arXiv subjects

Marc Vuffray

Publications and source records attributed to Marc Vuffray.

At least 37 records · Page 2Linked to original sources

arXiv2022

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims to explain the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM's quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

cs.ET↗

arXiv2022

Vector Field Visualization of Single-Qubit State Tomography

As the variety of commercially available quantum computers continues to increase so does the need for tools that can characterize, verify and validate these computers. This work explores using quantum state tomography for characterizing the performance of individual qubits and develops a vector field visualization for presentation of the results. The proposed protocol is demonstrated in simulation and on quantum computing hardware developed by IBM. The results identify qubit performance features that are not reflected in the standard models of this hardware, indicating opportunities to improve the accuracy of these models. The proposed qubit evaluation protocol is provided as free open-source software to streamline the task of replicating the process on other quantum computing devices.

quant-ph↗

arXiv2022

Learning Continuous Exponential Families Beyond Gaussian

We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing general continuous exponential families modeling higher-order moments of the data beyond the mean and the covariance. Here, we introduce a computationally efficient method for learning continuous graphical models based on the Interaction Screening approach. Through a series of numerical experiments, we show that our estimator maintains similar requirements in terms of accuracy and sample complexity scalings compared to alternative approaches such as maximization of conditional likelihood, while considerably improving upon the algorithm's run-time.

cs.LG↗

arXiv2022

High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware

Quantum Annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experiments on QA hardware platforms have demonstrated that, in the operating regime corresponding to weak interactions, the QA hardware behaves like a noisy Gibbs sampler at a hardware-specific effective temperature. This work builds on those insights and identifies a class of small hardware-native Ising models that are robust to noise effects and proposes a procedure for executing these models on QA hardware to maximize Gibbs sampling performance. Experimental results indicate that the proposed protocol results in high-quality Gibbs samples from a hardware-specific effective temperature. Furthermore, we show that this effective temperature can be adjusted by modulating the annealing time and energy scale. The procedure proposed in this work provides an approach to using QA hardware for Ising model sampling presenting potential new opportunities for applications in machine learning and physics simulation.

quant-ph↗

arXiv2021

Efficient Learning of Discrete Graphical Models

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for learning graphical models with least amount of data remains an active research topic. Reconstruction of graphical models that describe the statistics of discrete variables is a particularly challenging problem, for which the maximum likelihood approach is intractable. In this work, we provide the first sample-efficient method based on the Interaction Screening framework that allows one to provably learn fully general discrete factor models with node-specific discrete alphabets and multi-body interactions, specified in an arbitrary basis. We identify a single condition related to model parametrization that leads to rigorous guarantees on the recovery of model structure and parameters in any error norm, and is readily verifiable for a large class of models. Importantly, our bounds make explicit distinction between parameters that are proper to the model and priors used as an input to the algorithm. Finally, we show that the Interaction Screening framework includes all models previously considered in the literature as special cases, and for which our analysis shows a systematic improvement in sample complexity.

cs.LG↗

arXiv2021

Single-Qubit Cross Platform Comparison of Quantum Computing Hardware

As a variety of quantum computing models and platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. Despite being built of the same fundamental computational unit, radically different approaches have emerged for characterizing the performance of qubits in gate-based and quantum annealing computers, limiting and complicating consistent cross-platform comparisons. To fill this gap, this work proposes a single-qubit protocol (Q-RBPN) for measuring some basic performance characteristics of individual qubits in both models of quantum computation. The proposed protocol scales to large quantum computers with thousands of qubits and provides insights into the distribution of qubit properties within a particular hardware device and across families of devices. The efficacy of the Q-RBPN protocol is demonstrated through the analysis of more than 300 gate-based qubits spanning eighteen machines and 2000 annealing-based qubits from one machine, revealing some unexpected differences in qubit performance. Overall, the proposed Q-RBPN protocol provides a new platform-agnostic tool for assessing the performance of a wide range of emerging quantum computing devices.

quant-ph↗

arXiv2021

Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics

The usual setting for learning the structure and parameters of a graphical model assumes the availability of independent samples produced from the corresponding multivariate probability distribution. However, for many models the mixing time of the respective Markov chain can be very large and i.i.d. samples may not be obtained. We study the problem of reconstructing binary graphical models from correlated samples produced by a dynamical process, which is natural in many applications. We analyze the sample complexity of two estimators that are based on the interaction screening objective and the conditional likelihood loss. We observe that for samples coming from a dynamical process far from equilibrium, the sample complexity reduces exponentially compared to a dynamical process that mixes quickly.

