Rapid and unconditional parametric reset protocol for tunable superconducting qubits

The study addresses how to rapidly and unconditionally reset superconducting qubits to their ground state with high fidelity and scalability. Passive relaxation becomes impractically slow as qubit T1 exceeds ~100 microseconds. Existing active reset methods either rely on measurement and fast feedback, which is hardware-intensive and limited by readout fidelity, or on engineered dissipation schemes that can introduce crosstalk, require complex calibration, intense microwave drives, or additional resonator hardware. The authors propose using parametric modulation of a tunable transmon’s frequency to enable an effective, controllable interaction with its lossy readout resonator, transferring qubit excitations to the resonator, thus enabling fast, unconditional reset without extra chip components. This capability is important for quantum error correction (rapid syndrome qubit reset), reducing SPAM errors, and improving algorithmic throughput.

Reset protocols for superconducting qubits largely fall into two categories: measurement-based schemes (heralding or conditional pi pulses following measurement) and non-measurement-based schemes (coupling to a lossy environment, often a resonator). Measurement-based methods depend on high-fidelity readout and low-latency feedback, posing hardware challenges. Non-measurement methods include flux-tuning the qubit into resonance with a lossy mode, microwave-induced interactions, or specialized resonators; drawbacks include crosstalk to neighboring qubits, involvement of higher levels (|f⟩) requiring complicated calibration, intense drive requirements, and sometimes the need for an additional resonator for optimal performance. By contrast, parametric modulation has been used to activate tunable interactions for gates and state transfer, suggesting a route to a reset mechanism that avoids these issues while maintaining scalability.

Theory: Model the qubit–readout-resonator system with the Jaynes–Cummings Hamiltonian in the dispersive regime. Apply sinusoidal flux modulation to the transmon to modulate its frequency, generating sidebands. When a sideband satisfies the resonance condition n·omega_mod + Delta = 0 (n integer; Delta is qubit–resonator detuning), an effective tunable coupling is activated between the qubit |e,l⟩ and resonator |g,l+1⟩ states, causing Rabi-like swaps of the excitation into the rapidly decaying resonator. A non-Hermitian effective Hamiltonian with resonator decay rate kappa_r captures the population dynamics. Three regimes are possible depending on effective coupling |g| relative to kappa_r: overdamped (|g| < kappa_r/4), critically damped (|g| = kappa_r/4), and underdamped (|g| > kappa_r/4); the maximum reset rate saturates at kappa_r/2. Experimental setup: A chip with three transmon qubits, each capacitively coupled to its own readout resonator (6.44–6.68 GHz) with g_qr/2pi ~ 80 MHz and protected by individual lambda/4 Purcell filters. Control: XY drive and independent flux (Z) lines per qubit. Readout chain includes an impedance-matched Josephson parametric amplifier. A waveform generator provides the flux modulation pulse, attenuated by 30 dB before the Z line. Single-tone reset procedure: Prepare the target qubit (e.g., Q1) in |e⟩ via a pi pulse. Apply a sinusoidal flux modulation A·sin(omega t) for a calibrated duration tau and amplitude A, tuned so that a qubit frequency sideband (often at 2·omega near the flux sweet spot) aligns with the resonator frequency (first-order or higher-order n). Measure the residual excited-state population via dispersive readout. Map out P_e versus modulation amplitude and frequency to locate efficient reset “strips” corresponding to sideband resonances. Time-domain measurements at selected operating points (over-, critically-, and underdamped regimes) are fit to the theoretical model to extract kappa_r and reset rates. Residual thermal population is quantified using a Rabi Population Measurement (RPM) across |e⟩–|f⟩ to deduce p_e from oscillation amplitudes. Two-tone reset for |f⟩ leakage: Apply a two-tone flux modulation A1·sin(omega1 t) + A2·sin(omega2 t), creating frequency components at 2·omega1, 2·omega2, and omega1±omega2. Choose tones such that one component couples |f,0⟩ to |e,1⟩ (decaying to |e,0⟩ via resonator loss) and a second component couples |e,0⟩ to |g,1⟩ (decaying to |g,0⟩), thereby depleting |f⟩ via a cascaded process. Perform 2D scans over omega1, omega2 to identify intersecting regions where both processes occur, then measure time evolution of populations from initial |e⟩ or |f⟩ and fit to a multilevel decay model. Crosstalk and scalability characterization: Perform simultaneous single-tone resets on two qubits (Q1 and Q2) to test multi-qubit compatibility. Evaluate the effect of applying the reset modulation on neighboring qubits using Clifford randomized benchmarking on Q2 and Q3 while Q1 is being reset, and Ramsey measurements (in Supplementary) to assess frequency shifts or coherence degradation. Account for waveform generator analog reconstruction filter limits by incorporating low-pass effects in master-equation simulations and suggest replacing the AWG with a microwave source for high-frequency modulation needs. Photon depletion considerations: When immediate resonator photon depletion is required after reset, include a passive wait of ~5/kappa_r (~250 ns for kappa_r^-1 ~ 50 ns) or use active resonator reset methods.

