variable quantum systems. A fundamental challenge in this setting is to infer a continuous phase-space function from sparse pointwise measurement data, a task that becomes increasingly demanding as the effective dimension enlarges. Here, we develop a general machine learning framework to reconstruct Wigner functions directly as continuous functions from sparse phase-space data. For states with sparse Fock-space or coherent-state representations, such as binomial code states and cat states, we devise provably efficient regression models whose measurement complexity scales only logarithmically with the effective Hilbert-space dimension. For more general states, such as the Gottesman–Kitaev–Preskill (GKP) states, we design a deep learning model that reconstructs the Wigner function from sparse measurements and generalizes to arbitrary phase-space resolution. We demonstrate the broad applicability of our framework on both simulated data and experimental data from a circuit quantum electrodynamic (circuit-QED) system. Interestingly, on experimental data, we find that our model reconstructs Wigner functions of GKP code states across multiple rounds of quantum error correction and identifies the dominant error process using significantly fewer measurements than conventional estimation techniques.

Speakers: Ms Xinyu Tang (Shanghai Jiaotong University), Yi-hsin Lin

QTML_2026_Wigner_Learning.pdf

22 Harnessing imperfect quantum data through domain adaptation

Classical supervised learning from quantum measurements can extract useful physical information. However, regimes of interest often lack reliable labels and involve imperfect state preparation, while labels may be available only in easier regimes with different distributions. Can unlabeled measurement data from imperfectly prepared states be combined with these labeled data to learn an accurate predictor?

We address this question by constructing a practical end-to-end unsupervised domain adaptation (UDA) pipeline using Pauli classical shadows and conditional domain-adversarial learning. It requires neither labels in the regime of interest nor post-measurement quantum processing. Numerical studies and a 144-qubit real-device demonstration answer this question positively.

In numerical simulations, it considerably improves phase classification in the cluster model and ANNNI model using clean labeled data from restricted parameter regions and imperfect unlabeled data from broader regions. It also improves classification of separable and entangled states when data quality and partitions defining separability differ.

Our key result is a 144-qubit demonstration on the IBM Quantum processor ibm_kawasaki, classifying topological and trivial phases on a rotated surface code. The learner receives only unlabeled shadows of states generated and measured on real quantum hardware using non-Clifford random circuits, but can classically generate labeled measurement data for analogous Clifford-circuit examples. Training only on labeled simulated data fails on the hardware data (macro-F1 0.322), whereas UDA achieves 0.958 without hardware-data labels. This success with real experimental quantum data at an application-relevant scale motivates applying UDA to extend the practical reach of imperfect experimental quantum data when reliable labels are unavailable.

Speaker: Kosuke Ito (Toyota Motor Corporation)

Q_Domain_adaptation.pdf

23 One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective

Neural quantum states (NQS) provide a flexible and scalable framework for approximating quantum many-body wavefunctions. Among NQS parameterizations, autoregressive models are especially attractive because they enable exact, independent sampling from the Born distribution, avoiding the autocorrelation and mixing issues of Markov chain methods. Yet their optimization remains comparatively underexplored: Adam is a scalable method but ignores function space geometry, while stochastic reconfiguration is principled but costly and numerically fragile in large models. To address this gap, we show that variational energy minimization can be viewed as an advantage policy-gradient problem over the Born distribution, motivating trust-region optimization for NQS training. We introduce Proximal Wavefunction Optimization (PWO), a principled trust-region algorithm that clips probability-ratio changes in the amplitude channel and phase increments in the phase channel. PWO avoids explicit matrix inversion, reuses samples across multiple updates, and combines the scalability of first-order optimization with theoretical guarantees. Across Ising and frustrated $J_1$-$J_2$ one- and two-dimensional spin systems, PWO improves stability and wall-clock convergence over Adam, minSR, and SPRING. Finally, we fine-tune a $1.5$B-parameter RWKV-7 model, demonstrating NQS optimization at a scale over three orders of magnitude beyond prior work.

Speaker: Mr Sergio García Heredia (aQa, LION, Leiden University, Leiden, The Netherlands)

QTML_PWO_extended_abstract.pdf

24 Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model

Reinforcement learning is a subfield of machine learning that studies how an agent interacts with an environment in order to extract as large a reward as possible. A standard approach to study such interaction is through Markov Decision Processes (MDPs) and the choice for an optimal policy --- a function that tells the agent which action to take. In this work, we study two types of MDPs --- finite-horizon and infinite-horizon discounted --- and propose new quantum algorithms for computing approximate optimal policies. Our quantum algorithms are based on a new combination of standard value iteration and quantum subroutines like quantum mean estimation and quantum minimum finding, overall enhanced with techniques from the sample-optimal classical algorithms. Our resulting query complexities improve upon previous works, thus approaching already established quantum lower bounds.

Speaker: Joao F. Doriguello (HUN-REN Alfréd Rényi Institute of Mathematics)

Optimal_Policies_MDPs.pdf

12:30 Lunch

Invited talk: Ben Jaderberg

Contributed talks: Wednesday 3

25 Machine-learned syndrome post-selection for reliable quantum error correction

Quantum error correction can be enhanced by rejecting runs that are likely to fail logically, but the most informative confidence metrics often require costly decoder-level likelihood information. We introduce a decoder-agnostic post-selection method that learns an abort score directly from syndrome data. A supervised classifier is trained only to distinguish syndromes sampled from low- and high-noise regimes; its output is then used to rank new runs before decoding. No logical-error labels, correction operators, or code-specific likelihood calculations are required. We apply the method to experimental logical magic-state-distillation data from a QuEra neutral-atom processor. The classifier is trained entirely on simulated syndrome data generated from a calibrated noise model and is then transferred directly to experimental data. The learned score improves experimental fidelity beyond syndrome-weight filtering and, when combined with logical-gap post-selection, improves the fidelity-throughput trade-off beyond using the logical gap alone. We have also tested the method in circuit-level simulations of the $[[144,12,12]]$ Gross bivariate-bicycle code and code-capacity simulations of the surface code, with complete numerical results reported in an accompanying preprint. These results establish syndrome-only learning as a practical machine-learning layer for reliable quantum error correction.

