arXiv subjects

Abhijith Jayakumar

Publications and source records attributed to Abhijith Jayakumar.

16 recordsLinked to original sources

arXiv2026

Conditions for Quantum Advantage in AC Power Flow

This paper aims to contextualize the requirements for Quantum Computing (QC) algorithms to achieve a quantum advantage in solving the alternating current power flow (ACPF) problem, with a focus on runtime complexity. First, we establish a benchmark for a QC iterative solver to demonstrate an advantage over the classical Newton-Raphson Load Flow (NRLF) algorithm. Next, we derive a baseline expression for the end-to-end runtime complexity of any Gate-based QC algorithm as $\Omega(N \kappa/\varepsilon),$ reflecting dependence on system size $N$, condition number $\kappa$, and error tolerance $\varepsilon$. Finally, we highlight key areas where QC algorithms may offer potential benefits over NRLF in addressing the standard ACPF problem.

quant-ph↗

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

The Quantum Hamiltonian Analysis Toolkit: Lowering the Barrier to Quantum Computing with Hamiltonians

We present the Quantum Hamiltonian Analysis Toolkit (QHAT), a newly developed application that provides a user-friendly interface for studying Hamiltonians and performing Hamiltonian simulation on fault-tolerant quantum computers. QHAT enables the generation and analysis of Hamiltonians through a powerful and feature-rich application, driven by simple inputs designed to reflect user needs rather than algorithmic details, so that productive research on your application of interest can be done without needing a deep understanding of quantum computing algorithms. QHAT enables a streamlined workflow to analyze Hamiltonians and Hamiltonian simulation, supporting multiple choices of algorithms and analyses. It supports Hamiltonians from multiple sources but can also generate Hamiltonians based on a simple description of the system, saving intermediate data files for re-use when generating related Hamiltonians. Deriving the parameters for quantum computing algorithms can be a challenge, so QHAT is built around user-facing concepts such as maximum allowable error, rather than being built around algorithmic details such as steps counts or order parameters. An emphasis on user-friendly interfaces and efficient analysis means that the barrier to entry is low while rapidly providing results useful for a broad scope of studies.

quant-ph↗

arXiv2026

Discrete Diffusion with Sample-Efficient Estimators for Conditionals

We study a discrete denoising diffusion framework that integrates a sample-efficient estimator of single-site conditionals with round-robin noising and denoising dynamics for generative modeling over discrete state spaces. Rather than approximating a discrete analog of a score function, our formulation treats single-site conditional probabilities as the fundamental objects that parameterize the reverse diffusion process. We employ a sample-efficient method known as Neural Interaction Screening Estimator (NeurISE) to estimate these conditionals in the diffusion dynamics. Controlled experiments on synthetic Ising models, MNIST, and scientific data sets produced by a D-Wave quantum annealer, synthetic Potts model and one dimensional quantum systems demonstrate the proposed approach. On the binary data sets, these experiments demonstrate that the proposed approach outperforms popular existing methods including ratio-based approaches, achieving improved performance in total variation, cross-correlations, and kernel density estimation metrics.

cs.LG↗

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

Efficient Learning of Lattice Gauge Theories with Fermions

We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a popular learning method, is a special case of our construction of an infinite family of valid loss functions. Importantly, our general Schwinger-Dyson-based construction applies to gauge theories and models with Grassmann-valued fields used to represent dynamical fermions. In particular, we extend our method to realistic lattice field theories including quantum chromodynamics.

hep-lat↗

arXiv2025

Learning of Statistical Field Theories

Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting observables from an action or Hamiltonian. Here, we propose an approach for the inverse problem that uniformly accommodates systems with discrete, continuous, and hybrid variables. We demonstrate accurate parameter recovery in several benchmark systems-including Wegner's Ising gauge theory, $\phi^4$ theory, Schwinger and Sine-Gordon models, and mixed spin-gauge systems, and show how iterating the procedure under coarse-graining reconstructs full non-perturbative renormalization-group flows. This gives direct access to phase boundaries, fixed points, and emergent interactions without relying on perturbation theory. We also address a realistic setting where full gauge configurations may be unavailable, and reformulate learning algorithms for multiple field theories so that they are recovered directly using observables such as correlations from scattering data or quantum simulators. We anticipate that our methodology will find widespread use in practical learning of field theories in strongly coupled regimes where analytical tools might fail.

cond-mat.stat-mech↗

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

Optimization Proxies using Limited Labeled Data and Training Time -- A Semi-Supervised Bayesian Neural Network Approach

Constrained optimization problems arise in various engineering systems such as inventory management and power grids. Standard deep neural network (DNN) based machine learning proxies are ineffective in practical settings where labeled data is scarce and training times are limited. We propose a semi-supervised Bayesian Neural Networks (BNNs) based optimization proxy for this complex regime, wherein training commences in a sandwiched fashion, alternating between a supervised learning step for minimizing cost, and an unsupervised learning step for enforcing constraint feasibility. We show that the proposed semi-supervised BNN outperforms DNN architectures on important non-convex constrained optimization problems from energy network operations, achieving up to a tenfold reduction in expected maximum equality gap and halving the inequality gaps. Further, the BNN's ability to provide posterior samples is leveraged to construct practically meaningful probabilistic confidence bounds on performance using a limited validation data, unlike prior methods. The implementation code for this study is available at: https://github.com/kaarthiksundar/BNN-OPF/.

cs.LG↗

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

Limitations of Fault-Tolerant Quantum Linear System Solvers for Quantum Power Flow

Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for solving such a problem using a classical algorithm exceeds that required by a quantum algorithm. Reducing the power flow (PF) problem into a linear system of equations allows for the formulation of quantum PF (QPF) algorithms, which are based on solving methods for quantum linear systems such as the Harrow-Hassidim-Lloyd (HHL) algorithm. Speedup from using QPF algorithms is often claimed to be exponential when compared to classical PF solved by state-of-the-art algorithms. We investigate the potential for practical quantum advantage in solving QPF compared to classical methods on gate-based quantum computers. Notably, this paper does not present a new QPF solving algorithm but scrutinizes the end-to-end complexity of the QPF approach, providing a nuanced evaluation of the purported quantum speedup in this problem. Our analysis establishes a best-case bound for the HHL-based quantum power flow complexity, conclusively demonstrating that the HHL-based method has higher runtime complexity compared to the classical algorithm for solving the direct current power flow (DCPF) and fast decoupled load flow (FDLF) problem. Notably, our analysis and conclusions can be extended to any quantum linear system solver with rigorous performance guarantees, based on the known complexity lower bounds for this problem. Additionally, we establish that for potential practical quantum advantage (PQA) to exist it is necessary to consider DCPF-type problems with a very narrow range of condition number values and readout requirements.

quant-ph↗

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

Shot-frugal and Robust quantum kernel classifiers

Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and because of the constraints of near-term quantum hardware. We emphasize that for classification tasks, the aim is reliable classification and not precise kernel evaluation, and demonstrate that the former is far more resource efficient. Furthermore, it is shown that the accuracy of classification is not a suitable performance metric in the presence of noise and we motivate a new metric that characterizes the reliability of classification. We then obtain a bound for N which ensures, with high probability, that classification errors over a dataset are bounded by the margin errors of an idealized quantum kernel classifier. Using chance constraint programming and the subgaussian bounds of quantum kernel distributions, we derive several Shot-frugal and Robust (ShofaR) programs starting from the primal formulation of the Support Vector Machine. This significantly reduces the number of quantum measurements needed and is robust to noise by construction. Our strategy is applicable to uncertainty in quantum kernels arising from any source of unbiased noise.

quant-ph↗