README.md

Quantum Computing

This repository provides a comprehensive tutorial designed to initiate simulations of material interactions at the atomic level using quantum computers.

Sumário

1. Quantum Computing Theory

   • 1.1 Single Qubit System
   • 1.2 Two or more independent Qubit System
   • 1.3 Two or more correlated Qubit System
   • 1.4 Logic Operators
   • 1.5 Expected Value

2. NISC Hardware

   • 2.1 Quantum Hardwares
     • 2.1.1 Superconductor QPU
     • 2.1.2 Photonic QPU
     • 2.1.3 Neutral-Atom Based QPU
     • 2.1.4 Ion-Trapped QPU
   • 2.2 Quantum Noise
     • 2.2.1 Depolarization Error
     • 2.2.2 Initialization Error
     • 2.2.3 Phase Damping Error
     • 2.2.4 Readout Error
     • 2.2.4 Thermal Relaxation Error
   • 2.3 Quantum Noise Mitigation
     • 2.3.1 Clifford Regression
     • 2.3.2 Richardson Extrapolation

3. Ab-initio Calculation

   • 3.1 Building System's Hamiltonian
     • 3.1.1 Bohr-Oppenheimer Approximation
     • 3.1.2 Fock Space
     • 3.1.3 Fermionic Creation and Annihilation Operators
     • 3.1.4 Slater Type Orbitals
   • 3.2 Mapping Hamiltonian to Quantum Circuit
     • 3.2.1 Jordan-Wigner Transformation
     • 3.2.2 Parity Transformation
     • 3.2.3 Bravyi-Kitaev Transformation
     • 3.2.4 Bravyi-Kitaev Superfast Transformation
   • 3.3 Optimizing System Energy
     • 3.3.1 Optimization Algorithm
       • 3.3.1.1 Gradient-Free Optimizers
       • 3.3.1.2 Gradient-Descent Optimizers
     • 3.3.2 VQE
   • 3.4 Mitigating Noise
   • 3.5 Comparing Results