arXiv subjects

Shravan Veerapaneni

Publications and source records attributed to Shravan Veerapaneni.

At least 19 recordsLinked to original sources

arXiv2026

Scalable quantum simulation of continuous-time generative models via tensor networks

Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein folding to emerging adoption for modeling language, time series, and quantum states. After training, inferring statistical properties from continuous-time models is costly. Wavefunction flows target this cost by recasting learned transport as unitary evolution, whose final Born distribution approximates the target distribution. This prepares a coherent amplitude encoding (a qsample) that can be post-processed by quantum algorithms offering a quadratic advantage over Monte Carlo sampling. We present the first numerical study of these flows, in which we represent time-dependent potentials and states as tensor networks. At spatial dimension $d=8$, storage falls by $\sim 10^7\times$ relative to the dense grid of $N^d$ points, and evolution wall-clock time falls by $\gtrsim 10^3\times$ against a baseline extrapolated from the measured $d\le 5$ scaling. We validate our pipeline by reproducing the $O(1/\sqrt{p_{\rm rare}})$ scaling of rare-event sampling.

quant-ph↗

arXiv2026

A convergent finite element method for two-phase Stokes flow driven by surface tension

We present the first convergence proof for an iso-parametric finite element discretization of two-phase Stokes flow in $Ω\subset \mathbb{R}^d$, $d=2,3$, with interface dynamics governed by mean curvature. The proof relies on a crucial discrete coupled parabolicity structure of the error system and a powerful iso-parametric framework of convergence analysis where we do not really discriminate consistency and stability. This new mixing idea leads to a non-trivial construction of the bulk mesh in the consistency analysis. The techniques and analysis developed in this paper provide fundamental numerical analysis tools for general curvature-driven free boundary problems.

math.NA↗

arXiv2026

Equivariant Continuous Normalizing Flows with Offline Sampling for Fermionic Ground State Estimation

We introduce a framework for fermionic variational Monte Carlo (VMC) in which a continuous normalizing flow (CNF) refines a fixed antisymmetric base wavefunction. The flow is implemented as a permutation-equivariant neural ODE, a smooth, topology-preserving map that learns correlations not captured by the base; equivariance preserves the antisymmetry of the base, so the flow can in principle improve any antisymmetric ansatz that can be sampled efficiently. We demonstrate this using Slater and Jastrow-Slater bases, though more expressive choices are admissible. Exact samples from the flow's Born distribution are obtained by pushing pre-cached base samples through the forward ODE, requiring no Markov chain Monte Carlo (MCMC) at training time. The base samples are generated offline and reused across training batches and runs, decoupling sample generation from parameter optimization and enabling embarrassingly parallel training across multiple GPUs. We introduce three novel permutation-equivariant vector field architectures: Pairwise Deep Sets (PDS), FermiNet Vector Fields (FVF), and Pairwise Deep Sets Gradient (PDSG), each offering a different balance of expressivity and computational cost. We further introduce an augmented dynamics formulation for kinetic energy computation that co-evolves the required derivative quantities as ODE state variables, eliminating differentiation through the ODE trajectory and yielding significant reductions in wall-clock time and memory. Training runs on systems of harmonically trapped spinless electrons demonstrate ground-state energies below CISD reference values. Scaling experiments demonstrate near-ideal strong scaling from 1 to 128 NVIDIA A100s using 32 GPU nodes of NERSC's Perlmutter supercomputer for systems of up to $N = 48$ particles in three dimensions.

quant-ph↗

arXiv2026

A scalable Ewald-free BIE framework for periodic Stokes flow via hierarchical proxy sums

Particulate Stokes flow in confined, periodic geometries underlies a broad class of problems in biophysics, microfluidics, and the rheology of complex fluids. Boundary integral equation (BIE) methods are a natural tool for such problems, but existing periodization schemes rely either on periodic Green's functions, which are restrictive for complex confining geometries, or on free-space schemes that solve auxiliary proxy strengths alongside the surface densities in an extended linear system whose cost scales unfavorably in three dimensions. We present a BIE framework for three-dimensional particulate Stokes flow in periodic pipes with circular cross-sections, wall-bounded doubly-periodic, and triply-periodic geometries that uses only the free-space Green's function and avoids both Ewald summation and the extended linear system. Proxy sources placed on equivalent surfaces of the kernel-independent FMM (KIFMM) form the auxiliary basis, and contributions from far image boxes are captured by a hierarchical proxy sum made absolutely convergent by a net-force-zero compatibility condition. The resulting periodization precomputation depends only on the periodic-box geometry, independent of the kernel and of the surfaces inside the box, and is reused verbatim across the Stokeslet, stresslet, and rotlet. Combined with high-order adaptive surface discretizations, the method achieves high-order accuracy at $\mathcal{O}(N)$ cost with a single layer of image boxes in the near field. Numerical examples on dense polydisperse suspensions with thousands of particles and on flow through complex periodic channels, together with strong and weak scaling studies, demonstrate efficient performance on systems with millions of degrees of freedom on distributed-memory architectures.

