Related papers: A Second-Order Distributed Trotter-Suzuki Solver w…
The polyhedral homotopy method of Huber and Sturmfels is a particularly efficient and robust numerical method for solving system of (Laurent) polynomial equations. A central component in an implementation of this method is an efficient and…
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent…
The ability to model, analyze, and predict execution time of computations is an important building block supporting numerous efforts, such as load balancing, performance optimization, and automated performance tuning for high performance,…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators, for instance as local…
We propose a CPU-GPU heterogeneous computing method for solving time-evolution partial differential equation problems many times with guaranteed accuracy, in short time-to-solution and low energy-to-solution. On a single-GH200 node, the…
The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
In the rapidly evolving research on artificial intelligence (AI) the demand for fast, computationally efficient, and scalable solutions has increased in recent years. The problem of optimizing the computing resources for distributed machine…
Quantum systems are the future candidates for computers and information processing devices. Information about quantum states and processes may be incomplete and scattered in these systems. We use a quantum version of Belief Propagation(BP)…
The convergence of SGD based distributed training algorithms is tied to the data distribution across workers. Standard partitioning techniques try to achieve equal-sized partitions with per-class population distribution in proportion to the…
Product formulas for Trotter Suzuki simulation remain a practical route to Hamiltonian evolution on noisy intermediate scale quantum (NISQ) hardware, yet their accuracy hinges on three coupled choices: term grouping, product formula order,…
The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…
In distributed machine learning, a central node outsources computationally expensive calculations to external worker nodes. The properties of optimization procedures like stochastic gradient descent (SGD) can be leveraged to mitigate the…
In this paper we analyze the problem of optimal task scheduling for data centers. Given the available resources and tasks, we propose a fast distributed iterative algorithm which operates over a large scale network of nodes and allows each…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
Efficient simulation of the semiclassical Schr\"odinger equation has garnered significant attention in the numerical analysis community. While controlling the error in the unitary evolution or the wavefunction typically requires the time…
Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…
High-dimensional fractional reaction-diffusion equations have numerous applications in the fields of biology, chemistry, and physics, and exhibit a range of rich phenomena. While classical algorithms have an exponential complexity in the…
Since 2005 there has been a huge growth in the use of engineered control pulses to perform desired quantum operations in systems such as NMR quantum information processors. These approaches, which build on the original gradient ascent pulse…