Swap Network Augmented Ans\"atze on Arbitrary Connectivity

TL;DR

This paper introduces a swap network algorithm for arbitrary qubit connectivity, embedding it into ansätze to improve trainability and resource efficiency in quantum state parametrization for complex system simulations.

Contribution

It presents a novel algorithm for optimizing qubit routing and a co-designed ansatz that enhances trainability and reduces resource requirements on connectivity-limited quantum devices.

Findings

Lower energy errors with fewer gates and parameters.

Shallower circuits achieved compared to standard methods.

Consistent performance improvements across different connectivities.

Abstract

Efficient parametrizations of quantum states are essential for trainable hybrid classical-quantum algorithms. A key challenge in their design consists in adapting to the available qubit connectivity of the quantum processor, which limits the capacity to generate correlations between distant qubits in a resource-efficient and trainable manner. In this work we first introduce an algorithm that optimizes qubit routing for arbitrary connectivity graphs, resulting in a swap network that enables direct interactions between any pair of qubits. We then propose a co-design of circuit layers and qubit routing by embedding the derived swap networks within layered, connectivity-aware ans\"atze. This construction significantly improves the trainability of the ansatz, leading to enhanced performance with reduced resources. We showcase these improvements through ground-state simulations of strongly correlated systems, including spin-glass and molecular electronic structure models. Across exemplified connectivities, the swap-enhanced ansatz consistently achieves lower energy errors using fewer entangling gates, shallower circuits, and fewer parameters than standard layered-structured baselines. Our results indicate that swap network augmented ans\"atze provide enhanced trainability and resource-efficient design to capture complex correlations on devices with constrained qubit connectivity.