Chapter 5. Algorithms Based on Variational Quantum Circuits

In this chapter, we will learn about the most important application of NISQ devices, the quantum-classical hybrid algorithm based on variational quantum circuits. These algorithms are extremely important for the application of NISQ devices to real problems.

• 5-1. Variational Quantum Eigensolver（VQE)
  • Background
  • Variational Methods
  • What is VQE?
  • Variational Methods
  • Example Implementation
  • Preparation of quantum gates
  • Prepare the Hamiltonian.
  • Preparing a quantum circuit
  • Measuring the expected energy of a quantum state
  • Minimizing the energy expectation value
  • Reference
• 5-2. Quantum Circuit Learning (QCL)
  • Overview of QCL
  • Learning Procedure
  • Implementation using QURI Parts
    • Prepare training data
    • Composition of input state
    • Configuration of variational quantum circuit \(U(\theta)\)
      • 1. Creation of transverse magnetic field Ising Hamiltonian
      • 2. Creation of rotating gate, 3. Configuration of \(U(\theta)\)
    • Measurement
    • Organize a series of steps into a function
    • Cost function calculation
    • Learning (optimize with scipy.optimize.minimize)
      • Optimization loop with QURI Parts
      • Perform Quantum Circuit Learning on a real quantum computer
  • Reference
• 5-3. Quantum Approximate Optimization Algorithm (QAOA)
  • Overview
  • Problem setting
  • QAOA Algorithm Steps
  • Implementation: Solve the Maxcut problem with QAOA
    • \(p=1\) case
    • \(p=2\) case
  • Reference