5 citations · 8 across the 12 of their papers we have counts for
12 papers
Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation
Reuben Demirdjian, Thomas Hogancamp, Abeynaya Gnanasekaran +2
Nonlinear ordinary and partial differential equations are ubiquitous in science and engineering, yet finding their solutions is often computationally intractable for classical hard…
Quantum Lattice Boltzmann Solutions for Transport under 3D Spatially Varying Advection on Trapped Ion Hardware
Sayonee Ray, Jezer Jojo, Jason Iaconis +5
The Quantum Lattice Boltzmann Method (QLBM) has emerged as one of the most promising quantum computing approaches for the numerical simulation of problems in computational fluid dy…
Domain-Filtered Knowledge Graphs from Sparse Autoencoder Features
John Winnicki, Abeynaya Gnanasekaran, Eric Darve
Sparse autoencoders (SAEs) extract millions of interpretable features from a language model, but flat feature inventories aren't very useful on their own. Domain concepts get mixed…
Efficient Quantum Access Model for Sparse Structured Matrices using Linear Combination of Things
Abeynaya Gnanasekaran, Amit Surana
We present a novel framework for Linear Combination of Unitaries (LCU)-style decomposition tailored to structured sparse matrices, which frequently arise in the numerical solution…
Variational Quantum Framework for Nonlinear PDE Constrained Optimization Using Carleman Linearization
Abeynaya Gnanasekaran, Amit Surana, Hongyu Zhu
We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introdu…
Variational Quantum Framework for Partial Differential Equation Constrained Optimization
Amit Surana, Abeynaya Gnanasekaran
We present a novel variational quantum framework for linear partial differential equation (PDE) constrained optimization problems. Such problems arise in many scientific and engine…
Efficient Variational Quantum Linear Solver for Structured Sparse Matrices
Abeynaya Gnanasekaran, Amit Surana
We develop a novel approach for efficiently applying variational quantum linear solver (VQLS) in context of structured sparse matrices. Such matrices frequently arise during numeri…
On the Emergence of Ergodic Dynamics in Unique Games
Tuhin Sahai, Abeynaya Gnanasekaran
The Unique Games Conjecture (UGC) constitutes a highly dynamic subarea within computational complexity theory, intricately linked to the outstanding P versus NP problem. Despite mu…
Efficient Quantum Algorithms for Nonlinear Stochastic Dynamical Systems
Abeynaya Gnanasekaran, Amit Surana, Tuhin Sahai
In this paper, we propose efficient quantum algorithms for solving nonlinear stochastic differential equations (SDE) via the associated Fokker-Planck equation (FPE). We discretize…
An efficient quantum algorithm for simulating polynomial differential equations
Amit Surana, Abeynaya Gnanasekaran, Tuhin Sahai
We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical sy…
Hierarchical Orthogonal Factorization: Sparse Least Squares Problems
Abeynaya Gnanasekaran, Eric Darve
In this work, we develop a fast hierarchical solver for solving large, sparse least squares problems. We build upon the algorithm, spaQR (sparsified QR), that was developed by the…
Hierarchical Orthogonal Factorization: Sparse Square matrices
Abeynaya Gnanasekaran, Eric Darve
In this work, we develop a new fast algorithm, spaQR -- sparsified QR, for solving large, sparse linear systems. The key to our approach is using low-rank approximations to sparsif…