physics.flu-dyn↗

arXiv2026

Quantum Algorithms for Nonlinear Differential Equations via Pivot-Shifted Carleman Linearization

We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a Lyapunov transform and rescaling, we enlarge the class of nonlinear systems that can be efficiently simulated on quantum computers. For systems that exhibit stability in the shifted coordinates, we establish long time convergence of the truncated Carleman embedding. We prove that the truncation order scales only logarithmically with the simulation time and target precision, and we derive end-to-end quantum query complexity bounds for preparing a state proportional to the final solution. By introducing a modified nonlinearity condition, this framework entirely removes the conventional lower bound requirement on the initial condition. For more general systems that remain unstable after shifting, we provide short time convergence guarantees that are similarly free from the initial condition constraints. Numerical experiments on the logistic and the Lotka-Volterra equations demonstrate that an appropriate pivot choice improves stability and accuracy, and yields exponential error decay with truncation order. These results show that pivot shifting provides a practical and theoretically justified route for extending Carleman-based quantum algorithms to a broader class of nonlinear dynamical systems.

quant-ph↗

arXiv2026

Squirmers with arbitrary shape and slip: modeling, simulation, and optimization

We consider arbitrary-shaped microswimmers of spherical topology and propose a framework for expressing their slip velocity in terms of tangential basis functions defined on the boundary of the swimmer using the Helmholtz decomposition. Given a time-independent slip velocity profile, we show that the trajectory followed by the microswimmer is a circular helix. We derive analytical expressions for the translational and rotational velocities of a prolate spheroid swimmer in terms of its Helmholtz decomposition modes and explore the effect of aspect ratio on these rigid body velocities. Then, for a given arbitrary swimmer shape of spherical topology, we investigate which slip profile minimizes the total power loss. A partial minimization is performed in which the direction of net motion of the swimmer is prescribed, followed by a global optimization procedure in which the best net motion direction is determined. The optimization results suggest that the competition between linear and rotational optimal motion is linked to symmetries in the shape of the microswimmer.

physics.flu-dyn↗

arXiv2026

Slip optimization on arbitrary 3D microswimmers: a reduced-dimension and boundary-integral framework

This article presents a computational framework for determining the optimal slip velocity of a microswimmer with arbitrary three-dimensional geometry suspended in a viscous fluid. The objective is to minimize the hydrodynamic power dissipation required to maintain unit speed along the net swimming direction. By exploiting the linearity of the Stokes equations and the Lorentz reciprocal theorem, we derive an explicit linear operator that maps the tangential surface slip velocity to the resulting rigid-body translational and rotational velocities, effectively decoupling the hydrodynamic boundary value problem from the optimization loop. The a priori infinite-dimensional search space for the slip optimization is reduced to the finite dimension $r$ of rigid-body motions by finding an appropriate subspace of the operator's domain. This reduces the PDE-constrained optimization to a low-dimensional programming problem that can be solved at negligible computational cost once the system matrices are assembled. The optimization algorithm requires 2$r$ auxiliary flow problems that are solved numerically using a high-order boundary integral method. We validate the accuracy of the proposed method and present optimal slip profiles and swimming trajectories for a variety of microswimmer shapes. We investigate the effect of some common geometrical symmetries of the swimmer shape on the resulting optimal motion, and in particular present a modified version of the slip optimization algorithm for axisymmetric shapes, where tangential rigid-body velocities may occur

math.NA↗

arXiv2026

Convergence analysis for the Barrett--Garcke--Nurnberg method of transport type for evolving curves

In this paper, we propose a Barrett-Garcke-Nurnberg (BGN) method for evolving geometries under general flows and present the corresponding convergence analysis. Specifically, we examine the scenario where a closed curve evolves according to a prescribed background velocity field. Unlike mean curvature flow and surface diffusion, where the evolution velocities inherently exhibit parabolicity, this case is dominated by transport which poses a significant difficulty in establishing convergence proofs. To address the challenges imposed by this transport-dominant nature, we derive several discrete energy estimates of the transport type on discretized polynomial surfaces within the framework of the projection error. The use of the projection error is indispensable as it provides crucial additional stability through its orthogonality structure. We prove that the proposed method converges sub-optimally in the L2 norm, and this is the first convergence proof for a fully discrete numerical method solving the evolution of curves driven by general flows.