cs.LG↗

arXiv2021

Single-Qubit Fidelity Assessment of Quantum Annealing Hardware

As a wide variety of quantum computing platforms become available, methods for assessing and comparing the performance of these devices are of increasing interest and importance. Inspired by the success of single-qubit error rate computations for tracking the progress of gate-based quantum computers, this work proposes a Quantum Annealing Single-qubit Assessment (QASA) protocol for quantifying the performance of individual qubits in quantum annealing computers. The proposed protocol scales to large quantum annealers with thousands of qubits and provides unique insights into the distribution of qubit properties within a particular hardware device. The efficacy of the QASA protocol is demonstrated by analyzing the properties of a D-Wave 2000Q system, revealing unanticipated correlations in the qubit performance of that device. A study repeating the QASA protocol at different annealing times highlights how the method can be utilized to understand the impact of annealing parameters on qubit performance. Overall, the proposed QASA protocol provides a useful tool for assessing the performance of current and emerging quantum annealing devices.

quant-ph↗

arXiv2020

Learning of Discrete Graphical Models with Neural Networks

Graphical models are widely used in science to represent joint probability distributions with an underlying conditional dependence structure. The inverse problem of learning a discrete graphical model given i.i.d samples from its joint distribution can be solved with near-optimal sample complexity using a convex optimization method known as Generalized Regularized Interaction Screening Estimator (GRISE). But the computational cost of GRISE becomes prohibitive when the energy function of the true graphical model has higher-order terms. We introduce NeurISE, a neural net based algorithm for graphical model learning, to tackle this limitation of GRISE. We use neural nets as function approximators in an Interaction Screening objective function. The optimization of this objective then produces a neural-net representation for the conditionals of the graphical model. NeurISE algorithm is seen to be a better alternative to GRISE when the energy function of the true model has a high order with a high degree of symmetry. In these cases NeurISE is able to find the correct parsimonious representation for the conditionals without being fed any prior information about the true model. NeurISE can also be used to learn the underlying structure of the true model with some simple modifications to its training procedure. In addition, we also show a variant of NeurISE that can be used to learn a neural net representation for the full energy function of the true model.

cs.LG↗

arXiv2020

Programmable Quantum Annealers as Noisy Gibbs Samplers

Drawing independent samples from high-dimensional probability distributions represents the major computational bottleneck for modern algorithms, including powerful machine learning frameworks such as deep learning. The quest for discovering larger families of distributions for which sampling can be efficiently realized has inspired an exploration beyond established computing methods and turning to novel physical devices that leverage the principles of quantum computation. Quantum annealing embodies a promising computational paradigm that is intimately related to the complexity of energy landscapes in Gibbs distributions, which relate the probabilities of system states to the energies of these states. Here, we study the sampling properties of physical realizations of quantum annealers which are implemented through programmable lattices of superconducting flux qubits. Comprehensive statistical analysis of the data produced by these quantum machines shows that quantum annealers behave as samplers that generate independent configurations from low-temperature noisy Gibbs distributions. We show that the structure of the output distribution probes the intrinsic physical properties of the quantum device such as effective temperature of individual qubits and magnitude of local qubit noise, which result in a non-linear response function and spurious interactions that are absent in the hardware implementation. We anticipate that our methodology will find widespread use in characterization of future generations of quantum annealers and other emerging analog computing devices.

quant-ph↗

arXiv2020

The Potential of Quantum Annealing for Rapid Solution Structure Identification

The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. A meticulous comparison to a variety of algorithms spanning both complete and local search suggests that quantum annealing's performance on the proposed optimization tasks is distinct. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches.

math.OC↗

arXiv2020

The Impacts of Convex Piecewise Linear Cost Formulations on AC Optimal Power Flow

Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. These results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, a important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.

math.OC↗

arXiv2020

Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation

We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and Kirchhoff-Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the network nodes, and its movement throughout the network is controlled by nodal actuators. For a class of dissipative nonlinear parabolic partial differential equation (PDE) systems on networks, we derive conditions for monotonicity properties in steady-state flow, as well as for propagation of monotone ordering of states with respect to time-varying boundary condition parameters. In the latter case, initial conditions, as well as time-varying parameters in the coupling conditions at vertices, provide an initial boundary value problem (IBVP). We prove that ordering properties of the solution to the IBVP are preserved when the initial conditions and the parameters of the time-varying coupling law are appropriately ordered. Then, we prove that when monotone ordering is not preserved, the first crossing of solutions occurs at a network node. We consider the implications for robust optimization and optimal control formulations and real-time monitoring of uncertain dynamic flows on networks, and discuss application to subsonic compressible fluid flow with energy dissipation on physical networks. The main result and monitoring policy are demonstrated for gas pipeline test networks and a case study using data corresponding to a real working system. We propose applications of this general result to the control and monitoring of natural gas transmission networks.

