arXiv subjects

Christa Zoufal

Publications and source records attributed to Christa Zoufal.

At least 19 recordsLinked to original sources

arXiv2026

Learning ground state observables from quantum computing experiments

Recent theoretical progress has established conditions under which machine learning models can efficiently predict ground-state properties of gapped local Hamiltonians when trained on quantum-generated data. Previous experimental demonstrations in this paradigm, however, have largely been limited to small systems or highly structured states, due to the difficulty of preparing many-body ground states on quantum processors. In this work, we demonstrate learning from experimental quantum data generated from approximate ground states of the two-dimensional Heisenberg XXZ model with system sizes up to 115 qubits. We construct a dataset of single-site expectation values, two-point correlations, and 12-body loop correlations across the antiferromagnetic phase. We then train neural networks on this data and show that they can accurately predict spatially resolved observables for previously unseen Hamiltonian parameters, both within the training distribution and in an out-of-distribution regime approaching the phase boundary. Our results demonstrate the practical realization of learning from quantum data for an interacting two-dimensional many-body system at scale, motivating a path toward regimes where quantum processors could provide training data beyond the reach of classical approximation methods.

quant-ph↗

arXiv2026

Bowtie VarQTE: A Resource-Efficient Quantum State Preparation Primitive

The preparation of quantum states is a fundamental requirement for many quantum algorithms. A native route to preparing physically structured states is based on short-time simulation of dynamical processes, such as real or imaginary time evolution. This work presents a resource-efficient framework for the approximation thereof with \textit{bowtie \ac{VarQTE}} which uses classical simulation where possible and quantum resources where necessary. We introduce a framework that leverages existing causal light-cones to minimize quantum resource requirements in the evaluation of gradient and quantum geometric tensor terms by utilizing classical simulation methods for causally relevant subcircuits. This in turn enables exact parameter updates according to McLachlan's variational principle and, thereby, improves numerical stability. We conduct a comparison with a state preparation method that is based on a tensor-network compiled Trotter algorithm: approximate quantum compilation (AQC). In recent work, this approach has shown impressive performance. However, its key-bottleneck is the necessity to have a classical (approximate) representation of the target state. Our numerical experiments indicate that bowtie VarQTE can achieve comparable fidelities without this requirement. We further illustrate how bowtie VarQTE can facilitate a state-preparation pipeline that combines the simulation of imaginary and real time evolution for a sample-based quantum algorithm. In fact, results on 2D systems show how bowtie VarQTE can reduce the quantum requirements compared to standard, sample-based Krylov diagonalization calculations. Our results indicate that VarQTE is a promising primitive for the preparation of physically structured quantum states that reduces requirements on quantum resources by leveraging existing structures and the associated possibility of enabling classical simulations.

quant-ph↗

arXiv2026

Quantum-enhanced Markov Chain Monte Carlo for Combinatorial Optimization

Quantum computing offers an alternative paradigm for addressing combinatorial optimization problems compared to classical computing. Despite recent hardware improvements, the execution of empirical quantum optimization experiments at scales known to be hard for state-of-the-art classical solvers is not yet in reach. In this work, we offer a different way to approach combinatorial optimization with near-term quantum computing. Motivated by the promising results observed in using quantum-enhanced Markov chain Monte Carlo (QeMCMC) for approximating complicated probability distributions, we combine ideas of sampling from the device with QeMCMC together with warm-starting and parallel tempering, in the context of combinatorial optimization. We demonstrate empirically that our algorithm recovers the global optima for instances of the Maximum Independent Set problem (MIS) up to 117 decision variables using 117 qubits on IBM quantum hardware. We show early evidence of a scaling advantage of our algorithm compared to similar classical methods for the chosen instances of MIS. MIS is practically relevant across domains like financial services and molecular biology, and, in some cases, already difficult to solve to optimality classically with only a few hundred decision variables.

quant-ph↗

arXiv2025

Quantum Optimization Benchmarking Library - The Intractable Decathlon

Through recent progress in hardware development, quantum computers have advanced to the point where benchmarking of (heuristic) quantum algorithms at scale is within reach. Particularly in combinatorial optimization - where most algorithms are heuristics - it is key to empirically analyze their performance on hardware and track progress towards quantum advantage. To this extent, we present ten optimization problem classes that are difficult for existing classical algorithms and can (mostly) be linked to practically relevant applications, with the goal to enable systematic, fair, and comparable benchmarks for quantum optimization methods. Further, we introduce the Quantum Optimization Benchmarking Library (QOBLIB) where the problem instances and solution track records can be found. The individual properties of the problem classes vary in terms of objective and variable type, coefficient ranges, and density. Crucially, they all become challenging for established classical methods already at system sizes ranging from less than 100 to, at most, an order of 100,000 decision variables, allowing to approach them with today's quantum computers. We reference the results from state-of-the-art solvers for instances from all problem classes and demonstrate exemplary baseline results obtained with quantum solvers for selected problems. The baseline results illustrate a standardized form to present benchmarking solutions, which has been designed to ensure comparability of the used methods, reproducibility of the respective results, and trackability of algorithmic and hardware improvements over time. We encourage the optimization community to explore the performance of available classical or quantum algorithms and hardware platforms with the benchmarking problem instances presented in this work toward demonstrating quantum advantage in optimization.

