Exploring the role of qubit connectivity in expressibility and entanglement of parameterized quantum circuits architectures - Correr, Guilherme Ilário (2024)
Variational quantum algorithms are one of the promising methods to obtain quantum advantage in the noisy intermediate scale quantum computers era. They rely on a classical optimization procedure, a cost function and a parameterized quantum circuit to build the solution of a particular problem. Most of the work regarding the quantum circuits part is based on heuristic propositions for the circuit structure and reside only within the borders of VQA applications. In this context, the main objective of our work was the characterization of entanglement generation and distribution of generated states for different PQCs structures. Applying the mean entanglement considering the Scott entanglement measures and the expressibility quantifier, we studied the behavior of 5 possible connectivities between qubits that appear in the contemporary quantum computers: No connections, linear, ring, star and all-to-all, for different number of qubits and circuit concatenations (layers). For two circuit architectures with different local parameterizations, we discussed how entanglement and expressibility are connected, showing that the entanglement generation for only 1 layer is influential for the expressibility evolution as a function of the number of layers. Circuits generating mean and standard deviation for entanglement closer to the uniformly distributed states at 1 layer will have a steeper evolution of expressibility. This result is affected by the local parameterization and number of qubits. We then compared the circuits generated entanglement with the entanglement of paradigmatic states EPRn, GHZn and Wn to understand the entanglement characteristics of the different connections. The results showed how the different connectivities will influence parameterized quantum circuits for applications in VQAs and also that these can present the behavior of pseudorandom quantum circuits.