math.OC↗

arXiv2019

Real-time Anomaly Detection and Classification in Streaming PMU Data

Ensuring secure and reliable operations of the power grid is a primary concern of system operators. Phasor measurement units (PMUs) are rapidly being deployed in the grid to provide fast-sampled operational data that should enable quicker decision-making. This work presents a general interpretable framework for analyzing real-time PMU data, and thus enabling grid operators to understand the current state and to identify anomalies on the fly. Applying statistical learning tools on the streaming data, we first learn an effective dynamical model to describe the current behavior of the system. Next, we use the probabilistic predictions of our learned model to define in a principled way an efficient anomaly detection tool. Finally, the last module of our framework produces on-the-fly classification of the detected anomalies into common occurrence classes using features that grid operators are familiar with. We demonstrate the efficacy of our interpretable approach through extensive numerical experiments on real PMU data collected from a transmission operator in the USA.

eess.SP↗

arXiv2019

Efficient Polynomial Chaos Expansion for Uncertainty Quantification in Power Systems

Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos expansion (PCE) has been recently proposed as a tool for uncertainty quantification in power systems. The method produces results that are highly accurate, but has proved to be computationally challenging to scale to large systems. We propose a modified algorithm based on PCE with significantly improved computational efficiency that retains the desired high level of accuracy of the standard PCE. Our method uses computational enhancements by exploiting the sparsity structure and algebraic properties of the power flow equations. We show the scalability of the method on the 1354 pegase test system, assess the quality of the uncertainty quantification in terms of accuracy and robustness, and demonstrate an example application to solving the chance constrained optimal power flow problem.

math.OC↗

arXiv2018

Information Theoretic Optimal Learning of Gaussian Graphical Models

What is the optimal number of independent observations from which a sparse Gaussian Graphical Model can be correctly recovered? Information-theoretic arguments provide a lower bound on the minimum number of samples necessary to perfectly identify the support of any multivariate normal distribution as a function of model parameters. For a model defined on a sparse graph with $p$ nodes, a maximum degree $d$ and minimum normalized edge strength $κ$, this necessary number of samples scales at least as $d \log p/κ^2$. The sample complexity requirements of existing methods for perfect graph reconstruction exhibit dependency on additional parameters that do not enter in the lower bound. The question of whether the lower bound is tight and achievable by a polynomial time algorithm remains open. In this paper, we constructively answer this question and propose an algorithm, termed DICE, whose sample complexity matches the information-theoretic lower bound up to a universal constant factor. We also propose a related algorithm SLICE that has a slightly higher sample complexity, but can be implemented as a mixed integer quadratic program which makes it attractive in practice. Importantly, SLICE retains a critical advantage of DICE in that its sample complexity only depends on quantities present in the information theoretic lower bound. We anticipate that this result will stimulate future search of computationally efficient sample-optimal algorithms.

cs.LG↗

arXiv2017

Optimal structure and parameter learning of Ising models

Reconstruction of structure and parameters of an Ising model from binary samples is a problem of practical importance in a variety of disciplines, ranging from statistical physics and computational biology to image processing and machine learning. The focus of the research community shifted towards developing universal reconstruction algorithms which are both computationally efficient and require the minimal amount of expensive data. We introduce a new method, Interaction Screening, which accurately estimates the model parameters using local optimization problems. The algorithm provably achieves perfect graph structure recovery with an information-theoretically optimal number of samples, notably in the low-temperature regime which is known to be the hardest for learning. The efficacy of Interaction Screening is assessed through extensive numerical tests on synthetic Ising models of various topologies with different types of interactions, as well as on a real data produced by a D-Wave quantum computer. This study shows that the Interaction Screening method is an exact, tractable and optimal technique universally solving the inverse Ising problem.

cond-mat.stat-mech↗

arXiv2017

Online Learning of Power Transmission Dynamics

We consider the problem of reconstructing the dynamic state matrix of transmission power grids from time-stamped PMU measurements in the regime of ambient fluctuations. Using a maximum likelihood based approach, we construct a family of convex estimators that adapt to the structure of the problem depending on the available prior information. The proposed method is fully data-driven and does not assume any knowledge of system parameters. It can be implemented in near real-time and requires a small amount of data. Our learning algorithms can be used for model validation and calibration, and can also be applied to related problems of system stability, detection of forced oscillations, generation re-dispatch, as well as to the estimation of the system state.

eess.SY↗