Related papers: Using C++ to Calculate $\mathsf{SO(10)}$ Tensor Co…
The measurement of the triple Higgs coupling is a key benchmark for the LHC and future colliders. It directly probes the Higgs potential and its fundamental properties in connection to new physics beyond the Standard Model. There exist two…
We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand unified theory by gravitational interactions at the Planck scale MPl. These…
It is shown that the doublet-triplet splitting problem can be solved in SO(10) using the Dimopoulos-Wilczek mechanism with a very economical Higgs content and simple structure. Only one adjoint Higgs field is required, together with spinor…
The R package calculus implements C++ optimized functions for numerical and symbolic calculus, such as the Einstein summing convention, fast computation of the Levi-Civita symbol and generalized Kronecker delta, Taylor series expansion,…
A quantum compiling algorithm is an algorithm for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose $U_{in}$ is an $\nb$-bit unstructured unitary matrix (a unitary matrix with no…
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
We propose the first fast and certifiable algorithm for the registration of two sets of 3D points in the presence of large amounts of outlier correspondences. We first reformulate the registration problem using a Truncated Least Squares…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
Despite the importance of sparse matrices in numerous fields of science, software implementations remain difficult to use for non-expert users, generally requiring the understanding of underlying details of the chosen sparse matrix storage…
Assuming grand unified theory (GUT) and supersymmetry, we propose a simple model which can consistently accommodate the masses and mixings for quarks and leptons. The grand unified group is SO(10), and $\bf 10$, $\bf 120$, and $\bar {\bf…
The observation of a SM-like Higgs boson in multiple channels at the LHC allows the extraction of Higgs couplings to gauge bosons and fermions. The precision achievable at the LHC, for an integrated luminosity of 200 fb^{-1}, is reviewed…
From FORTRAN to NumPy, tensors have revolutionized how we express computation. However, tensors in these, and almost all prominent systems, can only handle dense rectilinear integer grids. Real world tensors often contain underlying…
An outstanding problem in quantum computing is the calculation of entanglement, for which no closed-form algorithm exists. Here we solve that problem, and demonstrate the utility of a quantum neural computer, by showing, in simulation, that…
We describe an abstract loop-based intermediate representation that can express fused implementations of relational algebra expressions on sets and bags (multisets). The loops are abstracted away from physical data structures thus making it…
We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by…
High precision atomic data is indispensable for experiments involving studies of fundamental interactions, astrophysics, atomic clocks, plasma science, and others. We develop new parallel atomic structure codes and explore the difficulties…
The SM-like Higgs pair productions are discussed in the framework of the general CP-violating two-Higgs-doublet model, where we find the CP-violating mixing angles can be related to the Higgs self couplings. Therefore, the future…
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
Deploying deep learning models on various devices has become an important topic. The wave of hardware specialization brings a diverse set of acceleration primitives for multi-dimensional tensor computations. These new acceleration…