Fig. 4: Arbitrary state injection in a distance-3 colour code.
From: Scaling and logic in the colour code on a superconducting quantum processor
a, Schematic of a distance-3 colour code. The arbitrary state |ψ⟩ is prepared on the data qubit indicated by a black arrow. The black line indicates the logical operators of the colour code, and the purple ellipses indicate Bell pairs, see the main text. b, Simplified circuit diagram for the state injection. Each line corresponds to one of the data qubits, on which we apply single-qubit Y- and Z-rotations (yellow boxes), Bell pair preparation circuits (purple boxes), a QEC cycle and a measurement in the X, Y or Z basis (MXYZ) for logical state tomography. c, Decoded (semi-transparent circles) and post-selected (solid dots) expectation value of the logical Pauli operators XL (blue), YL (red) and ZL (green) when sweeping the polar angle θ. The solid lines correspond to ideal expectation values. d, Decoded (semi-transparent circles) and post-selected (solid dots) infidelities for the prepared logical state |ψL⟩. e, Magic state |mL⟩ infidelity as a function of rejected data fraction for |AL⟩ (green squares), |HL⟩ (blue diamonds) and |TL⟩ (red triangles), see the main text and Supplementary Information section G. The dashed lines serve as a guide to the eye, and the error bars indicate a 95% bootstrapped confidence interval. Each state is shown on the Bloch sphere by an arrow of the corresponding colour.
