Explain the late-time classical-fidelity improvement caused by readout errors

Determine why readout errors appear to improve the classical fidelity of the domain-wall-encoded Heisenberg XXZ simulation at later times, despite thermal position fluctuations inhibiting excitation motion, and why the corresponding improvement is not observed for the quantum-state fidelity.

Background

The paper studies a domain-wall encoding of the one-dimensional Heisenberg XXZ model on a Rydberg atom array. Its numerical error model includes thermal motion of the atoms, laser imperfections, and asymmetric readout misclassification errors, together with post-selection onto the correct domain-wall-number sector.

The authors observe that readout errors slightly degrade the quantum-state fidelity at short times but appear to improve the classical fidelity at later times. They speculate that readout errors on qubits adjacent to a domain wall may effectively move the domain wall and partially counteract the transport inhibition caused by thermal fluctuations. However, they note that this mechanism does not provide a conclusive explanation, particularly because the same effect might be expected to improve the quantum-state fidelity.