Msc Thesis by Rafael Pereira da Silva
A Padé approximant of a real valued-function is a rational function such that the Maclaurin serie... more A Padé approximant of a real valued-function is a rational function such that the Maclaurin series coincides as far as possible with the Maclaurin series of the given function. The fact that Padé’s approximants are rational functions gives them the ability to sum up, for example, truncated series or to capture singularities of functions, offering an important tool for this kind of studies. The calculation of Padé’s approximantes can be carried out by direct or recursive methods. The goal of this thesis is to compare the direct method with the Baker’s recursive method, to compute an approximant of Padé with a finite precision. To confront these two approaches, we will perform the calculation of the Padé approximants with infinite precision, which will allow us to compare the direct versus the recursive methods. In this study, we used Python 3.7 and sympy library for the analytical calculations. For three series, we have constructed the corresponding Padé approximants, using analytical computation and finite arithmetic precision. Numerical evidences, based on the analysis of thousands of Padé approximants, show that the choice of the method depends on the class of functions, the degree of the approximations, and the collocation points under study.
Papers by Rafael Pereira da Silva
Shor's algorithm is a quantum algorithm for efficiently factoring large integers, which poses a s... more Shor's algorithm is a quantum algorithm for efficiently factoring large integers, which poses a significant threat to classical cryptography. Here, we explain it in four key steps, covering Euclid's algorithm, the quantum Fourier transform (QFT), the quantum phase estimation (QPE), and continued fractions. We also highlight the recent post-quantum encryption standards released by the National Institute of Standards and Technology (NIST) and their importance in response to the future cyber threat of quantum computers.
This work serves as a hands-on approach to understanding the fundamentals of oracle-based quantum... more This work serves as a hands-on approach to understanding the fundamentals of oracle-based quantum algorithms. In particular, we give an accessible and concise explanation of the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Grover quantum solutions to classical problems. We aim to offer a valuable resource for anyone interested in learning about quantum computing.
This paper outlines the use of noisy intermediate-scale quantum (NISQ) computers for Hamiltonian ... more This paper outlines the use of noisy intermediate-scale quantum (NISQ) computers for Hamiltonian minimization problems. We delve into the mathematical formulation of Variational Quantum Eigensolver (VQE), Quantum Annealing (QA) and Quantum Approximation Optimization Algorithm (QAOA), with computational results for a 3-qubit minimization problem and its extension to 6-qubit, 13-qubit and 140-qubit. We show how different initial parameters leads to optimal, less accurate, or no satisfactory solutions using the considered versions of VQE and QAOA, a well known challenge. For all problems, the optimal solution was found using QA and hybrid solvers. This work serves as a hands-on approach to understand quantum annealing, variational quantum algorithms, quantum hardware limitations and current landscape.
This Jupyter notebook (pdf version) is a supplementary resource to the author's preprint [1]. Her... more This Jupyter notebook (pdf version) is a supplementary resource to the author's preprint [1]. Here we discuss and provide guidance on the following: 1. Quandela Cloud account 2. Perceval local environment (Windows OS) 3. Unitary matrices and Optical Circuits 3.1. Run on a quantum simulator 3.2. Run on a real quantum processor 4. Optical Circuit from Gate Circuit.
This paper aims to provide an accessible overview of annealing quantum computing. We give high-le... more This paper aims to provide an accessible overview of annealing quantum computing. We give high-level explanations of the key quantum properties that are leveraged by a quantum annealer, along with the quantum mathematical formalism involved. Additionally, we provide information about hardware and software available for running quantum annealing algorithms, and references for further reading.
This Jupyter notebook (pdf version) is a supplementary resource to the author’s paper Annealing Q... more This Jupyter notebook (pdf version) is a supplementary resource to the author’s paper Annealing Quantum Computing: An Overview. Here we discuss and provide guidance on the following: 1. D-Wave Leap account, 2. Ocean local environment (Windows OS), 3. Ising and QUBO model, 3.1 Exact solution, 3.2 Simulated annealing, 4. Problem to QUBO, 4.1 Exact solver, 4.2 Run on a quantum annealer processor, 4.3 Run on a Hybrid solver, 5. Problem constrains, 5.1 Run on a Hybrid CQM solver, 6. Embedding.
This Jupyter notebook (pdf version) is a supplementary resource to the author's paper Quantum Com... more This Jupyter notebook (pdf version) is a supplementary resource to the author's paper Quantum Computing: An Overview. Here we discuss and provide guidance on the following: 1. IBM Quantum Experience account 2. Qiskit local environment (Windows OS) 3. One qubit circuit 3.1. Quantum Coin Game 4. Bell states circuit 4.1. Run on a quantum simulator 4.2. Run on a real quantum processor.
padepy is a Python library for Padé approximation calculation with infinite (algebric) and finite... more padepy is a Python library for Padé approximation calculation with infinite (algebric) and finite (floating) precision.
This paper aims to serve as a starting point for the reader interested in learning the fundamenta... more This paper aims to serve as a starting point for the reader interested in learning the fundamentals of photonic quantum computing. We cover fundamental quantum principles, mathematical foundations, hardware and software tools for programming photonic quantum circuits, and resources for further study.
This paper intends to be a starting point for the reader interested in learning the fundamentals ... more This paper intends to be a starting point for the reader interested in learning the fundamentals of quantum computing. For that purpose, we give high-level explanations of the key quantum properties leveraged by a quantum computer, the quantum mathematical formalism, information about current hardware and software available to run quantum algorithms, and references for further reading.
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Msc Thesis by Rafael Pereira da Silva
Papers by Rafael Pereira da Silva