Visão Geral
Este curso apresenta os principais conceitos matemáticos necessários para compreender a computação quântica, com foco em álgebra linear, números complexos, vetores, matrizes e fundamentos matemáticos usados na mecânica quântica. O objetivo é preparar o aluno para avançar com segurança em estudos e aplicações de computação quântica.
Conteúdo Programatico
Module 1 – Mathematical Foundations for Quantum Computing
- Role of mathematics in quantum computing
- Mathematical notation and conventions
- Review of basic algebra
- Logical and mathematical reasoning
Module 2 – Complex Numbers
- Definition of complex numbers
- Algebraic and polar forms
- Complex conjugates and modulus
- Euler’s formula and applications
Module 3 – Vectors and Vector Spaces
- Vectors and operations
- Vector spaces concepts
- Linear independence and basis
- Inner product and norms
Module 4 – Matrices and Linear Transformations
- Matrix operations
- Determinants and inverses
- Linear transformations
- Matrix representation of operators
Module 5 – Linear Algebra for Quantum Systems
- Eigenvalues and eigenvectors
- Diagonalization
- Hermitian and unitary matrices
- Tensor products basics
Module 6 – Probability and Statistics Basics
- Probability concepts
- Random variables
- Discrete probability distributions
- Measurement interpretation
Module 7 – Mathematical Representation of Quantum States
- State vectors and bra-ket notation
- Superposition and normalization
- Measurement probabilities
- Multi-state systems
Module 8 – Mathematical View of Quantum Operations
- Operators and observables
- Quantum gates as matrices
- State evolution
- Mathematical preparation for quantum algorithms