Speaker: Askery Canabarro (Technology Innovation Institute)

qtml_2026_dr_haug_fv.pdf

26 Multi-Agent Reinforcement Learning for Context-Aware Real-Time Error Suppression

Quantum processors are limited by coherent errors that depend on the circuit context in which each gate operates, a dependence that conventional calibration protocols do not capture because they characterize gates in isolation. We present CARTES (Context-Aware RealTime Error Suppression), a framework that applies model-free multiagent reinforcement learning (MARL) to adapt pulse-level gate parameters to the surrounding circuit context during execution.

Our work features two main contributions:

1. In simulations of a six-qubit superconducting chain that is subject to microwave crosstalk and static ZZ coupling, three RL agents calibrate three parallel two-qubit gates. The agents raise the local average gate fidelity of every gate above 0.9979 and recover 87% to 95% of the gap between the context-agnostic baseline and the numerical contextual optimum.

2. Experimentally, we integrate the MARL workflow directly into the Quantum Orchestration Platform, which reduces communication and compilation latency while it preserves a flexible parametrization of custom calibrations. This integration enables contextual calibration within minutes of wall-clock time, versus the many hours typical of traditional closed-loop methods.

The method requires no extra controller memory and no extra latency, since a compact classical neural network infers the corrections in real time during circuit execution. Because the framework embeds learning into the control stack, it provides context-dependent error suppression at the cost of standard circuit execution, with direct applications in drift compensation and quantum error correction.

Speakers: Arthur Strauss (National University of Singapore), Mr Lukas Voss (Ulm University)

QTML2026.pdf

15:10 Coffee break

Contributed talks: Wednesday 4

27 Feed-Forward-Free Logical Two-Qubit Randomized Benchmarking with Steane QEC and Residual Machine-Learning Decoders

Machine-learning residual decoders improve Steane QEC in a feed-forward-free logical two-qubit randomized benchmarking (RB) experiment on neutral-atom platforms such as QuEra, where mid-circuit conditional gates are unavailable. Two logical qubits are encoded in Steane [[7,1,3]] blocks and initialized via the Goto fault-tolerant procedure. Logical two-qubit Clifford RB is applied transversally, while syndrome-extraction rounds are inserted between RB segments using fresh ancillas. All measurements are performed during the protocol but no run-time branching is allowed: syndrome data are read out at the end and correction is handled offline via Pauli-frame tracking (PFT), yielding a fixed circuit suitable for hardware execution.

We develop an analytic baseline decoder, LUT-PFT, that uses Steane distance-three X- and Z-type syndromes with a weight-one lookup table to update the Pauli frame rather than applying physical recovery gates. Our ML approach does not relearn Steane decoding from scratch; it learns a residual correction that captures structured, correlated decoder failures relative to LUT-PFT. Two residual classifiers are studied: BoostTree (XGBoost) and a two-stage neural network, both combined with the analytic Pauli frame, with a confidence-based fallback to LUT-PFT.

Noisy simulations of logical 2Q RB (sequence lengths 60–360; QEC rounds R = 0..40) show an intermediate optimal R and, in the low-R regime most relevant for near-term machines, learned residual decoding yields the lowest logical error rates and can outperform an unencoded physical two-qubit RB reference under the same noise model.

Speaker: Jan Balewski (NERSC/LBNL, USA)

Balewski_QTML2026.pdf

28 AQER: A Scalable and Efficient Data Loader for Digital Quantum Computers

Digital quantum computers promise computational capabilities beyond classical systems, but scarce qubits and limited coherence make data loading a persistent bottleneck. Approximate quantum loaders (AQLs) address this bottleneck by trading preparation fidelity for circuit complexity. We develop AQER, an AQL method that constructs loading circuits through maximal entanglement reduction. We first cast tensor-network, variational, and non-variational loaders into a unified optimization framework and derive information-theoretic bounds showing that AQL infidelity is controlled by the single-qubit entanglement entropy of the inverse-evolved target state. Guided by this result, AQER appends two-qubit blocks to reduce entanglement, analytically fits a product-state approximation, and refines all parameters. Experiments on classical image and language data, random-circuit states, and transverse-field Ising ground states up to 50 qubits show consistently lower infidelity with equal or fewer two-qubit gates than representative baselines.

Speaker: Kaining Zhang (Nanyang Technological University)

abstract.pdf

Main_AKER.pdf

29 Breaking concentration barriers for quantum extreme learning on digital quantum processors

We present a large-scale experimental realization of quantum extreme learning machines (QELMs) on superconducting quantum processors, scaling up to 124 qubits and circuits with more than 5,000 two-qubit gates. While quantum reservoir approaches offer enhanced expressivity via high-dimensional Hilbert spaces, their scalability can be hindered by hardware noise and concentration phenomena that suppress input–output distinguishability. We overcome this limitation by identifying a principled operating regime that balances expressivity, complexity, and statistical resolvability, and exhibits strong transferability across system sizes and tasks. Furthermore, we introduce a local eigentask framework for noise-aware feature selection with polynomial overhead, enabling efficient extraction of statistically resolvable observables in large-scale settings. We validate our approach on time-series forecasting and satellite image classification, achieving competitive performance with strong classical baselines under realistic experimental conditions, including demonstrations on processors using up to 124 qubits. These results establish QELMs as a viable and scalable paradigm for quantum machine learning on near-term hardware, and delineate a practical route toward large-scale quantum information processing.

