Understanding the qubit environment is central to fault-tolerant superconducting quantum computation. Characterization typically relies on relaxation, leaving excitation largely underexplored.Here, we access this information with time-resolved broadband excitation spectroscopy. The resulting qubit excitation spectrum reveals a highly structured landscape, interspersed with cold regions. Combined with postselection, this technique enables full reconstruction of the noise power spectral density (PSD) and separates quantum from classical noise. With feed-forward, it exposes long-lived two-level-systems (TLSs), whose relaxation times span tens of microseconds to milliseconds – uncovering an intrinsic link between the qubit-TLS coupling and TLS relaxation. The data suggest that the long-lived TLSs are intrinsic to the qubit environment, and can cause excitation that lasts for many qubit operation cycles. Consequently, the environment retains a memory of prior dynamics, and properties like gate fidelity become non-Markovian and protocol-dependent. The presented approach enables identifying and bypassing the hidden roadblocks formed by long-lived TLSs in fault-tolerant quantum computation.
One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitionsfrom fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below 2.0×10−5, and obtain fidelities above 99.98% for pulse durations down to 6.8 ns for both X and X/2 gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below 10−6. The presented approach can be readily applied to other qubit types as well.