The algorithms in the last module, such as Shor's and Grover's, need large, reliable quantum computers. Today's machines are small and noisy, so a different approach is used for them: split the work between a quantum circuit and a classical computer. This module covers that hybrid approach.
It starts with the variational quantum eigensolver (VQE): how an ansatz circuit with adjustable parameters, an Estimator, and a classical optimizer work together to find the lowest-energy state of a system. It then covers the quantum approximate optimization algorithm (QAOA) and uses it to solve a max-cut problem with the Qiskit patterns workflow, first on a small graph and then at utility scale.
Watch the lessons in order, then continue on to Noise, Error Correction & Hardware.
Qiskit's overview of VQE as a hybrid quantum-classical algorithm: its main components (operator, ansatz, estimator, classical optimizer) and the factors that affect how well it works.
A friendly introduction to how VQE works and why it is one of the most promising algorithms for near-term quantum hardware.
A lecture from the Qiskit Global Summer School on estimating the lowest eigenvalue of a Hamiltonian by tuning circuit parameters to minimize its expectation value.
Solving the max-cut problem with QAOA: mapping the graph to a cost Hamiltonian, building the alternating cost and mixer layers, optimizing the parameters, and scaling the same workflow up to real hardware.