Deterministic entanglement of two transmon qubits by parity measurement and digital feedback

While quantum measurement typically collapses quantum superpositions into a basis state, a special type of joint measurement, detecting the parity of qubit excitations, can create entanglement. Building on recent developments in quantum nondemolition measurement and feedback control in circuit QED, we realize a continuous-time parity meter for two 3D-transmon qubits using a dispersively coupled cavity and Josephson parametric amplification. Starting from a maximal superposition, we first generate entanglement with up to $88\%$ fidelity to the closest Bell state by postselecting on the odd-parity result. The infidelity is due to measurement-induced dephasing, arising from imperfect cavity resonance matching in the odd-parity subspace and finite transmission in the even. We then incorporate the parity meter into a digital qubit feedback loop to turn the generation of entanglement from probabilistic to deterministic, achieving $66\%$ fidelity to the targeted Bell state. This combination of parity measurement and conditional qubit control is at the basis of modern error correction protocols.