Quantum Image Representation Methods Using Qutrits

Quantum Image Processing (QIP) is a recent highlight in the Quantum Computing field. All previous methods for representing the images as quantum states were defined using qubits. One Quantum Image Representation (QIR) method using qutrits is present in the literature. Inspired by the qubit methods and the higher state-space available for qutrits, multiple QIR methods using qutrits are defined. First, the ternary quantum gates required for the representations are described and then the implementation details for five qutrit-based QIR methods are given. All the methods have been simulated in software, and example circuits are provided.Comment: 8 pages, 11 figures, 1 tabl

Importance of Explicit Vectorization for CPU and GPU Software Performance

Much of the current focus in high-performance computing is on multi-threading, multi-computing, and graphics processing unit (GPU) computing. However, vectorization and non-parallel optimization techniques, which can often be employed additionally, are less frequently discussed. In this paper, we present an analysis of several optimizations done on both central processing unit (CPU) and GPU implementations of a particular computationally intensive Metropolis Monte Carlo algorithm. Explicit vectorization on the CPU and the equivalent, explicit memory coalescing, on the GPU are found to be critical to achieving good performance of this algorithm in both environments. The fully-optimized CPU version achieves a 9x to 12x speedup over the original CPU version, in addition to speedup from multi-threading. This is 2x faster than the fully-optimized GPU version.Comment: 17 pages, 17 figure

A Spectral Theory for Tensors

In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a summation of outer products of lower order tensors . Our proposed factorization shows the relationship between the eigen-objects and the generalised characteristic polynomials. Our framework is based on a consistent multilinear algebra which explains how to generalise the notion of matrix hermicity, matrix transpose, and most importantly the notion of orthogonality. Our proposed factorization for a tensor in terms of lower order tensors can be recursively applied so as to naturally induces a spectral hierarchy for tensors.Comment: The paper is an updated version of an earlier versio