Quantum measurements are ubiquitous in quantum information processing tasks, but errors can render their outputs unreliable. Here, we present a scheme that implements a robust projective measurement through measuring code-inspired observables. Namely, given a projective POVM, a classical code, and a constraint on the number of measurement outcomes each observable can have, we construct commuting observables whose measurement is equivalent to the projective measurement in the noiseless setting. Moreover, we can correct t errors on the classical outcomes of the observables’ measurement if the classical code corrects t errors. Since our scheme does not require the encoding of quantum data onto a quantum error correction code, it can help construct robust measurements for near-term quantum algorithms that do not use quantum error correction. Moreover, our scheme works for any projective POVM, and hence can allow robust syndrome extraction procedures in non-stabilizer quantum error correction codes.

量子测量在量子信息处理任务中无处不在，但错误会导致其输出不可靠。在这里，我们提出了一个方案，该方案通过测量受代码启发的 observable 来实现稳健的投影测量。也就是说，给定一个投影 POVM、一个经典代码以及每个可观察对象可以具有的测量结果数量的约束，我们构建了交换可观察对象，其测量等效于无噪声设置中的投影测量。此外，如果经典代码纠正了 t 错误，我们可以纠正可观察对象测量的经典结果上的 t 误差。由于我们的方案不需要将量子数据编码到量子纠错码上，因此它可以帮助为不使用量子纠错的近期量子算法构建稳健的测量。此外，我们的方案适用于任何射影 POVM，因此可以在非稳定器量子纠错码中允许稳健的综合征提取程序。