Speakers: Timothée Dao (IBM Research Europe - Zurich), Francesco Tacchino (IBM Research Europe - Zurich)

Dao_Extended_Abstract.pdf

30 Quantum Maximum Likelihood Prediction via Hilbert Space Embeddings

Maximum likelihood prediction (MLP) is a core task at the heart of modern large language models. Here, we study a quantum version of this task for a simplified data model consisting of independent and identically distributed samples, as a first step. The quantum maximum likelihood predictor (QMLP) is obtained by embedding of empirical probability distributions into quantum states and performing a minimization of quantum relative entropy over a given class of states. We derive non-asymptotic performance guarantees for QMLP in terms of convergence rates and concentration inequalities, both in trace norm and quantum relative entropy. Our approach provides a unified framework to handle MLP within both classical and quantum LLMs.

Speakers: Prof. Nir Weinberger (Technion-Israel Institute of Technology), Sreejith Sreekumar (L2S, CNRS, CentraleSupelec, University Paris-Saclay)

QMLP-QTML-extended_abstract.pdf

Open sessions: Industry session

Thursday 10 December

08:00 Registration

Invited talk: Supanut Thanasilp

Contributed talks: Thursday 1

31 Fragmentation is Efficiently Learnable by Quantum Neural Networks

In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically disconnected subspaces. We introduce a learning problem known as fragment classification, where given a quantum state input, one is interested in classifying to which subspace the state belongs. We prove that solving this learning problem is efficient on a quantum computer when the fragmentation phenomenon satisfies certain conditions. Furthermore, we give evidence supporting the classical hardness of this task by demonstrating that known dequantization techniques fail for the fragment classification problem. Consequently, this work provides a rare example of a physically motivated quantum machine learning task that is both efficient for quantum computers to perform and admits no known classical dequantization.

Speaker: Mikhail Mints (Caltech)

Fragmentation_QNN_Paper_QTML_Submission.pdf

32 Training Variational Quantum Algorithms Is NP-hard, Even Locally

It is well known that globally optimizing the training objectives of Variational Quantum Algorithms (VQAs) is $\mathsf{NP}$-hard. This motivates the use of local optimization methods in practice, raising the question of whether finding locally optimal parameters is computationally easier. We show that it is not: finding a local optimum for VQA training is also $\mathsf{NP}$-hard. Our proof proceeds by establishing a bridge between polynomial optimization and VQA training, exploiting the connection between VQA objective functions and Hermitian trigonometric polynomials.

Speaker: Triscia Mundo (Singapore University of Technology and Design)

training-vqa-np-hard-locally-QTML2026.pdf

10:30 Coffee break

Contributed talks: Thursday 2

33 Warm Starts, Cold States: Exploiting Adiabaticity for Variational Ground-States

This submission is based on [arXiv:2602.06137]

Reliable preparation of many-body ground states is an essential task in quantum computing, with applications spanning areas from chemistry and materials modeling to quantum optimization and benchmarking. A variety of approaches have been proposed to tackle this problem, including variational methods. However, variational training often struggle to navigate complex energy landscapes, frequently encountering suboptimal local minima or suffering from barren plateaus. In this work, we
introduce an iterative strategy for ground-state preparation based on a stepwise (discretized) Hamiltonian deformation. By complementing the Variational Quantum Eigensolver (VQE) with adiabatic principles, we demonstrate that solving a sequence of intermediate problems facilitates tracking the ground-state manifold toward the target system, even as we scale the system size. We provide a rigorous theoretical foundation for this approach, proving a lower bound on the loss variance that suggests trainability throughout the deformation, provided the system remains away from gap closings. Numerical simulations, including the effects of shot noise, confirm that this path-dependent tracking consistently converges to the target ground state.

Speaker: Ricard Puig (École Polytechnique Fédérale de Lausanne (EPFL))

WS___metavqa (20).pdf

34 Challenges in Barren Plateau Mitigation with Dynamic Parameterized Quantum Circuits

Variational quantum algorithms (VQAs) are a promising paradigm for quantum advantage, yet their trainability is severely hampered by barren plateaus (BPs). Several works have proposed using dynamic parameterized quantum circuits (DPQCs) which intersperse unitary layers with parameterized CPTP maps (e.g. engineered dissipation, feedforward gadgets, or periodic resets), as a potential route around BPs. We unite this class of circuits into a formalization for DPQCs. We identify constraints on the nature and the structure of DPQCs if they are to prevent a significant number of parameters from becoming untrainable. We further show via purification and Pauli path analysis, a mechanism with which cost function anti-concentrates in DPQCs while still suffering from untrainability of a significant number of parameters. Our analysis reveals ways to design DPQCs that do not have an exponentially concentrated cost function, and our results suggest that BP mitigation via DPQCs is at least as hard as designing BP-free unitaries.

Speaker: Sumeet Shirgure (University of Central Florida)

qtml2026_abstract.pdf

35 Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA

We study MaxCut on 3-regular graphs of minimum girth $g$ for various $g$'s. We obtain new lower bounds on the maximum cut achievable in such graphs by analyzing the Quantum Approximate Optimization Algorithm (QAOA). For $g\geq16$, at depth $p \geq 7$, the QAOA improves on previously known lower bounds. Our bounds are established through classical numerical analysis of the QAOA's expected performance. This analysis does not produce the actual cuts but establishes their existence. When implemented on a quantum computer, the QAOA provides an efficient algorithm for finding such cuts, using a constant-depth quantum circuit. To our knowledge, this gives an exponential speedup over the best known classical algorithm guaranteed to achieve cuts of this size on graphs of this girth. Furthermore, our guaranteed cut fractions apply to random instances of large 3-regular graphs since they are effectively large girth for our purposes. We also apply the QAOA to the Maximum Independent Set problem on the same class of graphs.

