Reducing the Amount of Single-Qubit Rotations in VQE and Related Algorithms

With the advent of hybrid quantum classical algorithms using parameterized quantum circuits, the question of how to optimize these algorithms and circuits emerges. In this paper, it is shown that the number of single-qubit rotations in parameterized quantum circuits can be decreased without compromising the relative expressibility or entangling capability of the circuit. It is also shown that the performance of a variational quantum eigensolver (VQE) is unaffected by a similar decrease in single-qubit rotations. Relative expressibility and entangling capability are compared across different number of qubits in parameterized quantum circuits. High-dimensional qudits as a platform for hybrid quantum classical algorithms is a rarity in the literature. Therefore, quantum frequency comb photonics is considered as a platform for such algorithms and it is shown that a relative expressibility and entangling capability comparable to the best regular parameterized quantum circuits can be obtained.