Expressibility, entangling power and quantum average causal effect for causally indefinite circuits

TL;DR

This paper compares the properties of parameterized quantum circuits with definite and indefinite causal order, showing indefinite circuits have higher expressibility and a correlation between causal effect and entanglement.

Contribution

It introduces a comparison of definite and indefinite causal order circuits focusing on expressibility, entanglement, and causal effects, highlighting advantages of indefinite circuits.

Findings

Indefinite circuits have higher expressibility than definite circuits.

Entanglement levels are maintained in indefinite circuits.

A correlation exists between quantum average causal effect and entangling power.

Abstract

Parameterized quantum circuits are the core of new technologies such as variational quantum algorithms and quantum machine learning, which makes studying its properties a valuable task. We implement parameterized circuits with definite and indefinite causal order and compare their performance under particular descriptors. One of these is the expressibility, which measures how uniformly a given quantum circuit can reach the whole Hilbert space. Another property that we focus on this work is the entanglement capability, more specifically the concurrence and the entangling power. We also find the causal relation between the qubits of our system with the quantum average causal effect measure. We have found that indefinite circuits offer expressibility advantages over definite ones while maintaining the level of entanglement generation. Our results also point to the existence of a correlation between the quantum average causal effect and the entangling power.