math.NA↗

arXiv2025

Space-time adaptive methods for parabolic evolution equations

We present a family of integral equation-based solvers for the heat equation, reaction-diffusion systems, the unsteady Stokes equation and the incompressible Navier-Stokes equations in two space dimensions. Our emphasis is on the development of methods that can efficiently follow complex solution features in space-time by refinement and coarsening at each time step on an adaptive quadtree. For simplicity, we focus on problems posed in a square domain with periodic boundary conditions. The performance and robustness of the methods are illustrated with several numerical examples.

math.NA↗

arXiv2025

Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistry

Scaling laws have been used to describe how large language model (LLM) performance scales with model size, training data size, or amount of computational resources. Motivated by the fact that neural quantum states (NQS) has increasingly adopted LLM-based components, we seek to understand NQS scaling laws, thereby shedding light on the scalability and optimal performance--resource trade-offs of NQS ansatze. In particular, we identify scaling laws that predict the performance, as measured by absolute error and V-score, for transformer-based NQS as a function of problem size in second-quantized quantum chemistry applications. By performing analogous compute-constrained optimization of the obtained parametric curves, we find that the relationship between model size and training time is highly dependent on loss metric and ansatz, and does not follow the approximately linear relationship found for language models.

cs.LG↗

arXiv2025

Enhancing the Clique Local Decoder to Correct Length-2 Space Errors in the Surface Code

The growing demand for fault-tolerant quantum computing drives the need for efficient, scalable Quantum Error Correction (QEC) strategies. Conventional decoders designed for worst-case error scenarios incur significant overhead, prompting the development of local decoders, that leverage the sparse and often trivial nature of many quantum errors, to support the conventional decoders. The previously proposed Clique decoder addresses this by handling isolated, length-1 space and time errors within the cryogenic environment with minimal hardware costs, thereby mitigating I/O bandwidth constraints between cryogenic quantum systems and room-temperature processors. Building on this foundation, we propose Clique_L2 that extends the Clique-based approach by relaxing some original constraints and incorporating additional low-cost logic to also correct length-2 error chains in space, which become non-trivial occurrences at higher physical error rates and code distances. This enhanced capability not only further reduces out-of-the-fridge data transmission but also adapts more effectively to clustered errors observed under a variety of noise models. Specifically, under data-qubit-only errors and uniformly random noise, Clique_L2 achieves up to 8.95x decoding bandwidth reduction over the original Clique (or Clique_L1) decoder, especially beneficial at higher code distances. When clustered errors and longer error chains are more likely to occur, Clique_L2 achieves up to 18.3x decoding bandwidth reduction over Clique_L1, achieving substantial benefits across a wide range of physical qubit error rates.

quant-ph↗

arXiv2025

Boundary integral equation analysis for spheroidal suspensions

In this work, we provide a fast, spectrally accurate method for the evaluation of boundary integral operators (BIOs) on a suspension of prolate and oblate spheroids. We first derive formulas for the standard layer potential operators for the Laplace equation applied to an expansion of the integral densities in the appropriate spheroidal harmonic basis. These then lead to analytical expressions in solid harmonics that allow spectrally accurate evaluation of near-field particle interactions. Finally, a standard quadrature scheme is used to evaluate smooth, far-field interactions; these are then accelerated using the fast multipole method. Through a number of numerical test cases, we verify the accuracy and efficiency of our BIO evaluation framework for dense, polydisperse suspensions of spheroids. Through the use of standard formulas linking Stokes and Laplace potentials, we show our scheme can be readily applied to problems involving particulate suspension flows. For both Laplace and Stokes, our method allows us to evaluate BIOs for suspensions up to hundreds of particles on a single processor.

math.NA↗

arXiv2025

Variational quantum and neural quantum states algorithms for the linear complementarity problem

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems -- and whether quantum-inspired classical algorithms can match their performance -- remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modeling certain physical systems.

cs.CE↗

arXiv2024

Retentive Neural Quantum States: Efficient Ansätze for Ab Initio Quantum Chemistry

Neural-network quantum states (NQS) has emerged as a powerful application of quantum-inspired deep learning for variational Monte Carlo methods, offering a competitive alternative to existing techniques for identifying ground states of quantum problems. A significant advancement toward improving the practical scalability of NQS has been the incorporation of autoregressive models, most recently transformers, as variational ansatze. Transformers learn sequence information with greater expressiveness than recurrent models, but at the cost of increased time complexity with respect to sequence length. We explore the use of the retentive network (RetNet), a recurrent alternative to transformers, as an ansatz for solving electronic ground state problems in $\textit{ab initio}$ quantum chemistry. Unlike transformers, RetNets overcome this time complexity bottleneck by processing data in parallel during training, and recurrently during inference. We give a simple computational cost estimate of the RetNet and directly compare it with similar estimates for transformers, establishing a clear threshold ratio of problem-to-model size past which the RetNet's time complexity outperforms that of the transformer. Though this efficiency can comes at the expense of decreased expressiveness relative to the transformer, we overcome this gap through training strategies that leverage the autoregressive structure of the model -- namely, variational neural annealing. Our findings support the RetNet as a means of improving the time complexity of NQS without sacrificing accuracy. We provide further evidence that the ablative improvements of neural annealing extend beyond the RetNet architecture, suggesting it would serve as an effective general training strategy for autoregressive NQS.

