arXiv subjects

Marc Vuffray

Publications and source records attributed to Marc Vuffray.

At least 19 recordsLinked to original sources

arXiv2026

General Revenue Adequacy Conditions for Energy Transport Networks

Optimization is widely used to determine the physical and financial exchange of wholesale electricity in organized markets. Guarantees of solution optimality and feasibility rest largely on convexity, which is not in general a characteristic of the governing equations for power grid and gas pipeline networks. Policy decisions that base the scheduling and locational pricing of electricity transactions on optimization rely on the guarantee of revenue adequacy, which ensures that the market administrator will collect enough payments in congestion rents to settle financial transmission rights. Developing a similar mechanism for locational trade valuation of natural gas also requires assurance that pricing outcomes are revenue adequate, and also cover the costs of gas compressor operation. However, it has been shown that the AC power flow equations are in general non-convex and hence conditions for guaranteeing revenue adequacy in optimal power flow solutions are challenging to generalize. In this study, we develop a general formal mathematical setting for nonlinear physical network flows and examine the conditions for revenue adequacy. The result is verified for DC and AC power flow as well as steady-state gas flow in a pipeline network.

math.OC↗

arXiv2026

Finite Sample Bounds for Learning with Score Matching

Learning of continuous exponential family distributions with unbounded support remains an important area of research for both theory and applications in high-dimensional statistics. In recent years, score matching has become a widely used method for learning exponential families with continuous variables due to its computational ease when compared against maximum likelihood estimation. However, theoretical understanding of the statistical properties of score matching is still lacking. In this work, we provide a non-asymptotic sample complexity analysis for learning the structure of exponential families of polynomials with score matching. The derived sample bounds show a polynomial dependence on the model dimension. These bounds are the first of its kind, as all prior work has shown only asymptotic bounds on the sample complexity.

cs.LG↗

arXiv2026

Selecting Optimal Variable Order in Autoregressive Ising Models

Autoregressive models enable tractable sampling from learned probability distributions, but their performance critically depends on the variable ordering used in the factorization via complexities of the resulting conditional distributions. We propose to learn the Markov random field describing the underlying data, and use the inferred graphical model structure to construct optimized variable orderings. We illustrate our approach on two-dimensional image-like models where a structure-aware ordering leads to restricted conditioning sets, thereby reducing model complexity. Numerical experiments on Ising models with discrete data demonstrate that graph-informed orderings yield higher-fidelity generated samples compared to naive variable orderings.

stat.ML↗

arXiv2026

Computationally sufficient statistics for Ising models

Learning Gibbs distributions using only sufficient statistics has long been recognized as a computationally hard problem. On the other hand, computationally efficient algorithms for learning Gibbs distributions rely on access to full sample configurations generated from the model. For many systems of interest that arise in physical contexts, expecting a full sample to be observed is not practical, and hence it is important to look for computationally efficient methods that solve the learning problem with access to only a limited set of statistics. We examine the trade-offs between the power of computation and observation within this scenario, employing the Ising model as a paradigmatic example. We demonstrate that it is feasible to reconstruct the model parameters for a model with $\ell_1$ width $\gamma$ by observing statistics up to an order of $O(\gamma)$. This approach allows us to infer the model's structure and also learn its couplings and magnetic fields. We also discuss a setting where prior information about structure of the model is available and show that the learning problem can be solved efficiently with even more limited observational power.

cs.LG↗

arXiv2025

Symmetric Linear Dynamical Systems are Learnable from Few Observations

We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$. We introduce and analyze a new estimator that achieves a small maximum element-wise error on the recovery of symmetric dynamic matrices using only $T=\mathcal{O}(\log N)$ observations, irrespective of whether the matrix is sparse or dense. This estimator is based on the method of moments and does not rely on problem-specific regularization. This is especially important for applications such as structure discovery.

stat.ML↗

arXiv2025

Autoregressive pairwise Graphical Models efficiently find ground state representations of stoquastic Hamiltonians

We introduce Autoregressive Graphical Models (AGMs) as an Ansatz for modeling the ground states of stoquastic Hamiltonians. Exact learning of these models for smaller systems show the dominance of the pairwise terms in the autoregressive decomposition, which informs our modeling choices when the Ansatz is used to find representations for ground states of larger systems. We find that simple AGMs with pairwise energy functions trained using first-order stochastic gradient methods often outperform more complex non-linear models trained using the more expensive stochastic reconfiguration method. We also test our models on Hamiltonians with frustration and observe that the simpler linear model used here shows faster convergence to the variational minimum in a resource-limited setting.

quant-ph↗

arXiv2025

Learning response functions of analog quantum computers: analysis of neutral-atom and superconducting platforms

