Extended Data Fig. 3: Bell states predicted from the quantum processes.
From: Quantum logic with spin qubits crossing the surface code threshold
Top panels show the real part of the reconstructed density matrices of the four Bell states \(|{\Psi }^{+}\rangle =(|01\rangle +|10\rangle )/\sqrt{2}\) (a), \(|{\Psi }^{-}\rangle =(|01\rangle -|10\rangle )/\sqrt{2}\) (b), \(|{\Phi }^{+}\rangle =(|00\rangle +|11\rangle )/\sqrt{2}\) (c) and \(|{\Phi }^{-}\rangle =(|00\rangle -|11\rangle )/\sqrt{2}\) (d). The colour code is the same as in Fig. 4. Bottom panels show the quantum circuit used to reconstruct the Bell states. \({{\rm{Z}}}_{{\rm{Q}}i}^{2}\) is a virtual π-rotation around the \(\hat{z}\) axis on the ith qubit, which is executed by a phase update on the microwave reference clock of the qubit and, therefore, is error-free. We numerically estimate the state fidelities to be 98.42% for the |Ψ+⟩ and |Ψ−⟩ states and 97.75% for the |Φ+⟩ and |Φ−⟩ states.
