Variational preparation of entangled states in a system of transmon qubits

The conventional method for generating entangled states in qubit systems relies on applying precise two-qubit entangling gates alongside single-qubit rotations. However, achieving high-fidelity entanglement demands high accuracy in two-qubit operations, requiring complex calibration protocols. In this work, we use a minimally calibrated two-qubit iSwap-like gate, tuned via straightforward parameter optimization (flux pulse amplitude and duration), to prepare Bell states and GHZ states experimentally in systems of two and three transmon qubits. By integrating this gate into a variational quantum algorithm (VQA), we bypass the need for intricate calibration while maintaining high fidelity. Our proposed methodology employs variational quantum algorithms (VQAs) to create the target quantum state through imperfect multiqubit operations. Furthermore, we experimentally demonstrate a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality for Bell states, confirming their high fidelity of preparation.