Chapter 6 Quantum chemistry calculation

In this chapter, we will learn about quantum chemical calculations, which is considered one of the most important and promising applications of NISQ devices. First, we will learn how to handle OpenFermion, a useful library for quantum chemical calculations, and how to convert quantum chemistry problems into a form that can be solved by a quantum computer. (chapter 6-1) After that, in chapter 6-2, we implement variational quantum eigensolver, which we learned in chapter 5-1 with Qulacs. In chapter 6-3, we learn about subspace-variational quantum eigensolver (SS-VQE) with which we can calculate not only the ground state but also the excited state.

*This chapter requires a prerequisite knowledge of quantum chemistry, so if you don’t understand what you are reading, please refer to other literature or skip over it.

• 6-1. OpenFermion Basics
  • Calculation of hydrogen molecule
  • Variable description
    • basis: basis function
    • multiplicity: spin multiplicity
    • charge: total charge
    • geometry: nuclear configuration
    • description
  • Calculatin with PySCF
  • HF & Full-CI energy
  • One-Electron integral \(h_{ij}\)・Two-Electron integral \(h_{ijkl}\)
  • Hamiltonian in second quantized form
  • Convert to tractable operators for quantum computers
  • Reference
• 6-2. Variational Quantum Eigensolver (VQE) Implementation using Qulacs
  • Install and Import of required packages
  • Creation of Hamiltonian
  • Convert Hamiltonian into qulacs Hamiltonian
  • compose ansatz
  • Define VQE cost function
  • Execute VQE
• 6-3. Calculation of Excited States using Subspace-Search Variational Quantum Eigensolver
  • Algorithm
  • SSVQE implementation
    • Preparation of Hamiltonian
    • preparation of ansatz
    • define cost function of SSVQE
    • Execution of SSVQE
  • Reference