Optimising logical measurements for the Toric QEC code
S.A.J.H. Camps (TU Delft - Electrical Engineering, Mathematics and Computer Science)
B.M. Terhal – Mentor (TU Delft - QCD/Terhal Group)
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Abstract
In this thesis we numerically investigate the performance of logical measurements on the toric quantum error correcting code using the ancilla construction of Cohen et al.[1], both with and without the morphing circuit design technique. We simulate the measurement of the logical Z1 observable on the toric code under circuit-level noise using the STIM package, exploring the effects of the number of ancilla layers and QEC rounds on the logical measurement and idle error rates. We find that for the toric code, a single dual layer performs best and that additional layers only increase the measurement error rate without improving the idle error rate. Regarding the number of QEC rounds, we find that performing at least as many rounds as the code distance is necessary to ensure the measurement error rate scales with the code distance rather than the weight of low-order measurement errors over different QEC rounds. Beyond this threshold, additional rounds improve the measurement error rate at the cost of a higher idle error rate, presenting a tunable trade-off. Finally, we compare the morphing and standard versions of the circuit. Despite the morphing version using half as many physical qubits, it achieves better logical measurement error rates and similar idle error rates relative to the standard circuit, leading us to conclude that the morphing version outperforms its standard counterpart.
Code appendix: https://github.com/SAJHCamps/Thesis-project-AM