arXiv subjects

Raffaele Miceli

Publications and source records attributed to Raffaele Miceli.

3 recordsLinked to original sources

arXiv2021

Quantum Walks, Feynman Propagators and Graph Topology on an IBM Quantum Computer

Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover features of a data graph on which the walk takes place. This can be done faster on quantum computers where all paths can be explored using superposition. We begin with simple walks on a polygon and move up to graphs described by higher dimensional meshes. We use insight from the physics description of quantum walks defined in terms of probability amplitudes to go from one site on a graph to another distant site and show how this relates to the Feynman propagator or Kernel in the physics terminology. Our results from quantum computation using IBM's Qiskit quantum computing software were in good agreement with those obtained using classical computing methods.

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arXiv2019

Thermo field dynamics on a quantum computer

In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we implemented a real-time thermo field dynamics formalism, which has the added benefit of being able to compute quantities that are both time- and temperature-dependent. To implement thermo field dynamics we apply a unitary transformation to discrete quantum mechanical operators to make new Hamiltonians with encoded temperature dependence. The method works normally for fermions, which have a finite representation, but needs some modification to work with bosons. These Hamiltonians are then processed into a Pauli matrix representation in order to be used as input for IBM's Qiskit package. We then use IBM's quantum simulator to calculate an approximation to the Hamiltonaian's ground state energy via the variational quantum eigensolver (VQE) algorithm. This approximation is then compared to a classically calculated value for the exact energy. The thermo field dynamics quantum algorithm has general applications to material science, high-energy physics and nuclear physics, particularly in those situations involving real-time evolution at high temperature.

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arXiv2018

Quantum Computation and Visualization of Hamiltonians using Discrete Quantum Mechanics and IBM QISKit

Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally important is the challenge of translating problems into a state that can be fed to these machines. Because quantum computers are in essence controllable quantum systems, the problems that most naturally map to them are those of quantum mechanics. Quantum chemistry has seen particular success in the form of the variational quantum eigensolver (VQE) algorithm, which is used to determine the ground state energy of molecular systems. The goal of our work has been to use the matrix formulation of quantum mechanics to translate other systems so that they can be run through this same algorithm. We describe two ways of accomplishing this using a position basis approach and a Gaussian basis approach. We also visualize the wave functions from the eigensolver and make comparisons to theoretical results obtained with continuous operators.

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