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Nuclear Electronic Orbital Method in Quantum Computing

Overview

This section of the tutorial introduces the Nuclear Electronic Orbital (NEO) Method within a quantum computing framework, highlighting its relevance and application in solving complex chemistry problems. The NEO method's integration with quantum computing represents a significant advancement in addressing electronic correlation challenges in molecular systems.

Tutorial Focus

  • Solving Electronic Structures on Classical Computers: A primer on electronic structure calculation in classical computing.

  • Encoding Chemistry Problems in Quantum Computing:

    1. Molecular Orbital Basis Transformation: Converting the problem into a form suitable for quantum computation.
    2. Second Quantization: Representing fermionic systems (like electrons) in a quantum computing framework.
    3. Qubit Encoding with Jordan-Wigner Map: Mapping fermionic states to qubit states.

  • Ansatz Representation:

    • Unitary Coupled Cluster with Singles and Doubles Excitations (UCCSD): An advanced method for representing the quantum state of a molecule.

Practical Applications

  • Application to [Molecule]: Step-by-step application of these methods to a specific molecule, demonstrating the process from classical to quantum representation.
  • NEO-VQE Application: The final section focuses on applying the NEO method within the Variational Quantum Eigensolver (VQE) framework, showcasing its potential in quantum chemistry.

Prerequisites

Familiarity with basic quantum mechanics and computational chemistry concepts is recommended to get the most out of this section.

Variational Quantum Eigensolver Tutorial

Overview

This tutorial focuses on the Variational Quantum Eigensolver (VQE), particularly in constructing potential energy surfaces for small molecules. It is designed for learners with an interest in quantum computing and its application in solving electronic structure problems.

Contents

  • Introduction: An overview of VQE and its significance in quantum computing.
  • Lecture Links: References to relevant lectures covering topics like electronic structure and variational approaches.
  • Tasks: Practical exercises using VQE for different molecules, both on classical and quantum computers.
  • Tutorial Steps:
    • Setting up the computer environment.
    • Generating potential energy surfaces (PES) using classical methods.
    • Generating the qubit Hamiltonian.
    • Unitary transformations.
    • Hamiltonian measurements.
    • Using quantum hardware.
  • Further Challenges: Advanced topics for those looking to deepen their understanding.
  • References: A comprehensive list of references for further reading.

Getting Started

Follow the steps outlined in the tutorial to gain hands-on experience with VQE. Ensure your computing environment is appropriately set up as per the instructions.

Additional Resources

Refer to the provided lecture links for a more in-depth understanding of the concepts.

Energy Gradients Calculation

Overview

This section of the tutorial covers the calculation of energy gradients, an essential aspect in understanding molecular dynamics and optimization problems in quantum chemistry. It is divided into two main parts, each covered by a separate file:

  1. Finite Differences Approach (File: F1_Finite_Differences.ipynb):

    • This part introduces the concept of finite differences as a method to approximate derivatives.
    • It includes practical examples and exercises to understand how finite differences can be applied to quantum systems.

  2. Force Operator Method (File: F2_Force_Operator.ipynb):

    • This section delves into the force operator method based on Hellman-Feynman theorem.
    • The tutorial guides through the theoretical background and practical implementation of this method.

Learning Objectives

  • Understand the basic principles of energy gradient calculation in quantum systems.
  • Learn how to apply finite differences and force operator methods in practical scenarios.
  • Gain insights into the applications of these methods in molecular dynamics and optimization.

Contributing

Feedback and contributions to this tutorial are welcome. Please adhere to the project's contribution guidelines.