• Single-tone parametric reset rapidly transfers qubit excitation to the readout resonator, achieving a minimum residual excited-state population of 0.08% ± 0.08% at tau = 34 ns, corresponding to the first minimum of the underdamped oscillation. Residual population stays below 0.1% after 1000 ns.
• Without reset, the residual thermal p_e ≈ 2.38% ± 0.06% (effective temperature ~75 mK). The parametric reset reduces thermal population by more than an order of magnitude.
• Readout fidelity improvement due to reduced thermal population: |g⟩ fidelity from 96.13% to 99.43%; |e⟩ fidelity from 92.69% to 96.05% (with a 34 ns reset pulse).
• Dynamical regimes confirmed experimentally: fitting yields kappa_r^-1 ≈ 46 ns, consistent with independent measurement of resonator photon decay (~50 ns). Reset rate saturates at ~kappa_r/2 in underdamped regime, as predicted.
• Two-tone modulation effectively depletes |f⟩ leakage by cascading |f,0⟩→|e,1⟩→|e,0⟩ and |e,0⟩→|g,1⟩→|g,0⟩ processes. Measured decay rates during reset: ~1/100 ns for |e⟩ and ~1/117 ns for |f⟩. Excited-state population reaches the readout floor within ~600 ns (initial |e⟩) and ~1000 ns (initial |f⟩). Measured reset fidelity 99.23%, limited by readout.
• Simultaneous resets on multiple qubits (Q1, Q2) feasible; excited-state populations decay quickly and remain low beyond ~2 microseconds.
• Negligible crosstalk: applying single-tone reset on Q1 reduces average single-qubit gate fidelity by only ~0.08% on neighbor Q2 and ~0.03% on next-nearest neighbor Q3 in RB tests; Ramsey measurements show negligible frequency/coherence impact (per Supplementary).
• Including resonator photon depletion: a passive wait of 5/kappa_r (~250 ns) reduces mean photon number below 0.01 (Stark shift ~51.5 kHz). Accounting for re-thermalization, net fidelity is ~99.86%. Without the extra wait, overall reset fidelity is ~99.92%.
• Simulations incorporating AWG low-pass filtering reproduce experimental features, highlighting hardware bandwidth as a practical consideration.

The protocol directly addresses the need for fast, high-fidelity, and unconditional qubit reset without measurement feedback or additional hardware. By parametrically activating a controllable interaction between a tunable transmon and its lossy readout resonator, qubit excitations are efficiently evacuated. The method operates across damping regimes and achieves a reset rate set by the resonator decay, enabling sub-50-ns-scale reset minima and sub-0.1% residual excitations within a microsecond. The approach reduces SPAM errors and substantially boosts readout fidelities by lowering thermal population. Compared to prior flux-pulse-based or microwave-activated schemes, the protocol minimizes crosstalk because the modulation is narrowband (one or two tones) and does not require large static flux excursions or strong continuous drives. Randomized benchmarking and Ramsey tests confirm negligible impact on neighboring qubits’ gate fidelities, frequencies, and coherence, supporting scalability. Extending to two-tone modulation enables effective |f⟩-state depletion, addressing leakage errors important for two-qubit gates and measurements. The method is flexible: users can prioritize speed (using the first minimum around 34 ns), steady-state robustness (longer modulation), or include a brief wait for resonator photon depletion when immediate reuse of the resonator is needed. The technique also provides a pathway to qubit–photon entanglement and broader applications in reservoir engineering and quantum networks.

The authors demonstrate a rapid, unconditional parametric reset for tunable transmon qubits by flux-modulating the qubit to activate an effective coupling to the lossy readout resonator. The scheme achieves a residual excited-state population of 0.08% ± 0.08% within 34 ns and remains below 0.1% after 1000 ns. With an additional ~250 ns passive wait for resonator photon depletion, the net reset fidelity is ~99.86%; without the wait, ~99.92%. The method exhibits negligible crosstalk to neighboring qubits and can be extended with two-tone modulation to efficiently deplete the second excited state, addressing leakage. These features make the protocol practical, flexible, and scalable for large-scale quantum processors. Future directions include further speeding reset by increasing modulation amplitude or engineered qubit–resonator coupling, optimizing control hardware bandwidth to support higher-frequency sidebands, integrating active resonator reset when required, and leveraging the technique for reservoir engineering, quantum simulations, and entanglement with itinerant photons in networked quantum systems.

• Hardware bandwidth limits: The AWG’s analog reconstruction filter heavily attenuates high-frequency modulation, constraining operation when large detuning favors high-frequency sidebands; a microwave source may be needed in such cases.
• Resonator photon depletion: If immediate reuse of the readout resonator without residual photons is required, additional wait time (~5/kappa_r ≈ 250 ns) or active resonator reset is necessary.
• Readout floor: Measured reset performance for multi-level depletion is limited by the readout floor (~0.77%), constraining observed fidelity.
• Thermal environment: Initial thermal excitation (~2.38%) indicates sensitivity to infrared radiation and thermalization quality; improved shielding and thermal contact can further reduce baseline excitation.
• Device requirements: The approach relies on flux-tunable transmons and calibrated modulation; while sweet-spot operation is not required, precise calibration of modulation amplitudes and frequencies is still needed for optimal performance.