Extended Data Fig. 7: Properties of encoded logical states.
From: A quantum processor based on coherent transport of entangled atom arrays
a, Summary of logical error probabilities for the various error correcting graphs made in this work (all in logical state |+⟩L), for raw measurements as well as implementing error correction and error detection in postprocessing. Error correction for the Steane code is implemented with the Steane code decoder36,73 and is implemented with the minimum-weight-perfect-matching algorithm for the surface and toric codes38. For the even-distance toric code, when correction is ambiguous we do not flip the logical qubit, and accordingly the distance d = 2 logical qubit does not change under the correction procedure. We remark that the observed fidelities are comparable to similar demonstrations in state-of-the-art experiments with other platforms8,74. These will need to be improved to surpass the threshold for practical error correction38 (see Methods text). b, Lifetime of the logical |+⟩L state on the surface code, with correction and detection performed in postprocessing as in a. After state preparation, the |+⟩L state is held for a variable time before projective measurement, with two π pulses applied for dynamical decoupling (lifetime can be extended significantly further by applying e.g. 128 π pulses as done in Extended Data Fig. 3b). Some experimental parameters are slightly different here compared to those in a, hence the higher error rates here at the time 0 point. c, Logical π/2 rotation on the Steane code to prepare logical qubit state |0L⟩. The Steane code, surface code, and toric code all have transversal single-qubit Clifford operations on the logical qubit8,36 (including in-software rotations of the lattice), which is a high-fidelity operation in our system since the transveral rotations are implemented in parallel with our global Raman laser and the physical single-qubit fidelities are high. We show a logical π/2 rotation here for the Steane code as an example but emphasize that we can readily realize the various basis states for all of these codes.