Paper: arXiv:2503.12789.

Speaker: Benjamin Villalonga (Google Quantum AI)

villalonga_QTML_2026_submission.pdf

36 Reconciling Theory and Practice: Quadratic Acceleration of Variational Quantum Algorithms with Rotosolve

The Rotosolve algorithm leverages explicit knowledge about the objective function to perform exact minimisation along one coordinate at a time. Recently, we established its convergence, and derived explicit rates which match those of gradient-based methods. However, since Rotosolve uses additional information about the objective function, it is expected to outperform generic gradient-based optimisers. Empirical studies indeed demonstrate its superior performance. Further, the variance in the performance of Rotosolve across multiple experiments was inexplicably found to be higher than gradient-based methods. In this extended abstract, we address these discrepancies between theory and practice.
1. We first argue that the establishment of better convergence rates for Rotosolve requires the consideration of a stronger measure of performance than first-order stationarity, and introduce the notion of coordinate-wise second-order stationarity.
2. We consider the convergence of Rotosolve and gradient-based methods in the noise-free case. While the latter are guaranteed to converge only to first-order stationary points, Rotosolve converges to coordinate-wise second-order stationary points, yielding a quadratic acceleration over gradient-based methods. We further show that even in the absence of noise, Rotosolve has a higher variance than its gradient-based counterparts.
3. Under an additive noise model, we establish conditions under which Rotosolve retains its noise-free iteration complexity. Since these assumptions are not guaranteed to hold in practice, we are motivated to consider a relative-error noise model instead, and modify Rotosolve accordingly. Owing to space constraints, discussion on the relative noise model, the modified algorithm, and its analysis are deferred to an extended version of this paper.

Speaker: Sayantan Pramanik (TATA Consultancy Services, Indian Institute of Science)

Rotosolve_QTML.pdf

37 QAOA-MaxCut has barren plateaus for almost all graphs

See attached PDF file for extended abstract.

Speakers: Dr Rui Mao (School of Computer Science and Technology, University of Chinese Academy of Sciences), Dr Pei Yuan (Tencent Quantum Lab)

QAOA_MaxCut_Barren_Plateaus__QTML_2026_.pdf

12:40 Lunch

Invited talk: Zoltán Zimborás

Contributed talks: Thursday 3

38 IQP Born Machines under Data-dependent and Agnostic Initializations

Instantaneous quantum polynomial-time (IQP) circuits provide a natural framework for quantum generative modeling and are believed to be classically hard to sample from in certain regimes. We study the optimization landscape of IQP-based quantum circuit Born machines trained with Maximum Mean Discrepancy (MMD) losses constructed from low-body Pauli-$Z$ correlators. We prove that random full-range initializations exhibit barren plateaus, while identity and unbiased data-agnostic initializations admit non-vanishing loss variance lower bounds. We further introduce a data-dependent initialization that better aligns with the target distribution, yielding provable gradients and faster convergence in practice, including experiments on 150-qubit genomic datasets.

Speaker: Supanut Thanasilp (Chulalongkorn University)

extended_abstract_IQP_warmstart.pdf

39 Classically trainable quantum generative modeling with Boson and Fermion Sampling

Sampling-based quantum advantage schemes currently serve as the leading experimental demonstrations of computational tasks deemed intractable for classical devices. However, their practical significance remains a subject of intense debate as these tasks are synthetically designed to maximize classical hardness rather than to solve meaningful real-world problems. In this contribution, we propose a generative learning application of two such schemes: Fermion Sampling and Gaussian Boson Sampling. We show that, despite the classical hardness of sampling from their output distributions, the generative models built on these schemes can nevertheless be trained efficiently by classical means. We numerically demonstrate their performance and scalability, training fermionic and bosonic models with up to 160 qubits and 805 photonic modes, respectively.

Speakers: Zoltán Kolarovszki (HUN-REN WIgner Research Centre for Physics), Zoltán Zimborás (University of Helsinki)

qtml_extended_abstract_final.pdf

15:10 Coffee break

Contributed talks: Thursday 4

40 Instantaneous Quantum Polynomial Circuit Born Machines: Trainability, Non-Simulability, Expressivity and Applications

Instantaneous Quantum Polynomial Quantum Circuit Born Machines (IQP-QCBM) are emerging quantum generative models that have attracted increasing attention. IQP-QCBMs represent probability distributions over bitstrings through Born-rule measurements of parameterized IQP circuits. IQP-QCBMs are distinguished from many other quantum machine learning (QML) models in two ways: First, the models are conjectured to inherit the classical sampling hardness from IQP circuits under standard complexity-theoretic assumptions. Second, as showed, by exploiting the special circuit architectures of IQP circuits, the models can be trained on a classical computer using the maximum mean discrepancy (MMD) loss, while deployment on a quantum computer is required for sample generation.

In this work, we show that whether an IQP-QCBM exhibits a barren plateau (BP) depends on two practical design choices: the IQP circuit architecture and the kernel used in the MMD. We derived the closed-form expression of variance of the MMD loss gradient, and we identified the "critical rank" of the IQP-QCBM model, the dimension of the space spanned by the anti-commuting generators w.r.t. the observable, as the deciding factor for the presence or absence of BP.

Our analytical work provides guidance for avoiding architectures that are provably susceptible to BPs and narrows the design space of trainable IQP-QCBMs.

