Suppressing spurious transitions using spectrally balanced pulse

TL;DR

The work addresses spurious transitions caused by parasitic couplings and TLS in superconducting qubits by introducing spectrally balanced dual-DRAG pulse shaping combined with virtual-Z compensation. The method creates symmetric spectral holes around the target frequency, suppressing weakly detuned transitions and off-resonant drive effects, and is compatible with standard U3-based single-qubit gates. Experimental results show an order-of-magnitude reduction in cross-qubit crosstalk for detunings around tens of MHz and substantial TLS-excitation suppression across a broad range of gate times, with improved RB performance. The approach generalizes to multiple spectators and leakage suppression via recursive DRAG, suggesting a scalable, hardware-agnostic strategy for high-fidelity control in frequency-crowded quantum processors.

Abstract

Achieving precise control over quantum systems presents a significant challenge, especially in many-body setups, where residual couplings and unintended transitions undermine the accuracy of quantum operations. In superconducting qubits, parasitic interactions -- both between distant qubits and with spurious two-level systems -- can severely limit the performance of quantum gates. In this work, we introduce a pulse-shaping technique that uses spectrally balanced microwave pulses to suppress undesired transitions. Experimental results demonstrate an order-of-magnitude reduction in spurious excitations between weakly detuned qubits, as well as a substantial decrease in single-qubit gate errors caused by a strongly coupled two-level defect over a broad frequency range. Our method provides a simple yet powerful solution to mitigate adverse effects from parasitic couplings, enhancing the fidelity of quantum operations and expanding feasible frequency allocations for large-scale quantum devices.

Figures (13)

• Figure 1: (a) Schematic diagram illustrating the unintended coupling ($g$) that can occur between two qubits or between a qubit and a spurious TLS. (b) Energy level diagram for the combined system of $\rm Q_0$ and $\rm Q_1$ (or TLS). Due to state dressing, driving $\rm Q_0$ with an amplitude $\Omega$ also cross-drives $\rm Q_1$ with a reduced amplitude of $\pm g \Omega / \Delta_0$ in the weak coupling limit ($g \ll |\Delta_0|$). Cross-driving can induce unwanted transitions in $\rm Q_1$ when using a pulse with finite width. (c) Time-domain pulse profiles and (d) their normalized Fourier spectra for a 25-ns pulse, showing its original sine-to-the-fourth-power form ($\rm \Omega^{(0)}$), the first-order DRAG-corrected pulse ($\rm \Omega^{(1)}$), and the spectrally balanced pulse with dual-DRAG corrections ($\rm \Omega^{(2)}$). Note that, in the time domain, the real part of $\Omega^{(0)}$ overlaps with that of $\Omega^{(1)}$, while the imaginary part of $\Omega^{(0)}$ overlaps with that of $\Omega^{(2)}$. The vertical dashed lines in (d) indicate the corresponding peak positions. In this case, the frequency to block is assumed to be $\rm \Delta/2\pi = 40\, MHz$.
• Figure 2: (a) Calibrating the pulse amplitude of the $\rm R$ gate ($t_g=25$ ns) which drives the qubit from its ground state to an equator state, as indicated by the arrow. The drive detuning is set at $\eta/2\pi=23\,{\rm MHz}$. The inset plots are the circuit and a sketch of the state evolution on the Bloch sphere. (b) Calibrating the compensating virtual-Z phase after the $\rm R$ gate, which yields an $\rm \sqrt{X}$ gate. By applying the combination twice, the qubit is rotated from the ground state to the excited state, as indicated by the arrow. The inset is the circuit. (c) Experimental results (top panel) showing the calibrated drive amplitude and virtual-Z phase for different drive detunings, compared with numerical simulations (bottom panel). (d) Measured error per Clifford (EPC) from randomized benchmarking using pulses with virtual-Z compensation (blue) for different drive detunings. Results using detuning compensation (without the appended virtual-Z phase, shown in red) are also included for comparison.
• Figure 3: (a) Experimental setup consisting of two transmon qubits and a tunable coupler, which is also a transmon qubit. The coupler is used to modulate the effective coupling strength between the qubits by adjusting its frequency. (b) Pulse sequence designed for detecting spurious transitions in a nearby qubit during single-qubit gate operations. Repeated $\pi$ gates, each consisting of two $\pi/2$ pulses and spaced by a waiting time $\tau$, are applied to $\rm Q_0$. (c) Measured excited-state populations of $\rm Q_0$ (top panel) and $\rm Q_1$ (bottom panel) using the detection sequence, as a function of the waiting time $\tau$. Results are shown with and without dual-DRAG. Both cases include DRAG correction at the leakage transition to the second excited state $\left|2\right\rangle$. The number of $\pi$ gate pairs is $N = 50$. Here, $g/2\pi = 1\,\rm{MHz}$, $\Delta_0/2\pi = 45\,\rm{MHz}$, and $t_g = 25\,\rm{ns}$. (d) Randomized benchmarking results for $\rm Q_0$, comparing cases with and without dual-DRAG. (e) Simultaneously monitored excited-state populations of $\rm Q_1$. The excitation rates per Clifford gate (ExPC) are $(0.8\pm0.3) \times 10^{-5}$ with dual-DRAG and $(1.6\pm0.2) \times 10^{-4}$ without dual-DRAG. (f) Error per Clifford for different coupling strengths, with a fixed detuning of $\Delta_0/2\pi = 45~\rm{MHz}$. (g) Excitation per Clifford for varying coupling strengths. The solid lines are the simulated ExPC averaged over 24 single-qubit Cliffords implemented with the U3 decomposition. The excitation rates are proportional to $g^2$ (see Supplemental Material SM for details).
• Figure 4: (a) Spectroscopy of a tunable transmon qubit coupled to a spurious TLS, showing an avoided crossing of approximately 10 MHz. The horizontal axis represents the voltage of the flux bias pulse applied to the coupler qubit. (b) Error per Clifford of the qubit as a function of detuning between the qubit and the TLS. Here $t_g=25$ ns. (c) Excitation per Clifford of the TLS for different gate times at $\Delta_0/2\pi = 42\,\rm{MHz}$. The solid lines are twice the simulated $\rm \sqrt{X}$ gate errors. (d) Excitation per Clifford of the TLS for varying detunings. The solid lines are twice the simulated $\rm \sqrt{X}$ gate errors.
• Figure 5: Calibration processes with the interference error filter method. Measured $P^{\rm e}$ of $\rm Q_1$ using the same detection circuit as in Fig. 3(b) of the main text, but with dual-DRAG, plotted against the waiting time $\tau$ and the spectral hole-related detuning $\Delta$. The white dashed line indicates the optimized $\Delta$ value used for subsequent experiments.