Maximizing the nondemolition nature of a quantum measurement via an adaptive readout protocol

Quantum error correction (QEC) requires non-invasive measurements for fault tolerant quantum computing. Deviations from ideal quantum non-demolition (QND) measurements can disturb the encoded information. To address this challenge, we develop a readout protocol for a D-dimensional system that, after a single positive outcome, switches to probing only the D{-}1 remaining subspace. This adaptive switching strategy minimizes measurement-induced errors by relying on negative-result measurement results that do not perturb the Hamiltonian. We apply the protocol on an 8-dimensional ¹²³{rm Sb} nuclear qudit in silicon, and achieve an increase in the readout fidelity from \(98.93pm0.07\)\% to \(99.61pm0.04\)\%, while reducing threefold the overall readout time. To highlight the broader relevance of measurement-induced errors, we study a 10-dimensional ⁷³{rm Ge} nuclear spin read out through Pauli spin blockade, revealing nuclear spin flips arising from hyperfine and quadrupole interactions. These results unveil the effect of non-ideal QND readout across diverse platforms, and introduce an efficient readout protocol that can be implemented with minimal FPGA logic on existing hardware.