Specifically, we show that IQP-QCBMs whose architecture connectivity is generated by a sparse ER graph with $\mathcal{O}(n\log n)$ edges are trainable, while their output distribution family remains hard to approximate classically.

The full presentation will also include the characterization of IQP-QCBM’s expressivity and experiment results for material science applications.

Speaker: Kevin Shen

IQP_QTML (3).pdf

41 Classically trained, quantum-deployed generative models: universality and kernel-adaptive training

A fundamental bottleneck holds back quantum machine learning: heuristic quantum methods cannot yet be meaningfully tested, since current hardware cannot run them at interesting scales. The train-classically, deploy-quantumly paradigm offers a seemingly impossible guarantee: the training objective is evaluated efficiently on a classical computer, while sampling from the trained model may remain classically intractable. We show this paradigm can yield genuinely universal quantum generative models, on two very different classically hard sampling models: the instantaneous quantum polynomial (IQP) quantum circuit Born machine (QCBM) and the boson sampling Born machine (BSBM). For the IQP-QCBM, we give the first universality result for the model class: $n$ hidden qubits make an $n$-qubit generator universal in the worst case. We also introduce adversarial kernel-adaptive training, proving it strictly more discriminative than the fixed Gaussian kernel, and validate it with up to 784 qubits. We then realize the same paradigm in a very different model of computation, introducing the BSBM: a boson sampler with trainable optical parameters. We establish that it can be trained classically w.r.t. wide families of MMD losses. Its bare form is not universal, but a fixed postprocessing map restores universality, and we construct a sequence of models whose expressivity grows monotonically to universality while provably retaining classical sampling hardness. Together, these results advance the theory of classically trained, quantum-deployed generative modeling across two models of computation.

Speaker: Andrii Kurkin (Leiden Universiteit)

QTML_2026 (2).pdf

42 Spectral Born machines: Classically trainable quantum generative models for discrete data

We present \emph{spectral Born machines}, a class of quantum generative models that results from viewing and generalizing the class of IQP Born machines through the lens of group Fourier analysis. These quantum models exploit the quantum Fourier transform in order to induce smoothness priors that make them naturally suited to learning integer-structured data, while remaining classically hard to sample from in general. Similar to IQP Born machines, spectral Born machines can be trained efficiently at scale on classical hardware via a maximum mean discrepancy loss based on graph spectral analysis, which we make available in a new \emph{tcdq} module of the PennyLane software platform. In numerical experiments, we show how the spectral bias of the model leads to significantly reduced parameter counts compared to unstructured approaches, and demonstrate the scalability of the software by training a 190-qubit model with over 1 million parameters to successfully learn a distribution of 93 nucleotide-long ribosomal RNA. Our results suggest that highly over-parameterized spectral Born machines may be immune to overfitting, even in strongly data-scarce regimes.

Speaker: Joseph Bowles (Xanadu)

qtml_submission.pdf

43 Quantum thermodynamics and semidefinite optimization: Boltzmann, Fermi-Dirac, and Bose-Einstein frameworks

We show how quantum thermodynamics offers a unifying interpretation for a wide class of semidefinite programs (SDPs) that arise in quantum information. Three SDP variable constraints, namely trace-one density operators, operator-bounded measurements, and the unbounded positive semidefinite cone, admit thermodynamic regularizations associated with Boltzmann, Fermi-Dirac, and Bose-Einstein statistics, respectively. In each case the entropy-regularized dual is unconstrained and concave in a chemical-potential vector, and the primal optimum is a thermal operator of the matched statistics. The dual gradient and Hessian are thermal expectation values, enabling hybrid quantum-classical algorithms for solving a wide variety of SDPs. Building on the Boltzmann framework presented at QTML 2025 (arXiv:2505.04514), this extended abstract presents a unified picture of quantum thermodynamics and SDPs that incorporates the more recent Fermi-Dirac (arXiv:2603.04061) and Bose-Einstein (arXiv:2605.27228) works, which natively address measurement-bounded SDPs (and in particular quantum hypothesis testing) and standard-form SDPs over the unbounded positive semidefinite cone, respectively.

Speaker: Michele Minervini (Cornell University)

main.pdf

Open sessions: QTML Session

Friday 11 December

08:00 Registration

Contributed talks: Friday 1

44 Hamiltonian learning via quantum Zeno effect

Determining the Hamiltonian of a quantum system is essential for understanding its dynamics and validating its behavior. Hamiltonian learning provides a data-driven approach to reconstruct the generator of the dynamics from measurements on the evolved system, enabling the characterization and learning of quantum devices from experimental data. Among its applications, it is particularly important for benchmarking and validating quantum hardware, such as quantum computers and simulators. However, as these devices grow in size and complexity, this task becomes increasingly challenging. To address this, we propose a scalable and experimentally friendly Hamiltonian learning protocol for geometrically local Hamiltonians. It leverages the quantum Zeno effect as a reshaping tool to localize the system's dynamics and then applies quantum process tomography to learn the coefficients of local Hamiltonian terms acting on selected qubits. Unlike existing approaches, our method does not require complex state preparations and uses experimentally accessible, coherence-preserving operations. By decomposing a global Hamiltonian learning problem into independent local learning problems, the proposed framework also provides a natural starting point for learning-based approaches to the characterization and modeling of complex quantum systems. We derive theoretical performance guarantees and demonstrate the feasibility of our protocol through numerical simulations and an experimental implementation on IBM's superconducting quantum hardware, successfully reconstructing the coefficients of a 109-qubit Hamiltonian.