quant-ph↗

arXiv2025

Dynamic parameterized quantum circuits: expressive and barren-plateau free

Classical optimization of parameterized quantum circuits is a widely studied methodology for the preparation of complex quantum states, as well as the solution of machine learning and optimization problems. However, it is well known that many proposed parameterized quantum circuit architectures suffer from drawbacks which limit their utility, such as their classical simulability or the hardness of optimization due to a problem known as "barren plateaus". We propose and study a class of dynamic parameterized quantum circuit architectures. These are parameterized circuits containing intermediate measurements and feedforward operations. In particular, we show that these architectures: 1. Provably do not suffer from barren plateaus. 2. Are expressive enough to describe arbitrarily deep unitary quantum circuits. 3. Are competitive with state of the art methods for preparing ground states and facilitating the representation of nontrivial thermal states. These features make the proposed architectures promising candidates for a variety of applications.

quant-ph↗

arXiv2025

A Framework for Quantum Advantage

As quantum computing approaches the threshold where certain tasks demonstrably outpace their classical machines, the need for a precise, clear, consensus-driven definition of quantum advantage becomes essential. Rapid progress in the field has blurred this term across companies, architectures, and application domains. Here, we aim to articulate an operational definition for quantum advantage that is both platform-agnostic and empirically verifiable. Building on this framework, we highlight the algorithmic families most likely to achieve early advantage. Finally, we outline our vision for the near future, in which quantum computers enhance existing high-performance computing platforms, enabling new frontiers in chemistry, materials discovery, optimization, and beyond.

quant-ph↗

arXiv2025

Towards Practical Quantum Neural Network Diagnostics with Neural Tangent Kernels

Knowing whether a Quantum Machine Learning model would perform well on a given dataset before training it can help to save critical resources. However, gathering a priori information about model performance (e.g., training speed, critical hyperparameters, or inference capabilities on unseen data) is a highly non-trivial task, in general. Recently, the Quantum Neural Tangent Kernel (QNTK) has been proposed as a powerful mathematical tool to describe the behavior of Quantum Neural Network (QNN) models. In this work, we propose a practical framework allowing to employ the QNTK for QNN performance diagnostics. More specifically, we show how a critical learning rate and a characteristic decay time for the average training error can be estimated from the spectrum of the QNTK evaluated at the initialization stage. We then show how a QNTK-based kernel formula can be used to analyze, up to a first-order approximation, the expected inference capabilities of the quantum model under study. We validate our proposed approach with extensive numerical simulations, using different QNN architectures and datasets. Our results demonstrate that QNTK diagnostics yields accurate approximations of QNN behavior for sufficiently deep circuits, can provide insights for shallow QNNs, and enables detecting - hence also addressing - potential shortcomings in model design.

quant-ph↗

arXiv2024

Challenges and Opportunities in Quantum Optimization

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of different approaches for major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions. This work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory - highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains - finance and sustainability - as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

quant-ph↗

arXiv2024

Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits

The training of a parameterized model largely depends on the landscape of the underlying loss function. In particular, vanishing gradients are a central bottleneck in the scalability of variational quantum algorithms (VQAs), and are known to arise in various ways. However, a caveat of most existing gradient bound results is the requirement of t-design circuit assumptions that are typically not satisfied in practice. In this work, we loosen these assumptions altogether and derive tight upper and lower bounds on loss and gradient concentration for a large class of parameterized quantum circuits and arbitrary observables, which are significantly stronger than prior work. Moreover, we show that these bounds, as well as the variance of the loss itself, can be estimated efficiently and classically-providing practical tools to study the loss landscapes of VQA models, including verifying whether or not a circuit/observable induces barren plateaus. In particular, our results can readily be leveraged to rule out barren plateaus for a realistic class of ansätze and mixed observables, namely, observables containing a non-vanishing local term. This insight has direct implications for hybrid Quantum Generative Adversarial Networks (qGANs). We prove that designing the discriminator appropriately leads to 1-local weights that stay constant in the number of qubits, regardless of discriminator depth. This implies that qGANs with appropriately chosen generators do not suffer from barren plateaus even at scale-making them a promising candidate for applications in generative quantum machine learning. We demonstrate this result by training a qGAN to learn a 2D mixture of Gaussian distributions with up to 16 qubits, and provide numerical evidence that global contributions to the gradient, while initially exponentially small, may kick in substantially over the course of training.