Analog quantum computation is an attractive paradigm for the simulation of time-dependent quantum systems. Programmable analog quantum computers have been realized in hardware using a variety of physical principles, including neutral-atom and superconducting technologies. The input parameters of the physical Hamiltonians that are used to program the quantum simulator generally differ from the parameters that characterize the output distribution of data produced under a specified quantum dynamics. The relationship between the input and output parameters is known as the response function of the analog device. Here, we introduce a streaming algorithm for learning the response function of analog quantum computers from arbitrary user inputs, thus not requiring special calibration runs. We use the method to learn and compare the response functions of several generations of analog quantum simulators based on superconducting and neutral-atom programmable arrays.

quant-ph↗

arXiv2024

Discrete distributions are learnable from metastable samples

Physically motivated stochastic dynamics are widely used to sample from high-dimensional distributions. However, such samplers often get trapped in metastable states, approximately sampling from a distribution that differs significantly from the desired stationary state. We rigorously show that for multivariable discrete distributions, the true stationary model can nevertheless be recovered from these metastable samples. This relies on a fundamental observation: for distributions satisfying a strong metastability condition, their single-variable conditional probabilities are on average extremely close to those of the true stationary distribution. This remains true even when the two distributions are far apart under global metrics such as Kullback-Leibler divergence. Consequently, we can effectively learn the true model using a conditional-likelihood estimator even when the samples are drawn from a restricted state space. Extending these general results to Ising models, we prove rigorous parameter and structure learning guarantees. Finally, we demonstrate this phenomenon numerically on higher-alphabet spin glass models.

stat.ML↗

arXiv2024

Potential Applications of Quantum Computing at Los Alamos National Laboratory

The emergence of quantum computing technology over the last decade indicates the potential for a transformational impact in the study of quantum mechanical systems. It is natural to presume that such computing technologies would be valuable to large scientific institutions, such as United States national laboratories. However, detailed descriptions of what these institutions would like to use these computers for are limited. To help provide some initial insights into this topic, this report develops detailed use cases of how quantum computing technology could be utilized to enhance a variety of quantum physics research activities at Los Alamos National Laboratory, including quantum magnetic materials, high-temperature superconductivity and nuclear astrophysics simulations. The report discusses how current high-performance computers are used for scientific discovery today and develops detailed descriptions of the types of quantum physics simulations that Los Alamos National Laboratory scientists would like to conduct, if a sufficient computing technology became available. While the report strives to highlight the breadth of potential application areas for quantum computation, this investigation has also indicated that many more use cases exist at Los Alamos National Laboratory, which could be documented in similar detail with sufficient time and effort.

quant-ph↗

arXiv2024

QuantumAnnealing: A Julia Package for Simulating Dynamics of Transverse Field Ising Models

Analog Quantum Computers are promising tools for improving performance on applications such as modeling behavior of quantum materials, providing fast heuristic solutions to optimization problems, and simulating quantum systems. Due to the challenges of simulating dynamic quantum systems, there are relatively few classical tools for modeling the behavior of these devices and verifying their performance. QuantumAnnealing.jl provides a toolkit for performing simulations of Analog Quantum Computers on classical hardware. This package includes functionality for simulation of the time evolution of the Transverse Field Ising Model, replicating annealing schedules used by real world annealing hardware, implementing custom annealing schedules, and more. This allows for rapid prototyping of models expected to display interesting behavior, verification of the performance of quantum devices, and easy comparison against the expected behavior of quantum devices against classical approaches for small systems. The software is provided as open-source and is available through Julia's package registry system.

quant-ph↗

arXiv2024

An Efficient Quantum Algorithm for Linear System Problem in Tensor Format

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of the problem dimension. However, low-complexity circuit implementations of the oracles assumed in these QLSAs constitute the major bottleneck for practical quantum speed-up in solving linear systems. In this work, we focus on the application of QLSAs for linear systems that are expressed as a low rank tensor sums, which arise in solving discretized PDEs. Previous works uses modified Krylov subspace methods to solve such linear systems with a per-iteration complexity being polylogarithmic of the dimension but with no guarantees on the total convergence cost. We propose a quantum algorithm based on the recent advances on adiabatic-inspired QLSA and perform a detailed analysis of the circuit depth of its implementation. We rigorously show that the total complexity of our implementation is polylogarithmic in the dimension, which is comparable to the per-iteration complexity of the classical heuristic methods.

quant-ph↗

arXiv2024

Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model

Demonstrations of quantum advantage for certain sampling problems have generated considerable excitement for quantum computing and have further spurred the development of circuit-model quantum computers, which represent quantum programs as a sequence of quantum gates acting on a finite number of qubits. Amongst this excitement, analog quantum computation has become less prominent, with the expectation that circuit-model quantum computers will eventually be sufficient for emulating analog quantum computation and thus rendering analog quantum computation obsolete. In this work we explore the basic requirements for emulating a specific analog quantum computation in the circuit model: the preparation of a biased superposition of degenerate ground states of an Ising Hamiltonian using an adiabatic evolution. We show that the overhead of emulation is substantial even for this simple problem. This supports using analog quantum computation for solving time-dependent Hamiltonian dynamics in the short term and midterm, assuming analog errors can be made low enough and coherence times long enough to solve problems of practical interest.

