Qubit measurements are central to quantum information processing. In the field of superconducting qubits, standard readout techniques are limited not only by the signal-to-noise ratio, but also by state relaxation during the measurement. In this work, we demonstrate that the limitation due to relaxation can be suppressed by using the many-level Hilbert space of superconducting circuits: In a multilevel encoding, the measurement is corrupted only when multiple errors occur. Employing this technique, we show that we can directly resolve transmon gate errors at the level of one part in $10^3$. Extending this idea, we apply the same principles to the measurement of a logical qubit encoded in a bosonic mode and detected with a transmon ancilla, implementing a proposal by Hann et al. [Phys. Rev. A 98, 022305 (2018)]. Qubit state assignments are made based on a sequence of repeated readouts, further reducing the overall infidelity. This approach is quite general, and several encodings are studied; the codewords are more distinguishable when the distance between them is increased with respect to photon loss. The trade-off between multiple readouts and state relaxation is explored and shown to be consistent with the photon-loss model. We report a logical assignment infidelity of $5.8\times {10}^{-5}$ for a Fock-based encoding and $4.2\times {10}^{-3}$ for a quantum error correction code (the $S=2$, $N=1$ binomial code). Our results not only improve the fidelity of quantum information applications, but also enable more precise characterization of process or gate errors.

中文翻译：

---

多级超导电路中编码的位的高保真度测量

量子位测量对于量子信息处理至关重要。在超导量子位领域，标准的读出技术不仅受到信噪比的限制，而且还受到测量过程中状态松弛的限制。在这项工作中，我们证明了通过使用超导电路的多级希尔伯特空间可以抑制由于弛豫引起的限制：在多级编码中，仅当发生多个错误时，测量才被破坏。通过这项技术，我们证明了我们可以直接解决跨门错误的一部分。$\mathrm{1个}{0}^3$。扩展这个想法，我们将相同的原理应用于以玻色子模式编码并由跨门辅助检测的逻辑量子比特的测量，从而实现了Hann等人的建议。[物理 A 98版，022305（2018）。基于一系列重复读出进行Qubit状态分配，从而进一步降低了整体不忠感。这种方法非常通用，并且研究了几种编码。当码字之间的距离相对于光子损失增加时，码字更容易区分。探索了多个读数和状态弛豫之间的权衡，并证明与光子损耗模型一致。我们报告逻辑上的不忠行为$5.8\times {10}^{-5}$ 用于基于Fock的编码和 $4.2\times {10}^{-3}$ 用于量子纠错码（ $\mathrm{小号}=2$， $ñ=\mathrm{1个}$二项式代码）。我们的结果不仅提高了量子信息应用程序的保真度，而且还使过程或门错误的表征更加精确。