Environmental Pursuits In Nanomaterial Systems Science With Indian Exemplars

The behavior and pattern of NPs of minerals in the evolutionary history of the earth vis – a –vis the environmental context are inquired into, with a riverine system as a model. The study of fractal dimensions of NPs of interest serves as an aid to obtain a comprehensive view of natural NPs in the model system. The present study combines inputs from work done on nanoparticles, derived from the Subanarekha River System and products of base metal mine effluents that are rich in NPs of minerals. The authors believe this study would help to establish certain universalities about NPs and provide an updated framework for understanding the current state of nanomineral science

Multilevel Combinatorial Optimization Across Quantum Architectures

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave's quantum annealer and IBM's gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution

Fault-ignorant Quantum Search

We investigate the problem of quantum searching on a noisy quantum computer. Taking a 'fault-ignorant' approach, we analyze quantum algorithms that solve the task for various different noise strengths, which are possibly unknown beforehand. We prove lower bounds on the runtime of such algorithms and thereby find that the quadratic speedup is necessarily lost (in our noise models). However, for low but constant noise levels the algorithms we provide (based on Grover's algorithm) still outperform the best noiseless classical search algorithm.Comment: v1: 15+8 pages, 4 figures; v2: 19+8 pages, 4 figures, published version (Introduction section significantly expanded, presentation clarified, results and order unchanged

Faster quantum mixing for slowly evolving sequences of Markov chains

Markov chain methods are remarkably successful in computational physics, machine learning, and combinatorial optimization. The cost of such methods often reduces to the mixing time, i.e., the time required to reach the steady state of the Markov chain, which scales as $\delta^{-1}$, the inverse of the spectral gap. It has long been conjectured that quantum computers offer nearly generic quadratic improvements for mixing problems. However, except in special cases, quantum algorithms achieve a run-time of $\mathcal{O}(\sqrt{\delta^{-1}} \sqrt{N})$, which introduces a costly dependence on the Markov chain size $N,$ not present in the classical case. Here, we re-address the problem of mixing of Markov chains when these form a slowly evolving sequence. This setting is akin to the simulated annealing setting and is commonly encountered in physics, material sciences and machine learning. We provide a quantum memory-efficient algorithm with a run-time of $\mathcal{O}(\sqrt{\delta^{-1}} \sqrt[4]{N})$, neglecting logarithmic terms, which is an important improvement for large state spaces. Moreover, our algorithms output quantum encodings of distributions, which has advantages over classical outputs. Finally, we discuss the run-time bounds of mixing algorithms and show that, under certain assumptions, our algorithms are optimal.Comment: 20 pages, 2 figure

On the construction of model Hamiltonians for adiabatic quantum computation and its application to finding low energy conformations of lattice protein models

In this report, we explore the use of a quantum optimization algorithm for obtaining low energy conformations of protein models. We discuss mappings between protein models and optimization variables, which are in turn mapped to a system of coupled quantum bits. General strategies are given for constructing Hamiltonians to be used to solve optimization problems of physical/chemical/biological interest via quantum computation by adiabatic evolution. As an example, we implement the Hamiltonian corresponding to the Hydrophobic-Polar (HP) model for protein folding. Furthermore, we present an approach to reduce the resulting Hamiltonian to two-body terms gearing towards an experimental realization.Comment: 35 pages, 8 figure