quant-ph↗

arXiv2023

Forced oscillation source localization from generator measurements

Malfunctioning equipment, erroneous operating conditions or periodic load variations can cause periodic disturbances that would persist over time, creating an undesirable transfer of energy across the system -- an effect referred to as forced oscillations. Wide-area oscillations may damage assets, trigger inadvertent tripping or control actions, and be the cause of equipment failure. Unfortunately, for wide-area oscillations, the location, frequency, and amplitude of these forced oscillations may be hard to determine. Recently, a data-driven maximum-likelihood-based method was proposed to perform source localization in transmission grids under wide-area response scenarios. However, this method relies on full PMU coverage and all buses having inertia and damping. Here, we extend this method to realistic scenarios which includes buses without inertia or dumping, such as passive loads and inverter-based generators. Incorporating Kron reduction directly into the maximum likelihood estimator, we are able to identify the location and frequency of forcing applied at both traditional generators and loads.

eess.SY↗

arXiv2023

Universal framework for simultaneous tomography of quantum states and SPAM noise

We present a general denoising algorithm for performing simultaneous tomography of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.

quant-ph↗

arXiv2023

Learning Energy-Based Representations of Quantum Many-Body States

Efficient representation of quantum many-body states on classical computers is a problem of enormous practical interest. An ideal representation of a quantum state combines a succinct characterization informed by the system's structure and symmetries, along with the ability to predict the physical observables of interest. A number of machine learning approaches have been recently used to construct such classical representations [1-6] which enable predictions of observables [7] and account for physical symmetries [8]. However, the structure of a quantum state gets typically lost unless a specialized ansatz is employed based on prior knowledge of the system [9-12]. Moreover, most such approaches give no information about what states are easier to learn in comparison to others. Here, we propose a new generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets, and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the hardness of learning for a given class of quantum states.

quant-ph↗

arXiv2022

Locating the source of forced oscillations in transmission power grids

Forced oscillation event in power grids refers to a state where malfunctioning or abnormally operating equipment causes persisting periodic disturbances in the system. While power grids are designed to damp most of perturbations during standard operations, some of them can excite normal modes of the system and cause significant energy transfers across the system, creating large oscillations thousands of miles away from the source. Localization of the source of such disturbances remains an outstanding challenge due to a limited knowledge of the system parameters outside of the zone of responsibility of system operators. Here, we propose a new method for locating the source of forced oscillations which addresses this challenge by performing a simultaneous dynamic model identification using a principled maximum likelihood approach. We illustrate the validity of the algorithm on a variety of examples where forcing leads to resonance conditions in the system dynamics. Our results establish that an accurate knowledge of system parameters is not required for a successful inference of the source and frequency of a forced oscillation. We anticipate that our method will find a broader application in general dynamical systems that can be well-described by their linearized dynamics over short periods of time.

nlin.AO↗

arXiv2022

On the Emerging Potential of Quantum Annealing Hardware for Combinatorial Optimization

Over the past decade, the usefulness of quantum annealing hardware for combinatorial optimization has been the subject of much debate. Thus far, experimental benchmarking studies have indicated that quantum annealing hardware does not provide an irrefutable performance gain over state-of-the-art optimization methods. However, as this hardware continues to evolve, each new iteration brings improved performance and warrants further benchmarking. To that end, this work conducts an optimization performance assessment of D-Wave Systems' most recent Advantage Performance Update computer, which can natively solve sparse unconstrained quadratic optimization problems with over 5,000 binary decision variables and 40,000 quadratic terms. We demonstrate that classes of contrived problems exist where this quantum annealer can provide run time benefits over a collection of established classical solution methods that represent the current state-of-the-art for benchmarking quantum annealing hardware. Although this work does not present strong evidence of an irrefutable performance benefit for this emerging optimization technology, it does exhibit encouraging progress, signaling the potential impacts on practical optimization tasks in the future.

math.OC↗

arXiv2022

Signatures of Open and Noisy Quantum Systems in Single-Qubit Quantum Annealing

We propose a quantum annealing protocol that more effectively probes the dynamics of a single qubit on D-Wave's quantum annealing hardware. This protocol uses D-Wave's h-gain schedule functionality, which allows the rapid quenching of the longitudinal magnetic field at arbitrary points during the anneal. This features enables us to distinguish between open and closed system dynamics as well as the presence or absence of longitudinal magnetic field noise. We show that both thermal and magnetic field fluctuations are key sources of noise that need to be included in an open quantum system model to reproduce the output statistics of the hardware.

quant-ph↗