Fig. 3: Performance of repetitive QEC operations.
From: Beating the break-even point with a discrete-variable-encoded logical qubit
a–d, Bar charts of the real parts of the process matrices for an encode and decode process (a), a waiting time of about 105 μs without QEC (b), a cycle time of about 90 μs with one-layer QEC operation (c) and a cycle time of about 180 μs with two-layer QEC operation (d). The numbers in brackets represent the process fidelities for each case. e, Process fidelity decays as a function of time for different encodings. Error bars correspond to 1 s.d. of several repeated measurements. The process fidelities for both the corrected binomial code with one-layer QEC (red triangles) and two-layer QEC (blue circles) exhibit slow decay, compared with the uncorrected Fock states \(\{\left|0\right\rangle ,\left|1\right\rangle \}\) encoding (black squares), which defines the break-even point in this system. The corrected binomial code with two-layer QEC offers an improvement over the break-even point by a factor of 1.2, and also surpasses the uncorrected binomial code (yellow stars) by a factor of 2.9 and the uncorrected transmon qubit (green diamonds) by a factor of 8.8. All curves are fitted using Fχ = Ae−t/τ + 0.25 to extract the lifetimes τ of the corresponding encodings. Uncertainties on τ are obtained from the fittings.