cs.LG↗

arXiv2024

An application of continuous-variable gate synthesis to quantum simulation of classical dynamics

Although quantum computing holds promise to accelerate a wide range of computational tasks, the quantum simulation of quantum dynamics as originally envisaged by Feynman remains the most promising candidate for achieving quantum advantage. A less explored possibility with comparably far-reaching technological applicability is the quantum simulation of classical nonlinear dynamics. Attempts to develop digital quantum algorithms based on the Koopman von Neumann formalism have met with challenges because of the necessary projection step from an infinite-dimensional Hilbert space to the finite-dimensional subspace described by a collection of qubits. This finitization produces numerical artifacts that limit solutions to very short time horizons. In this paper we review continuous-variable quantum computing (CVQC), which naturally avoids such obstacles, and a CVQC algorithm for KvN simulation of classical nonlinear dynamics is advocated. In particular, we present explicit gate synthesis for product-formula Hamiltonian simulation of anharmonic vibrational dynamics.

quant-ph↗

arXiv2024

Shape optimization of slip-driven axisymmetric microswimmers

In this work, we develop a computational framework that aims at simultaneously optimizing the shape and the slip velocity of an axisymmetric microswimmer suspended in a viscous fluid. We consider shapes of a given reduced volume that maximize the swimming efficiency, i.e., the (size-independent) ratio of the power loss arising from towing the rigid body of the same shape and size at the same translation velocity to the actual power loss incurred by swimming via the slip velocity. The optimal slip and efficiency (with shape fixed) are here given in terms of two Stokes flow solutions, and we then establish shape sensitivity formulas of adjoint-solution that provide objective function derivatives with respect to any set of shape parameters on the sole basis of the above two flow solutions. Our computational treatment relies on a fast and accurate boundary integral solver for solving all Stokes flow problems. We validate our analytic shape derivative formulas via comparisons against finite-difference gradient evaluations, and present several shape optimization examples.

math.OC↗

arXiv2023

Quantum-inspired nonlinear Galerkin ansatz for high-dimensional HJB equations

Neural networks are increasingly recognized as a powerful numerical solution technique for partial differential equations (PDEs) arising in diverse scientific computing domains, including quantum many-body physics. In the context of time-dependent PDEs, the dominant paradigm involves casting the approximate solution in terms of stochastic minimization of an objective function given by the norm of the PDE residual, viewed as a function of the neural network parameters. Recently, advancements have been made in the direction of an alternative approach which shares aspects of nonlinearly parametrized Galerkin methods and variational quantum Monte Carlo, especially for high-dimensional, time-dependent PDEs that extend beyond the usual scope of quantum physics. This paper is inspired by the potential of solving Hamilton-Jacobi-Bellman (HJB) PDEs using Neural Galerkin methods and commences the exploration of nonlinearly parametrized trial functions for which the evolution equations are analytically tractable. As a precursor to the Neural Galerkin scheme, we present trial functions with evolution equations that admit closed-form solutions, focusing on time-dependent HJB equations relevant to finance.

math.NA↗

arXiv2023

An Incremental Tensor Train Decomposition Algorithm

We present a new algorithm for incrementally updating the tensor train decomposition of a stream of tensor data. This new algorithm, called the {\em tensor train incremental core expansion} (TT-ICE) improves upon the current state-of-the-art algorithms for compressing in tensor train format by developing a new adaptive approach that incurs significantly slower rank growth and guarantees compression accuracy. This capability is achieved by limiting the number of new vectors appended to the TT-cores of an existing accumulation tensor after each data increment. These vectors represent directions orthogonal to the span of existing cores and are limited to those needed to represent a newly arrived tensor to a target accuracy. We provide two versions of the algorithm: TT-ICE and TT-ICE accelerated with heuristics (TT-ICE$^*$). We provide a proof of correctness for TT-ICE and empirically demonstrate the performance of the algorithms in compressing large-scale video and scientific simulation datasets. Compared to existing approaches that also use rank adaptation, TT-ICE$^*$ achieves $57\times$ higher compression and up to $95\%$ reduction in computational time.

math.NA↗