High-fidelity measurement of qubits encoded in multilevel superconducting circuits

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 x 10(-5) for a Fock-based encoding and 4.2 x 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.