Related papers: Optimization of Generalized Jacobian Chain Product…
When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum…
Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…
Most nonlinear partial differential equation (PDE) solvers require the Jacobian matrix associated to the differential operator. In PETSc, this is typically achieved by either an analytic derivation or numerical approximation method such as…
This paper is concerned with finite-level quantum memory systems for retaining initial dynamic variables in the presence of external quantum noise. The system variables have an algebraic structure, similar to that of the Pauli matrices, and…
This study proposes a simple procedure to compute Efficient Pseudo Likelihood (EPL) estimator proposed by Dearing and Blevins (2024) for estimating dynamic discrete games, without computing Jacobians of equilibrium constraints. EPL…
Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device. Implementing…
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not involve the calculation of codimension-sized minors of the…
Recommender systems can be formulated as a matrix completion problem, predicting ratings from user and item parameter vectors. Optimizing these parameters by subsampling data becomes difficult as the number of users and items grows. We…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
Classic cache-oblivious parallel matrix multiplication algorithms achieve optimality either in time or space, but not both, which promotes lots of research on the best possible balance or tradeoff of such algorithms. We study modern…
Quantum computers offer the potential to simulate nuclear processes that are classically intractable. With the goal of understanding the necessary quantum resources to realize this potential, we employ state-of-the-art…
Recent work has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We derive an explicit formula, as well as an efficient procedure, for constructing a generalized Jacobian for the projector of a given square matrix onto the Birkhoff polytope, i.e., the set of doubly stochastic matrices. To guarantee the…
Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete…
Processing data collected by a network of agents often boils down to solving an optimization problem. The distributed nature of these problems calls for methods that are, themselves, distributed. While most collaborative learning problems…
Most computational approaches to Bayesian experimental design require making posterior calculations repeatedly for a large number of potential designs and/or simulated datasets. This can be expensive and prohibit scaling up these methods to…
In spite of remarkable progress in machine learning techniques, the state-of-the-art machine learning algorithms often keep machines from real-time learning (online learning) due in part to computational complexity in parameter…
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
Quantum computers promise to dramatically outperform their classical counterparts. However, the non-classical resources enabling such computational advantages are challenging to pinpoint, as it is not a single resource but the subtle…