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Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…
NVIDIA Tensor Cores and AMD Matrix Cores (together called Matrix Accelerators) are of growing interest in high-performance computing and machine learning owing to their high performance. Unfortunately, their numerical behaviors are not…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and…
We develop the first constructive algorithms for compiling single-qubit unitary gates into circuits over the universal $V$ basis. The $V$ basis is an alternative universal basis to the more commonly studied $\{H,T\}$ basis. We propose two…
A collection of algorithms in object-oriented MATLAB is described for numerically computing with smooth functions defined on the unit ball in the Chebfun software. Functions are numerically and adaptively resolved to essentially machine…
The simulation of the two-dimensional Ising model is used as a benchmark to show the computational capabilities of Graphic Processing Units (GPUs). The rich programming environment now available on GPUs and flexible hardware capabilities…
Quantum circuit mapping is a crucial process in the quantum circuit compilation pipeline, facilitating the transformation of a logical quantum circuit into a list of instructions directly executable on a target quantum system. Recent…
In recent years graphical processing units (GPUs) have become a powerful tool in scientific computing. Their potential to speed up highly parallel applications brings the power of high performance computing to a wider range of users.…
The supercomputing platforms available for high performance computing based research evolve at a great rate. However, this rapid development of novel technologies requires constant adaptations and optimizations of the existing codes for…
A theoretical memory with limited processing power and internal connectivity at each element is proposed. This memory carries out parallel processing within itself to solve generic array problems. The applicability of this in-memory…
Over the last ten years, graphics processors have become the de facto accelerator for data-parallel tasks in various branches of high-performance computing, including machine learning and computational sciences. However, with the recent…
Computing-in-memory (CIM) promises to alleviate the Von Neumann bottleneck and accelerate data-intensive applications. Depending on the underlying technology and configuration, CIM enables implementing compute primitives in place, such as…
Quantum circuit equivalence checking asks whether two circuits implement the same unitary. It guarantees compiler correctness and safe optimization, yet most existing approaches scale exponentially with the number of qubits or the circuit…
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…
Circular targets are widely used in LiDAR-camera extrinsic calibration due to their geometric consistency and ease of detection. However, achieving accurate 3D-2D circular center correspondence remains challenging. Existing methods often…
Despite extensive research on symmetric polynomial quadrature rules for triangles, as well as approaches to their calculation, few studies have focused on non-polynomial functions, particularly on their integration using symmetric triangle…
General Matrix Multiplication (GEMM) has a wide range of applications in scientific simulation and artificial intelligence. Although traditional libraries can achieve high performance on large regular-shaped GEMMs, they often behave not…
Convolution layers are prevalent in many classes of deep neural networks, including Convolutional Neural Networks (CNNs) which provide state-of-the-art results for tasks like image recognition, neural machine translation and speech…