Model-Based Optimization of Superconducting Qubit Readout
Andreas Bengtsson, Alex Opremcak, Mostafa Khezri, D. Sank, Alexandre Bourassa, Kevin J. Satzinger, Sabrina Hong, Catherine Erickson, Brian Lester, Kevin C. Miao, Alexander N. Korotkov, J. Kelly, Zijun Chen, Paul V. Klimov
Measurement is an essential component of quantum algorithms, and for superconducting qubits it is often the most error prone. Here, we demonstrate model-based readout optimization achieving low measurement errors while avoiding detrimental side effects. For simultaneous and midcircuit measurements across 17 qubits, we observe 1.5% error per qubit with a 500 ns end-to-end duration and minimal excess reset error from residual resonator photons. We also suppress measurement-induced state transitions achieving a leakage rate limited by natural heating. This technique can scale to hundreds of qubits and be used to enhance the performance of error-correcting codes and near-term applications.
Measurement is an essential component of quantum algorithms, and for superconducting qubits it is often the most error prone. Here, we demonstrate model-based readout optimization achieving low measurement errors while avoiding detrimental side effects. For simultaneous and midcircuit measurements across 17 qubits, we observe 1.5% error per qubit with a 500 ns end-to-end duration and minimal excess reset error from residual resonator photons. We also suppress measurement-induced state transitions achieving a leakage rate limited by natural heating. This technique can scale to hundreds of qubits and be used to enhance the performance of error-correcting codes and near-term applications.
Readout of superconducting qubits faces a trade-off between measurement speed and unwanted backaction on the qubit caused by the readout drive, such as T_{1} degradation and leakage out of the computational subspace. The readout is typically benchmarked by integrating the readout signal and choosing a binary threshold to extract the "readout fidelity." We show that readout fidelity may significantly overlook readout-induced leakage errors. Such errors are detrimental for applications that rely on continuously repeated measurements, e.g., quantum error correction. We introduce a method to measure the readout-induced leakage rate by repeatedly executing a composite operation-a readout preceded by a randomized qubit flip. We apply this technique to characterize the readout of a superconducting qubit, optimized for fidelity across four different readout durations. Our technique highlights the importance of an independent leakage characterization by showing that the leakage rates vary from 0.12% to 7.76% across these readouts even though the fidelity exceeds 99.5% in all four cases.
Fast, accurate, and low-leakage qubit measurement is a key requirement for quantum error correction. Here, we demonstrate measurement of a superconducting transmon qubit with a total duration of 97(1) ns, defined as the time from the start of the measurement pulse until the measurement-induced error on a subsequent π-pulse operation falls below 10−4. By combining a large state-averaged resonator decay rate of κeff/2π = 30.8 MHz with a dispersive shift close to the optimal SNR-per-photon condition, we achieve an assignment error of 0.17(1)% using a 58-ns measurement pulse, with residual readout photons depleting passively in tens of nanoseconds without an active depletion pulse. Using a repeated-measurement sequence together with a leakage-sensitive measurement, we benchmark the measurement-induced state transitions, finding a per-measurement leakage rate of 2.7(2)×10−5, only twice the background rate and two orders of magnitude below the measurement-induced relaxation rate, which dominates the assignment error. Floquet simulations indicate that the multiphoton resonances present at the operating point are weakly coupled and traversed diabatically, without causing leakage. These results demonstrate that a large resonator decay rate, combined with a dispersive shift close to the optimal SNR-per-photon condition, can enable fast, high-fidelity, low-leakage dispersive readout at small qubit-resonator detuning.
Fast, high-fidelity, and low back-action readout plays a crucial role in the advancement of quantum error correction (QEC). Here, we demonstrate high-performance multiplexed readout of superconducting qubits using a tunable broadband Purcell filter, effectively resolving the fundamental trade-off between measurement speed and photon-noise-induced dephasing. By dynamically tuning the filter parameters, we suppress photon-noise-induced dephasing by a factor of 7 in idle status, while enabling rapid, high-fidelity readout in measurement status. We achieve 99.6\% single-shot readout fidelity with 100~ns readout pulse, limited primarily by relaxation errors during readout. Using a multilevel readout protocol, we further attain 99.9\% fidelity in 50~ns. Simultaneous readout of three qubits using 100~ns pulses achieves an average fidelity of 99.5\% with low crosstalk. Additionally, the readout exhibits high quantum-nondemolition (QND) performance: 99.4\% fidelity over repeated measurements and a low leakage rate below 0.1\%. Building on the tunable broadband filter, we further propose a scalable readout scheme for surface code QEC with enhanced multiplexing capability, offering a promising solution for fast and scalable QEC.
Reading a qubit is a fundamental operation in quantum computing. It translates quantum information into classical information enabling subsequent classification to assign the qubit states '0' or '1'. Unfortunately, qubit readout is one of the most error-prone and slowest operations on a superconducting quantum processor. On state-of-the-art superconducting quantum processors, readout errors can range from 1--10%. These errors occur for various reasons - crosstalk, spontaneous state transitions, and excitation caused by the readout pulse. The error-prone nature of readout has resulted in significant research to design better discriminators to achieve higher qubit-readout accuracies. High readout accuracy is essential for enabling high fidelity for near-term noisy quantum computers and error-corrected quantum computers of the future.
The performance of a wide range of quantum computing algorithms and protocols depends critically on the fidelity and speed of the employed qubit readout. Examples include gate sequences benefiting from midcircuit real-time measurement-based feedback, such as qubit initialization, entanglement generation, teleportation, and, perhaps most importantly, quantum error correction. A prominent and widely used readout approach is based on the dispersive interaction of a superconducting qubit strongly coupled to a large-bandwidth readout resonator, frequently combined with a dedicated or shared Purcell filter protecting qubits from decay. By dynamically reducing the qubit-resonator detuning and thus increasing the dispersive shift, we demonstrate a beyond-state-of-the-art two-state-readout error of only 0.25% in 100-ns integration time. Maintaining low-readout-drive strength, we nearly quadruple the signal-to-noise ratio of the readout by doubling the readout-mode line width, which we quantify by considering the hybridization of the readout resonator and its dedicated Purcell filter. We find excellent agreement between our experimental data and our theoretical model. The presented results are expected to further boost the performance of new and existing algorithms and protocols critically depending on high-fidelity fast midcircuit measurements. Published by the American Physical Society 2024
The majority of quantum-error-detection and correction protocols assume that the population in a qubit does not leak outside of its computational subspace. For many existing approaches, however, the physical qubits do possess more than two energy levels and consequently are prone to such leakage events. Analyzing the effects of leakage is therefore essential to devise optimal protocols for quantum gates, measurement, and error correction. In this article, we present a detailed study of leakage in a two-qubit superconducting stabilizer measurement circuit. We simulate the repeated ancilla-assisted measurement of a single ${\ensuremath{\sigma}}^{z}$ operator for a data qubit, record the outcome at the end of each measurement cycle, and explore the signature of leakage events in the obtained readout statistics. An analytic model is also developed that closely approximates the results of our numerical simulations. We find that leakage leads to destructive features in the quantum-error-detection scheme, making additional hardware and software protocols necessary.