Algorithm Details

This section introduces the theoretical framework of the quantum optimization algorithms supported by the Amplify SDK.

Each algorithm’s page explains the details of the algorithm and its underlying theory.

• QAOA Algorithm: A representative variational quantum algorithm that combines a quantum computer with classical optimization to solve combinatorial optimization problems (PUBO). It constructs a Hamiltonian corresponding to the problem and approximately searches for its ground state using a parametric quantum circuit (ansatz).

• Constrained QAOA Algorithm: A QAOA that uses an ansatz accounting for N-HOT constraints (equality constraints where exactly \(n\) variables take the value \(-1\)). By optimizing within the subspace of quantum states restricted by the constraints, it is expected to handle constrained problems more efficiently than the penalty method.

• Recursive QAOA Algorithm: A method that repeatedly executes shallow QAOA, progressively reducing the problem’s variables before identifying the optimal solution. It aims to apply QAOA to larger-scale problems while keeping the circuit depth low.