quant-ph↗

arXiv2024

Quantum Theory and Application of Contextual Optimal Transport

Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbolμ, \boldsymbolν)$ are coupled to covariates, a challenging conditional distribution learning setting arises. Existing approaches for learning a $\textit{global}$ transport map parameterized through a potentially unseen context utilize Neural OT and largely rely on Brenier's theorem. Here, we propose a first-of-its-kind quantum computing formulation for amortized optimization of contextualized transportation plans. We exploit a direct link between doubly stochastic matrices and unitary operators thus unravelling a natural connection between OT and quantum computation. We verify our method (QontOT) on synthetic and real data by predicting variations in cell type distributions conditioned on drug dosage. Importantly we conduct a 24-qubit hardware experiment on a task challenging for classical computers and report a performance that cannot be matched with our classical neural OT approach. In sum, this is a first step toward learning to predict contextualized transportation plans through quantum computing.

cs.LG↗

arXiv2023

Quantum Generative Adversarial Networks For Anomaly Detection In High Energy Physics

The standard model (SM) of particle physics represents a theoretical paradigm for the description of the fundamental forces of nature. Despite its broad applicability, the SM does not enable the description of all physically possible events. The detection of events that cannot be described by the SM, which are typically referred to as anomalous, and the related potential discovery of exotic physical phenomena is a non-trivial task. The challenge becomes even greater with next-generation colliders that will produce even more events with additional levels of complexity. The additional data complexity motivates the search for unsupervised anomaly detection methods that do not require prior knowledge about the underlying models. In this work, we develop such a technique. More explicitly, we employ a quantum generative adversarial network to identify anomalous events. The method learns the background distribution from SM data and, then, determines whether a given event is characteristic for the learned background distribution. The proposed quantum-powered anomaly detection strategy is tested on proof-of-principle examples using numerical simulations and IBM Quantum processors. We find that the quantum generative techniques using ten times fewer training data samples can yield comparable accuracy to the classical counterpart for the detection of the Graviton and Higgs particles. Additionally, we empirically compute the capacity of the quantum model and observe an improved expressivity compared to its classical counterpart.

quant-ph↗

arXiv2023

Error Bounds for Variational Quantum Time Evolution

Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We derive global phase agnostic error bounds for the state simulation accuracy with variational quantum time evolution that improve the tightness of fidelity estimates over existing error bounds. These analysis tools are practically crucial for assessing the quality of the simulation and making informed choices about simulation hyper-parameters. The efficient, a posteriori evaluation of the bounds can be tightly integrated with the variational time simulation and, hence, results in a minor resource overhead which is governed by the system's energy variance. The performance of the novel error bounds is demonstrated on numerical examples.

quant-ph↗

arXiv2023

Stochastic Approximation of Variational Quantum Imaginary Time Evolution

The imaginary-time evolution of quantum states is integral to various fields, ranging from natural sciences to classical optimization or machine learning. Since simulating quantum imaginary-time evolution generally requires storing an exponentially large wave function, quantum computers are emerging as a promising platform for this task. However, variational approaches, suitable for near-term quantum computers, struggle with a prohibitive number of measurements and impractical runtimes for relevant system sizes. Here, we suggest a stochastic approach to variational quantum imaginary-time evolution, which allows a significant reduction in runtimes. Our approach allows trading off invested resources and accuracy, which makes it also suitable for ground state preparation, where simulating the exact dynamics is not required. We demonstrate the efficiency of our algorithm in simulations and show a hardware experiment performing the imaginary-time evolution of the transverse field Ising model on 27 qubits.

quant-ph↗

arXiv2023

Quantum Kernel Alignment with Stochastic Gradient Descent

Quantum support vector machines have the potential to achieve a quantum speedup for solving certain machine learning problems. The key challenge for doing so is finding good quantum kernels for a given data set -- a task called kernel alignment. In this paper we study this problem using the Pegasos algorithm, which is an algorithm that uses stochastic gradient descent to solve the support vector machine optimization problem. We extend Pegasos to the quantum case and and demonstrate its effectiveness for kernel alignment. Unlike previous work which performs kernel alignment by training a QSVM within an outer optimization loop, we show that using Pegasos it is possible to simultaneously train the support vector machine and align the kernel. Our experiments show that this approach is capable of aligning quantum feature maps with high accuracy, and outperforms existing quantum kernel alignment techniques. Specifically, we demonstrate that Pegasos is particularly effective for non-stationary data, which is an important challenge in real-world applications.

