Problem-specific Parameterized Quantum Circuits of the VQE Algorithm for Optimization Problems
The Variational Quantum Eigensolver (VQE) algorithm is attracting much attention to utilize current limited quantum devices. The VQE algorithm requires a quantum circuit with parameters, called a parameterized quantum circuit (PQC), to prepare a quantum state, and the quantum state is used to calculate the expectation value of a given Hamiltonian. Creating sophisticated PQCs is important from the perspective of the convergence speed. Thus, we propose problem-specific PQCs of the VQE algorithm for optimization problems. Our idea is to dynamically create a PQC that reflects the constraints of an optimization problem. With a problem-specific PQC, it is possible to reduce a search space by restricting unitary transformations in favor of the VQE algorithm. As a result, we can speed up the convergence of the VQE algorithm. Experimental results show that the convergence speed of the proposed PQCs is significantly faster than that of the state-of-the-art PQC.