Chip-to-chip entanglement of transmon qubits using engineered measurement fields

While the on-chip processing power in circuit QED devices is growing rapidly, an open challenge is to establish high-fidelity quantum links between qubits on different chips. Here, we show entanglement between transmon qubits on different cQED chips with $49\%$ concurrence and $73\%$ Bell-state fidelity. We engineer a half-parity measurement by successively reflecting a coherent microwave field off two nearly-identical transmon-resonator systems. By ensuring the measured output field does not distinguish $\vert 01 \rangle$ from $\vert 10 \rangle$, unentangled superposition states are probabilistically projected onto entangled states in the odd-parity subspace. We use in-situ tunability and an additional weakly coupled driving field on the second resonator to overcome imperfect matching due to fabrication variations. To demonstrate the flexibility of this approach, we also produce an even-parity entangled state of similar quality, by engineering the matching of outputs for the $\vert 00 \rangle$ and $\vert 11 \rangle$ states. The protocol is characterized over a range of measurement strengths using quantum state tomography showing good agreement with a comprehensive theoretical model.