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

Exploring the synergistic potential of quantum annealing and gate model computing for portfolio optimization

Portfolio optimization is one of the most studied problems for demonstrating the near-term applications of quantum computing. However, large-scale problems cannot be solved on today's quantum hardware. In this work, we extend upon a study to use the best of both quantum annealing and gate-based quantum computing systems to enable solving large-scale optimization problems efficiently on the available hardware. The existing work uses a method called Large System Sampling Approximation (LSSA) that involves dividing the large problem into several smaller problems and then combining the multiple solutions to approximate the solution to the original problem. This paper introduces a novel technique to modify the sampling step of LSSA. We divide the portfolio optimization problem into sub-systems of smaller sizes by selecting a diverse set of assets that act as representatives of the entire market and capture the highest correlations among assets. We conduct tests on real-world stock data from the Indian stock market on up to 64 assets. Our experimentation shows that the hybrid approach performs at par with the traditional classical optimization methods with a good approximation ratio. We also demonstrate the effectiveness of our approach on a range of portfolio optimization problems of different sizes. We present the effects of different parameters on the proposed method and compare its performance with the earlier work. Our findings suggest that hybrid annealer-gate quantum computing can be a valuable tool for portfolio managers seeking to optimize their investment portfolios in the near future.Comment: 12 pages, 4 figures, 1 tabl

On Modifying the Variational Quantum Singular Value Decomposition Algorithm

In this work, we discuss two modifications that can be made to a known variational quantum singular value decomposition algorithm popular in the literature. The first is a change to the objective function which hints at improved performance of the algorithm and decreases the depth of the circuits. The second modification introduces a new way of computing expectation values of general matrices, which is a key step in the algorithm. We then benchmark this modified algorithm and compare the performance of our new objective function with the existing one.Comment: 8 pages, 10 figures, 2 table

Determination of Fatty Acid Methyl Esters Derived from Algae Scenedesmus dimorphus Biomass by GC-MS with One-step Esterification of Free Fatty Acids and Transesterification of Glycerolipids

Algae can synthesize, accumulate and store large amounts of lipids in its cells, which holds immense potential as a renewable source of biodiesel. In this work, we have developed and validated a GC–MS method for quantitation of fatty acids and glycerolipids in forms of fatty acid methyl esters derived from algae biomass. Algae Scenedesmus dimorphus drymass was pulverized by mortar and pestle, then extracted by the modified Folch method and fractionated into free fatty acids and glycerolipids on aminopropyl solid-phase extraction cartridges. Fatty acid methyl esters were produced by an optimized one-step esterification of fatty acids and transesterification of glycerolipids with boron trichloride/methanol. The matrix effect, recoveries and stability of fatty acids and glycerolipids in algal matrix were first evaluated by spiking stable isotopes of pentadecanoic-2,2-d2 acid and glyceryl tri(hexadecanoate-2,2-d2) as surrogate analytes and tridecanoic-2,2-d2 acid as internal standard into algal matrix prior to sample extraction. Later, the method was validated in terms of lower limits of quantitation, linear calibration ranges, intra- and inter-assay precision and accuracy using tridecanoic-2,2-d2 acid as internal standard. The method developed has been applied to the quantitation of fatty acid methyl esters from free fatty acid and glycerolipid fractions of algae Scenedesmus dimorphus