This chapter introduces Variational Quantum Algorithms (VQAs), a hybrid quantum-classical framework often considered suitable for near-term quantum processors. We begin with the variational principle that underpins these methods and proceed to the practical elements of constructing VQAs specifically for machine learning tasks.

You will learn about:

• Designing effective Parameterized Quantum Circuits (PQCs), also known as ansätze.
• Formulating cost functions based on quantum measurement outcomes tailored to ML problems like classification or regression.
• Calculating gradients of quantum circuit expectation values, with a focus on techniques like the parameter-shift rule.
• Applying both advanced classical optimization algorithms (e.g., Adam, SPSA) and quantum-aware methods like Quantum Natural Gradient ($QNG$) to train VQAs.
• Understanding the training challenge posed by barren plateaus and strategies to mitigate their impact.

The chapter includes hands-on implementation of a Variational Quantum Classifier (VQC), integrating the concepts of PQC design, cost function definition, and optimization.