Active reset returns a superconducting qubit to its ground state: read it out, apply a π-pulse if it reads excited. The classical decision between the two takes time, and the qubit relaxes meanwhile. Salathé and co-workers tied this cost to the ratio of feedback latency to lifetime and expected the error to scale as one minus its exponential, and Ristè and co-workers had already written the reset error to first order as readout errors plus equilibration terms linear in the latency. This work makes that accounting exact at a fixed evaluation time. A transmon with T₁ = 50 μs is prepared in its excited state and read out by an ideal terminal projection followed by a classical confusion channel with symmetric assignment error P_AE. Under that instrument the ensemble-averaged residual population after one feedback cycle is an exact weighted sum of four deterministic Lindblad evolutions, conditioned on the projected and the reported outcome. The sum is evaluated in closed form, together with the critical latency τ_crit at which the residual exceeds its zero-latency value by a chosen budget, defined throughout as an absolute increase in excitation probability of 0.01, that is one percentage point. To leading order τ_crit is the budget times T₁ divided by the pulse-firing probability p_pulse, times a prefactor of 1.019 for the parameters considered here. Discarding that prefactor while retaining the division by p_pulse costs under 2%; the further simplification to budget times T₁ carries 3.4% to 7.3% error across P_AE = 1% to 5%. Because P_AE enters only through p_pulse, the budget is weakly sensitive to assignment error over the tested range for an initially excited qubit, giving 518 to 539 ns; the readout duration enters separately, through the observation window and the post-readout population. A critical latency exists only for budgets below the maximum excess attainable within that window. The four-branch representation is exact for the stated measurement model; the finite-pulse map used to evaluate it is approximate, and is replaced here by its exact affine propagator. The closed form agrees with a master-equation solver to 3.3×10⁻⁷ and is cross-checked against stochastic trajectories.
Active reset returns a superconducting qubit to its ground state: read it out, apply a π-pulse if it reads excited. The classical decision between the two takes time, and the qubit relaxes meanwhile. Salathé and co-workers tied this cost to the ratio of feedback latency to lifetime and expected the error to scale as one minus its exponential, and Ristè and co-workers had already written the reset error to first order as readout errors plus equilibration terms linear in the latency. This work makes that accounting exact at a fixed evaluation time. A transmon with T₁ = 50 μs is prepared in its excited state and read out by an ideal terminal projection followed by a classical confusion channel with symmetric assignment error P_AE. Under that instrument the ensemble-averaged residual population after one feedback cycle is an exact weighted sum of four deterministic Lindblad evolutions, conditioned on the projected and the reported outcome. The sum is evaluated in closed form, together with the critical latency τ_crit at which the residual exceeds its zero-latency value by a chosen budget, defined throughout as an absolute increase in excitation probability of 0.01, that is one percentage point. To leading order τ_crit is the budget times T₁ divided by the pulse-firing probability p_pulse, times a prefactor of 1.019 for the parameters considered here. Discarding that prefactor while retaining the division by p_pulse costs under 2%; the further simplification to budget times T₁ carries 3.4% to 7.3% error across P_AE = 1% to 5%. Because P_AE enters only through p_pulse, the budget is weakly sensitive to assignment error over the tested range for an initially excited qubit, giving 518 to 539 ns; the readout duration enters separately, through the observation window and the post-readout population. A critical latency exists only for budgets below the maximum excess attainable within that window. The four-branch representation is exact for the stated measurement model; the finite-pulse map used to evaluate it is approximate, and is replaced here by its exact affine propagator. The closed form agrees with a master-equation solver to 3.3×10⁻⁷ and is cross-checked against stochastic trajectories.
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.
Reset performance in superconducting qubits is often summarized by the population that remains at the end of the pulse. This is an important number, but it does not describe what happens during the reset itself. A protocol may reach a small final residual while keeping the qubit in a leakage state for a comparatively long part of the trajectory. In this work, we therefore use time-integrated leakage, together with the usual endpoint population, to study a multi-mode dissipative reset model under flux-frequency control. We examine finite thermal occupation, parameter sweeps, frequency disorder, an auxiliary-chain ablation, and a literature-based rate benchmark. At the representative ablation point, adding the auxiliary chain reduces Lf from 8.56 to 0.78 ns and shifts the sustained Pf less-than- 10-2 crossing from 39.5 to 9.8 ns. Interestingly, the configuration without the chain still reaches the smaller long-time residual. The two metrics can therefore favor different reset configurations. For the same 300 ns analysis window, an effective rate model built from the f-ket and e-ket decay rates reported by Zhou et al. gives Lf is 108.0 ns, while the complete simulated configuration gives 0.783 ns. We use this only as a kinetic reference and not as a reproduction of the experiment. In the wider set of simulations, thermal occupation is the main source of degradation, while the frequency disorder considered here has a much weaker effect. The results suggest that time-integrated leakage is a useful quantity to report alongside endpoint residuals, especially when reset is part of repeated quantum-error-correction cycles.
