Shallow-depth GHZ state generation on NISQ devices

In this work, we focus on GHZ state generation under the practical constraint of limited qubit connectivity, a hallmark of current NISQ hardware. We study the GHZ state preparation across different connectivity graphs inspired by IBM and Google chip architectures, as well as random graphs that reflect distributed quantum systems. Our approach is a measurement-based protocol designed to utilize qubit connectivity constraints for the generation of GHZ states on NISQ devices. We benchmark this against a tailored version of state-of-the-art unitary-based protocols, also incorporating physical connectivity limitations. To evaluate the performance of the protocols under realistic conditions, we conducted implementations on the IBM Eagle r3 chip. Additionally, to explore near-term scalability, we performed simulations across a range of graph sizes and connectivity configurations, assessing performance based on circuit depth, the number of two-qubit gates, and measurement overhead. We observe a trade-off between the two protocols across different figures of merit. For current state-of-the-art NISQ architectures, the unitary-based protocol is more suitable, as it avoids mid-circuit measurements and classical feedforward. However, the measurement-based protocol is expected to become more advantageous in the future with more error-resilient quantum devices, owing to its reduced circuit depth and consequently shorter execution times. In both settings, our proposed method provides an efficient means of leveraging the topology of qubit connections available on a given device.