Abstract
Qubit measurements are central to quantum information processing. In the field of superconducting qubits, standard readout techniques are not only limited 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 only corrupted 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 \textbf{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 tradeoff 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 QEC code (the $S=2,N=1$ binomial code). Our results will not only improve the fidelity of quantum information applications, but also enable more precise characterization of process or gate errors.
Highlights
Quantum information processing (QIP) involves many tasks
A canonical example of qubit measurement is at the end of a quantum computation, after which the experimenter measures the qubit array and infers a useful result
In the standard approach to superconducting qubit measurement, a readout resonator is dispersively coupled to a transmon, meaning that the frequency of the resonator mode is shifted if the transmon is in an excited state
Summary
Quantum information processing (QIP) involves many tasks. One requirement, crucial to any QIP experiment, is the ability to measure a qubit or qubit register. Experimental implementations of quantum computing requirements, including feedbackbased state preparation [1], gate calibration, and errorsyndrome extraction for quantum error correction (QEC) [2,3,4,5,6], rely on qubit measurements. If the physical states representing the 0 and 1 bit are separated by multiple energy levels, a single relaxation event will not corrupt the 0 or 1 which is encoded For this reason, qubit encodings with a larger distance between codewords with respect to the dominant error channel can be measured with much improved fidelity. Using a bosonic mode allows us to systematically explore different qubit encodings, including Fock-based encodings as well as errorcorrectable binomial codes [25] The information in this “storage” mode (s) is read out using the dispersively coupled transmon as an ancilla according to a recent proposal [26]. The storage-ancilla interaction is used to map information from the storage onto the ancilla, and the ancilla-readout interaction is used to read out the ancilla state
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