Active reset of qubits is a critical step toward realizing large-scale quantum error correction(QEC) algorithms, as it enables rapid initialization of qubits to the ground state and enhances the accuracy of quantum computing. In this paper, we address the issues of existing active reset schemes that require faster feedback speeds, higher flexibility, and integration in multichannel operations. We propose a highly scalable, integrated, low-latency feedback closed-loop measurement and control system that supports local decision-making and independent judgment. The system achieves precise timing control, parameterized waveform generation, high-fidelity demodulation and decision-making computations, and rapid closed-loop feedback links. Experimental results show that the total latency of the closed-loop feedback is 243 ns, and the active reset test success rate reaches 99.5%, representing significant improvements in both efficiency and precision compared to traditional passive reset methods. Through modular design, the system supports multi-board expansion and can be adapted for concurrent reset control of large-scale qubit chips.
Stochastic resetting drives quantum systems into nonequilibrium stationary states unreachable under uninterrupted unitary evolution, and their entanglement depends on whether the reset history is resolved or averaged over. We study this interplay in the transverse-field Ising chain, deriving closed-form results for two qubits and evaluating chains of up to 12 qubits exactly. In the two-qubit system, these closed-form results show that phase matching between energy eigenstates produces resonances, and their visibility in the stationary state is determined by the symmetry of the reset state. Measurements on an IBM superconducting processor show the entropies evaluated before and after the reset average closely following noiseless predictions with no fitted parameter, while concurrence lies below prediction across most of the hardware measurements. The two diagnostics respond differently because they read different components of the same reconstructed state, and a depolarizing model captures the concurrence suppression with one fitted parameter. The difference between the two entropies, i. e., the Jensen gap of entanglement entropy, equals the Holevo information that a subsystem retains about the time since the last reset. With a Bell-state reset, this information grows with chain length across a half-chain cut over the sizes studied, without visible saturation at the smaller reset probabilities. Since reset times are sampled and recorded classically, the trajectory-averaged entropy, and with it the Jensen gap, is obtained without postselection, in contrast to monitored circuits, where trajectory-resolved entanglement requires sampling exponentially rare measurement records.
Fast, high-fidelity qubit initialization is a key primitive for scalable quantum information processing, but conventional reset protocols either require long relaxation times or discard information contained in continuous measurement records. We demonstrate an adaptive measurement-based reset protocol for superconducting qubits that uses Bayesian inference to update the qubit-state estimate after each readout and dynamically adjust the feedback threshold. Unlike fixed-threshold or repeat-until-success (RUS) protocols, the method utilizes the full analog measurement history, enabling the reset decision to become progressively more conservative as confidence in ground-state preparation increases. Implemented with real-time FPGA-based feedback on a dispersively readout transmon qubit, the protocol achieves a ground-state initialization fidelity of 99.44±0.04% after a small number of reset rounds. We further compare adaptive reset with RUS strategies in multi-qubit experiments and show that adaptive thresholding provides deterministic reset duration while maintaining a five-qubit simultaneous-reset fidelity of 98.78±0.19%. These results establish Bayesian adaptive thresholding as a practical and scalable route to fast qubit reset in superconducting quantum processors.
The ability to fast reset a qubit state is crucial for quantum information processing. However, to actively reset a qubit requires engineering a pathway to interact with a dissipative bath, which often comes at the cost of reduced qubit protection from the environment. Here, we present a multipurpose architecture that enables fast reset and protection of superconducting qubits during control and readout. In our design, two on-chip diplexers are connected by two transmission lines. The high-pass branch provides a flat passband for convenient allocation of readout resonators above the qubit frequencies, which is preferred for reducing measurement-induced state transitions. In the low-pass branch, we leverage a standing-wave mode below the maximum qubit frequency for a rapid reset. The qubits are located in the common stopband to inhibit dissipation during coherent operations. We demonstrate resetting a transmon qubit from its first excited state to the ground state in 100 ns, achieving a residual population of 2.7%. The reset time may be further shortened to 27 ns by exploiting the coherent population inversion effect. We further extend the technique to resetting the qubit from its second excited state. Our approach promises scalable implementation of fast reset and qubit protection during control and readout, adding to the toolbox of dissipation engineering.