We define the reset error as the likelihood of producing any state other than the ground state. The qubit starts at its idle frequency, moves past the resonator at 4.67 GHz, and is held 1 GHz below it, followed by a fast return to the idle frequency. The selected qubit has an idle frequency of 6.09 GHz and a nonlinearity of −200 MHz. The reset gate is implemented using flux-tuning pulses to steer the qubit’s frequency to interact with the resonator, see Fig. Resonators are coupled to the outside environment through a Purcell filter 35. Each qubit is coupled to a readout resonator with strength g ≈ 120 MHz, and having a frequency ~1.5 GHz below the qubit. We experimentally test our reset gate on a Sycamore processor 29, consisting of an array of flux-tunable superconducting transmon qubits 4, 32 with tunable couplers 17, 29, 33, 34. The reset dynamics of the \(\left|2\right\rangle\) and \(\left|3\right\rangle\) states is similar, with multiple adiabatic transitions moving 2 and 3 photons to the resonator respectively, after which they undergo rapid decay. Since the frequency changes more slowly near the level crossing than a linear ramp, the probability of a diabatic error \(\). We adopt a fast quasi-adiabatic approach 28, where the qubit frequency changes rapidly when far detuned from the resonator level crossing but changes slowly when near the level crossing. Pulse engineering of the “swap” stage is critical to achieving efficient population transfer. We use these pair probabilities to inform the identification and correction of errors, improving the code’s performance and stability over time. We find applying reset reduces the magnitude of correlations. Finally, we introduce a technique for computing the probabilities of error pairs, which allows identifying the distinctive patterns of correlations introduced by leakage. By purposefully injecting leakage, we also quantify the gate’s impact on errors detected in the code.
#Error code#
We benchmark the reset gate using the bit-flip error correction code 5 and measure growth and removal of leakage in-situ. Further, it uses only existing hardware as needed for normal operation and readout, and does not involve strong microwave drives that might induce crosstalk, making it attractive for large-scale systems. The gate is straightforward to calibrate and robust to drift due to the adiabaticity. This fidelity is achieved simultaneously on all of the first three excited states for a single parameter choice. It requires only 250 ns to produce the ground state with fidelity over 99%, with gate error accurately predicted by an intuitive semi-classical model. Here we introduce a multi-level reset gate using an adiabatic swap operation between the qubit and the readout resonator combined with a fast return. This calls for analysis methods that use the errors detected during the stabilizer code’s operation to find and visualize undesired correlated errors. Directly quantifying leakage during normal operation presents another challenge, as optimizing measurement for detecting multiple levels is hard to combine with high speed and fidelity. However, the fundamental operations, such as single-qubit gates 14, 15, entangling gates 16, 17, 18, 19, 20, and measurement 21 are known to populate non-computational levels, creating a demand for a reset protocol 22, 23, 24, 25, 26, 27 that can remove leakage population from these higher states without adversely impacting performance in a large-scale system. Superconducting transmon qubits are an appealing platform for the implementation of quantum error correction 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. Quantum error correction stabilizes logical states by operating on arrays of physical qubits in superpositions of their computational basis states 1, 2, 3. Nature Communications volume 12, Article number: 1761 ( 2021) Removing leakage-induced correlated errors in superconducting quantum error correction
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