Speaker: Egle Pagliaro (ICFO - The Institute of Photonic Sciences)

hamiltonian_learning_zeno_effect_extended_abstract.pdf

45 Reversing Unknown Hamiltonian Evolutions through Algebraic Structure

Coherent inverse access is needed in amplitude amplification, time-reversal tests, and scrambling probes, but exact black-box inversion of an unknown $d$-dimensional unitary has quadratic query cost. We ask what changes when the oracle is a Hamiltonian evolution $U(x)=\exp(i\sum_j x_j H_j)$ with known generators and unknown couplings. In a compiled-structure query model, fixed gates may depend on the known generator algebra while only coherent calls to the unknown forward evolution are counted. For one Hamiltonian with known eigenspaces, $K-1$ queries suffice for $K$ distinct eigenvalues, and the optimum is an additive sumset condition on the distinct spectrum. For multi-parameter families, Wedderburn reduction removes passive multiplicity wires, and local active-block inverses can be recombined by synchronizing their query lengths and residual scalar phases. Determinant, trace-vector, and automatic-completion constructions give explicit exact protocols. Exchange, hopping, and collective-spin examples show query budgets controlled by active representation data rather than by the full many-body Hilbert space.

Speakers: Jizhe Lai (The Hong Kong University of Science and Technology (Guangzhou)), Mingrui Jing (The Hong Kong University of Science and Technology (Guangzhou)), Erdong Huang (The Hong Kong University of Science and Technology (Guangzhou))

Inverse_Structured_Hamiltonian_ext_abs_QTML.pdf

46 Imposing Constraints on Driver Hamiltonians and Mixing Operators: From Theory to Practical Implementation

We present a general algebraic framework for constructing constraint preserving driver Hamiltonians and mixing operators, a central challenge in constrained quantum optimization. We characterize the operators that preserve embedded classical constraints, establish the computational complexity of finding them, and then develop practical algorithms for constructing them when locality bounds are known or desired.

We prove that deciding whether constraint preserving operators exist is NP-complete in the general case, while showing that operators with constant locality can be found in worst-case polynomial time. Since many practical optimization problems admit local constraint preserving operators, these results provide an efficient route to ansatz construction despite the intractability of the unrestricted problem.

Building on this framework, we develop algorithmic procedures that transform these algebraic primitives into driver Hamiltonians and mixing operators suitable for Constrained Quantum Annealing (CQA) and the Quantum Alternating Operator Ansatz (QAOA), providing a systematic alternative to handcrafted constructions.

Speaker: Hannes Leipold (Fujitsu Research of America)

Imposing_General-6.pdf

47 Learning k-body Hamiltonians via sublinear-time sparse recovery

We present a protocol for learning an unknown $n$-qubit Hamiltonian
supported on Pauli strings of weight at most $k$, with what is, to our
knowledge, the first instance-optimal $\ell_2/\ell_2$ recovery guarantee
that is simultaneously efficient in total evolution time, measurement
count, and classical decoding time, all scaling sublinearly in the
$O(n^k)$-dimensional ambient space. The protocol requires only time
evolution interleaved with single-qubit Pauli operations, together with
GHZ-type probe states for Heisenberg-limited phase estimation, and it
assumes no prior knowledge of the interaction terms.

The structural observation at its heart is that the quantum experiment
natively implements the measurements of sublinear-time sparse recovery:
within a commuting Pauli sector, a Walsh--Hadamard transform of estimated
eigenvalue differences yields signed hash buckets in the sense of
CountSketch, and sign shifts imprint the coordinates of a binary linear
code onto isolated coefficients. Identification decodes this robust
sparse-label code in time $\mathrm{poly}(k, \log n)$, and estimation takes
candidate-isolated medians on a fresh sketch. The analysis is carried out
in a deterministic residual model in which arbitrary, possibly biased and
correlated, measurement and modeling errors are charged only by their
total energy. Random basis selection lifts the sector result to full
$k$-body Hamiltonians. For an $M$-term Hamiltonian and target error
$\epsilon_H$, the protocol uses $\widetilde{O}(M \log n)$ measurements,
evolution time $\widetilde{O}(M \log n / \epsilon_H)$ at the Heisenberg
limit, and $\widetilde{O}(M\,\mathrm{polylog}(n))$ decoding time, with the
exponential-in-$k$ but $n$-independent overheads quantified explicitly.

Speaker: Franz J. Schreiber (Freie Universität Berlin)

extended_abstract.pdf

10:30 Coffee break

Contributed talks: Friday 2

48 Nearly Time-Optimal Pure State Tomography with Pauli Measurements

We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $\widetilde{O}(2^n/\epsilon)$ copies of an unknown $n$-qubit pure state $|\psi\rangle$, the algorithm performs only \textit{nonadaptive Pauli measurements}, runs in time $\widetilde{O}(2^n/\epsilon)$, and outputs $|\widehat{\psi}\rangle$ with fidelity at least $1-\epsilon$ with $|\psi\rangle$ with high probability. Aside from using essentially the simplest possible measurements, this is the first algorithm for pure state tomography that achieves near-optimal running time.

Speaker: Sabee Grewal (IBM Quantum, Columbia University)

qtml-single-qubit.pdf

49 A hidden bottleneck in classical and quantum linear reservoir computing

We identify a hidden bottleneck in the information processing capacity of linear reservoir computers. When the measured features evolve linearly in the reservoir and the output is formed by linear readout with bias, we show that the capacity available at any fixed delay is limited by what is already present in the preprocessed input. Linear reservoir dynamics can therefore redistribute features, but cannot create new fixed-delay expressive power on their own. This limitation is hidden by global capacity measures, since contributions from different delays can accumulate even when each individual delay is strongly constrained. As an experimentally important realization of this general result, we derive the corresponding Gaussian limit for covariance-based continuous-variable quantum reservoirs. Numerical experiments show that experimentally accessible single-photon operations surpass this limit, establishing them as a genuine resource for quantum reservoir computing. The resulting excess capacity also provides an operational witness of non-Gaussian processing in black-box continuous-variable systems under minimal assumptions.

