CHSH Violations using Dynamic Circuits

Abstract: Scalable quantum computing relies on high-quality, long-range entanglement, a challenge on noisy, near-term devices. The need for practical insights for near-term algorithm design calls for trade-offs exploration in implementing dynamic circuits on current hardware. In this work, we experimentally compare three CNOT implementations for generating Bell states across varying qubit separations on a 127-qubit IBM Quantum Eagle processor ibm_quebec: a unitary (SWAP-based) approach, a dynamic approach with mid-circuit measurements and classical feedforward, and a post-processed approach. We use Clauser-Horne-Shimony-Holt (CHSH) inequality violations to quantify entanglement quality. We observe that, beyond 10 qubits, dynamic circuits surpass the unitary approach, demonstrating improved distance-dependent entanglement preservation. The post-processed approach consistently yields the highest CHSH values, reaching |S| > 2 up to 13 qubits. Our results underscore the critical need for faster classical feedforward and higher readout fidelity.