Reducing the amount of single-qubit rotations in VQE and related algorithms

TL;DR

This paper demonstrates that reducing single-qubit rotations in parameterized quantum circuits does not impair their expressibility, entangling ability, or the performance of VQE, and explores high-dimensional qudits as a promising platform.

Contribution

It introduces a method to decrease single-qubit rotations without losing circuit expressibility or VQE performance, and evaluates high-dimensional qudits for hybrid algorithms.

Findings

Reduced single-qubit rotations do not affect VQE performance.

High-dimensional qudits offer comparable expressibility to standard circuits.

Decreased rotations maintain entangling capability.

Abstract

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 we show 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. We also show that the performance of a variational quantum eigensolver is unaffected by a similar decrease in single-qubit rotations. We compare relative expressibility and entangling capability 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 we consider quantum frequency comb photonics as a platform for such algorithms and show that we can obtain an relative expressibility and entangling capability comparable to the best regular parameterized quantum circuits.