Speaker: Francesco Arzani (INRIA Paris, ENS-PSL)

Non_Gaussian_QRC.pdf

50 Efficient Characterization of Coherent and Correlated Low-Degree Noise in Layers of Gates

Quantum process tomography provides complete information about the dynamics of a quantum system, but its practical use is severely limited by the exponential resources required to characterize generic quantum channels. This challenge is particularly relevant for the characterization of noise in quantum devices, where understanding coherent and correlated errors is essential for benchmarking, error mitigation, and fault-tolerant quantum computing.

In this work, we introduce an efficient and experimentally feasible protocol for the complete reconstruction of low-degree noise channels. Our approach assumes access only to single-qubit state preparation and measurement, making it directly compatible with current quantum hardware. The protocol builds on the framework of shadow tomography, but departs from standard constructions by exploiting the non-uniqueness of the reconstruction function. By tailoring this reconstruction map to the low-degree structure of the noise, we obtain a rigorous reduction of the sample complexity from exponential to polynomial in the system size.

We further show how to isolate the noise associated with a layer of quantum gates without averaging away coherent information, enabling the characterization of both coherent and correlated errors. The resulting method provides complete tomography of a broad class of physically relevant noise processes while retaining the scalability and experimental simplicity of randomized-measurement protocols.

Our results establish low-degree channels as a tractable regime for quantum process tomography and provide a practical framework for noise diagnostics in near-term quantum devices.

Speaker: Marianna Crupi (Max Planck Institute of Quantum Optics)

abstract_qtml.pdf

51 Measurements as a design principle for quantum reservoirs: enhancing and enabling online temporal learning

Quantum reservoir computing offers a near-term route to temporal learning by using fixed quantum dynamics as a processor and training only a classical readout. However, moving from classical to quantum reservoirs introduces two central difficulties: the need for an input-update mechanism that provides nonlinearity and fading memory, and the tension between extracting observables and preserving the quantum state that stores temporal information. In this extended abstract, based on two recent works, we present measurements as a design principle to address both issues. Mid-circuit measurement and reset implement the trace-and-replace update required by amplitude encoding, yielding an online protocol in which the input register is refreshed while the memory register carries information forward. At the same time, indirect measurements of the memory register provide online access to reservoir observables without projectively measuring the memory state. We show that their strength should not simply be minimized: finite measurement backaction can enhance temporal-processing performance, this advantage persists under finite measurement resources, and can outperform feedback-based strategies on memory tasks. These ingredients are combined into a dynamic-circuit implementation of online amplitude-encoded quantum reservoir computing, demonstrated on superconducting quantum hardware. Overall, the results support a view of measurement not only as a readout mechanism, but as an architectural resource for quantum temporal learning.

Speaker: Giacomo Franceschetto (ICFO - The Institute of Photonic Sciences)

qtml_extended_abstract.pdf

52 Kicked-Ising Online Quantum Reservoirs: Operating Regimes and Hardware Tests

Quantum reservoir computing processes temporal data with fixed quantum dynamics and a trained classical readout. We convert the hardware-tested kicked-Ising circuit family used in dual-unitary chaos simulations and large-scale quantum extreme learning machines into an online quantum reservoir. Unlike feedforward QELM feature maps, the circuit is recurrent. A visible register is measured and reset at each time step, while hidden qubits carry memory across the input stream.

Exact noiseless simulations reveal a structured operating regime, not a single optimum. Memory capacity forms a broad intermediate band, observable variability peaks elsewhere, and many-body scrambling increases toward the dual-unitary corner. We choose a compromise regime where memory is high, Pauli features remain resolvable, and the dynamics remain nontrivial. Observable variability acts as an anti-concentration diagnostic, and tensor-network bond-dimension diagnostics provide a compressibility check.

The memory analysis separates memory formation from memory readout. The hidden subsystem retains finite fading memory whose timescale increases with hidden-register size over the checked range. Observable-subset sweeps show that this extra memory becomes recoverable only when the measured Pauli feature space is sufficiently rich. Scaling therefore requires both recurrent memory and observable access.

We implement the selected reservoir on IBM superconducting hardware with repeated mid-circuit measurement and reset. Our short-term memory capacity and NARMA task results using exact, finite-shot simulated, and hardware features show that short-delay memory survives on hardware. Longer-horizon recovered memory is limited by finite-shot precision and device-level distortions beyond sampling noise.

Speaker: Ahmet Ege Yilmaz

QRC_QTML26_v2_2.pdf

53 Optimal randomized measurements for a family of non-linear quantum properties

Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal sample complexity for specific tasks like state purity estimation, generalizing these protocols to estimate broader classes of non-linear properties without sacrificing optimality remains an open problem. In this work, we introduce the observable-driven randomized measurement (ORM) protocol enabling the estimation of ${\rm Tr}(O\rho^2)$ for an arbitrary observable $O$---an essential quantity in quantum computing and many-body physics. We establish an upper bound for ORM's sample complexity and show its optimality for observables with a large trace-norm, including Pauli and local observables, closing a gap in the literature. For these observables, ORM admits an efficient implementation with Clifford circuits. Numerical experiments validate that ORM requires substantially fewer state samples to achieve the same precision compared to classical shadows. Additionally, we introduce a braiding randomized measurement protocol for multiple low-rank non-linear observables, reducing circuit complexities in practical applications.