quant-ph↗

arXiv2023

Variational quantum algorithm for unconstrained black box binary optimization: Application to feature selection

We introduce a variational quantum algorithm to solve unconstrained black box binary optimization problems, i.e., problems in which the objective function is given as black box. This is in contrast to the typical setting of quantum algorithms for optimization where a classical objective function is provided as a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum of Pauli operators. Furthermore, we provide theoretical justification for our method based on convergence guarantees of quantum imaginary time evolution. To investigate the performance of our algorithm and its potential advantages, we tackle a challenging real-world optimization problem: feature selection. This refers to the problem of selecting a subset of relevant features to use for constructing a predictive model such as fraud detection. Optimal feature selection -- when formulated in terms of a generic loss function -- offers little structure on which to build classical heuristics, thus resulting primarily in 'greedy methods'. This leaves room for (near-term) quantum algorithms to be competitive to classical state-of-the-art approaches. We apply our quantum-optimization-based feature selection algorithm, termed VarQFS, to build a predictive model for a credit risk data set with 20 and 59 input features (qubits) and train the model using quantum hardware and tensor-network-based numerical simulations, respectively. We show that the quantum method produces competitive and in certain aspects even better performance compared to traditional feature selection techniques used in today's industry.

quant-ph↗

arXiv2022

A variational quantum algorithm for the Feynman-Kac formula

We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the correspondence between the Feynman-Kac partial differential equation (PDE) and the Wick-rotated Schrödinger equation for this purpose. The results for a $(2+1)$ dimensional Feynman-Kac system obtained through the variational quantum algorithm are then compared against classical ODE solvers and Monte Carlo simulation. We see a remarkable agreement between the classical methods and the quantum variational method for an illustrative example on six and eight qubits. In the non-trivial case of PDEs which are preserving probability distributions -- rather than preserving the $\ell_2$-norm -- we introduce a proxy norm which is efficient in keeping the solution approximately normalized throughout the evolution. The algorithmic complexity and costs associated to this methodology, in particular for the extraction of properties of the solution, are investigated. Future research topics in the areas of quantitative finance and other types of PDEs are also discussed.

quant-ph↗

arXiv2022

On Quantum Circuits for Discrete Graphical Models

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research topic. Sampling from graphical models that describe the statistics of discrete variables is a particularly challenging problem, which is intractable in the presence of high dimensions. In this work, we provide the first method that allows one to provably generate unbiased and independent samples from general discrete factor models with a quantum circuit. Our method is compatible with multi-body interactions and its success probability does not depend on the number of variables. To this end, we identify a novel embedding of the graphical model into unitary operators and provide rigorous guarantees on the resulting quantum state. Moreover, we prove a unitary Hammersley-Clifford theorem -- showing that our quantum embedding factorizes over the cliques of the underlying conditional independence structure. Importantly, the quantum embedding allows for maximum likelihood learning as well as maximum a posteriori state approximation via state-of-the-art hybrid quantum-classical methods. Finally, the proposed quantum method can be implemented on current quantum processors. Experiments with quantum simulation as well as actual quantum hardware show that our method can carry out sampling and parameter learning on quantum computers.

quant-ph↗

arXiv2021

Generative Quantum Machine Learning

The goal of generative machine learning is to model the probability distribution underlying a given data set. This probability distribution helps to characterize the generation process of the data samples. While classical generative machine learning is solely based on classical resources, generative quantum machine learning can also employ quantum resources - such as parameterized quantum channels and quantum operators - to learn and sample from the probability model of interest. Applications of generative (quantum) models are multifaceted. The trained model can generate new samples that are compatible with the given data and extend the data set. Additionally, learning a model for the generation process of a data set may provide interesting information about the corresponding properties. With the help of quantum resources, the respective generative models have access to functions that are difficult to evaluate with a classical computer and may improve the performance or lead to new insights. Furthermore, generative quantum machine learning can be applied to efficient, approximate loading of classical data into a quantum state which may help to avoid - potentially exponentially - expensive, exact quantum data loading. The aim of this doctoral thesis is to develop new generative quantum machine learning algorithms, demonstrate their feasibility, and analyze their performance. Additionally, we outline their potential application to efficient, approximate quantum data loading. More specifically, we introduce a quantum generative adversarial network and a quantum Boltzmann machine implementation, both of which can be realized with parameterized quantum circuits. These algorithms are compatible with first-generation quantum hardware and, thus, enable us to study proof of concept implementations not only with numerical quantum simulations but also real quantum hardware available today.

quant-ph↗