Speaker: Yifan Tang

ORM_extended_abstract.pdf

13:00 Lunch

Contributed talks: Friday 3

54 Temporal information processing on a 4,500-qubit quantum annealer

Quantum machine learning could uncover statistical structure beyond the reach of classical models, but realizing this potential requires scaling quantum models to large, expressive regimes while still reading out useful information at acceptable cost. Most approaches rely on optimizing many quantum parameters, a process hampered by expensive training loops and vanishing gradients. Here we report a quantum machine-learning model, implemented on a programmable superconducting quantum annealer, that processes temporal data at utility scale using up to 4,500 qubits, to our knowledge the largest quantum machine-learning experiment performed to date. Following the quantum reservoir-computing paradigm, the native many-body dynamics generated by reverse annealing of a transverse-field Ising system transform a streaming input into a high-dimensional representation, while a delayed-feedback channel supplies tunable memory and only a single linear output layer is trained. The reservoir displays non-Markovian memory, with capacity revivals rather than exponential forgetting, and we prove that the interactions produced during annealing are indispensable, a non-interacting reservoir retains no memory of its input. We evaluate our model experimentally on standard memory benchmarks and demonstrate that it can successfully forecast chaotic time series. These results establish quantum annealers as a scalable, optimization-free platform for temporal information processing and chart a practical route toward machine learning on large-scale quantum hardware.

Speaker: Mr Antonio Sannia (Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC; Theoretical Division, Los Alamos National Laboratory;USRA Research Institute for Advanced Computer Science (RIACS))

QTML2026.pdf

55 Sampling from Thermal Quantum States via Pauli Propagation

Pauli propagation is a powerful framework for simulating quantum systems by tracking the evolution of Pauli operators, yet its scope has so far been limited to estimating expectation values. We extend it to sampling from quantum states, introducing an algorithm that draws bitstrings directly from truncated Pauli expansions. While the very truncation that makes Pauli propagation efficient renders the represented operator non-positive-semidefinite - so that its Born ''probabilities'' can be negative and standard sampling is ill-defined - we resolve this with a locally normalized conditional sampling procedure that builds a valid distribution on the fly, bypassing the intractable global renormalization over all $2^n$ bitstrings. We prove that the total variation distance to the true Born distribution scales linearly with the truncation error, and that the cost per sample is linear in the number of retained Pauli terms. We deploy the sampler on thermal states prepared by imaginary-time Pauli propagation - a natural setting, since the evolution starts from the identity, the sparsest Pauli operator. Because quantum Boltzmann machines (QBMs) are parameterized thermal states, this combination further enables their training for generative learning tasks; numerically, we demonstrate both accurate sampling from truncated thermal states and successful training of these models. More broadly, our method offers a new pathway for simulating, sampling from, and training models of complex quantum systems on classical hardware.

Speaker: Michele Minervini (Cornell University)

Pauli Propagation for Sampling.pdf

56 Quantum simulation in the Heisenberg picture: Algorithms and Learning Separations

In the first work of this joint submission (Ref. 18), we introduce a general framework for quantum simulation in the Heisenberg picture using quantum computers. Central to our approach are the vectorization and transfer matrix formalisms, which we exploit to encode Heisenberg operators $O(t)= e^{iHt} O e^{-iHt}$ as quantum states $|{O(t)}\rangle\!\rangle$ in a structure-preserving manner. As a consequence, any task naturally defined in the Heisenberg picture -- including sampling from the Pauli distribution of an operator, the computation of OTOCs (Out-of-Time-Order Correlators), two-point correlators, operator stabilizer entropies, local operator entanglement, and more -- can be mapped to tasks in the Schrodinger picture, yielding novel algorithms for their computation.

In the second work of this submission, Ref. 19, we focus on the task of simultaneously learning many correlators at once. Introducing the notion of the shadow of a Heisenberg operator, we show how it can be obtained efficiently via randomized measurements with either local or global Clifford measurements. This enables, respectively, the efficient simultaneous estimation of all low-weight OTOCs and all possible two-point correlators. Moreover, treating this as a novel information-theoretic framework to model OTOC-learning protocols, we prove fundamental information-theoretic lower bounds for the task of simultaneously estimating many OTOCs. Considering general OTOC learning protocols with various capabilities such as access to ancillas, adaptivity, and quantum memory (i.e. the ability to entangle multiple copies of the state), we prove lower bounds on certain OTOC learning tasks, which imply both the optimality of our algorithms, and exponential learning separations in several situations.

Speaker: Shao Hen Chiew (École Polytechnique Fédérale de Lausanne (EPFL))

QTML_Heisenberg.pdf

57 Stochastic Pauli-Path Simulator for Large-Scale Quantum Optimization

Pauli-based simulation offers a promising route to large-scale classical simulation of quantum circuits in structured regimes, but existing truncation-based Pauli simulators are mainly designed for forward expectation estimation. When embedded in gradient-driven quantum optimization, these truncations can produce systematically biased gradients and distorted optimization trajectories. We propose the stochastic Pauli-path simulator (\texttt{SPPS}), a Pauli-propagation framework for large-scale quantum optimization. \texttt{SPPS} samples from the full Pauli-path space, uses importance reweighting to obtain unbiased estimates, and applies path automatic differentiation to estimate all gradient components from sampled paths. We prove that truncation can approximate objective values while retaining non-vanishing gradient error, whereas \texttt{SPPS} gives unbiased gradients with high-probability accuracy and convergence guarantees. Experiments on VQE pre-training up to 100 qubits and QNN pre-training up to 40 qubits show faithful optimization dynamics and improved accuracy-runtime trade-offs.

Speaker: Dr Kaining Zhang (Nanyang Technological University)

abstract.pdf

arxiv.pdf