Scalable Pulse-Level Control Framework

• The scalable pulse-level control framework is a pulse-engineering protocol that actively modulates qubit parameters to suppress XY crosstalk and maintain high-fidelity operations.
• It employs frequency modulation (FM) and dynamical decoupling (DD) strategies to cancel error terms independent of the coupling strength, ensuring precise multi-qubit calibration.
• Numerical simulations demonstrate orders-of-magnitude infidelity reductions for both idle and active gate operations in various qubit topologies.

A scalable pulse-level control framework refers to the set of pulse-engineering protocols and theoretical tools that enable the suppression of direct exchange-type (XY) crosstalk in multi-qubit superconducting quantum processors by actively modulating the control parameters of qubits at the pulse level, rather than relying solely on static hardware design. Such frameworks are critical for maintaining high-fidelity gates in dense architectures where hardware detuning alone is insufficient due to frequency crowding constraints. The latest results establish pulse-level XY-crosstalk suppression as a universal, coupling-independent, and multi-qubit scalable scheme—leading to substantial error reductions for both idle and active gate operations (Chen et al., 8 Jan 2026).

1. System Hamiltonian and Pulse-Level Crosstalk Error Model

The foundational system is composed of fixed-frequency superconducting qubits (typically transmons) with a Hamiltonian: $$\begin{aligned} H_{\rm total}(t) &= H_{0} + H_{\rm XY} + H_{\rm drive}(t) \ H_{0} &= -\tfrac{1}{2}\omega_1\sigma_1^z - \tfrac{1}{2}\omega_2\sigma_2^z \ H_{\rm XY} &= J(\sigma_1^+\sigma_2^- + \sigma_1^-\sigma_2^+) = \tfrac{J}{2}(\sigma_1^x\sigma_2^x + \sigma_1^y\sigma_2^y) \end{aligned}$$ where $J$ is the residual exchange coupling between neighboring qubits, and $H_{\rm drive}(t)$ includes the intended gate-control drives (e.g., single-qubit $X$ or $Y$ rotations).

Transforming to the rotating frame of $H_0$, the exchange term oscillates at detuning $\Delta = \omega_1 - \omega_2$. Analysis of the time evolution via Magnus expansion produces "cross-driving" error terms that do not average out unless specific timing conditions are met. The first-order residual Hamiltonian after time $T$ is: $$\overline{H}_{\rm XY}^{(1)} = \frac{J}{i\Delta T}[e^{i\Delta T} - 1]\,\sigma_1^+\sigma_2^- + \mathrm{h.c.}$$ If $T \neq 2\pi m / |\Delta|$, this term does not vanish, causing spurious population exchange and phase errors.

2. Frequency Modulation (FM) Protocol for XY Crosstalk Suppression

Pulse-level control employs active frequency modulation (FM) on one of the coupled qubits, generally by modulating its qubit frequency as: $$\omega_2(t) = \omega_2^{(0)} + \delta\omega\cdot f(t),\quad f(t) = \sin(2\pi N t/T)$$ Here $N$ is the modulation cycle number, $T$ is the gate or idle time, and $\delta\omega$ is the modulation amplitude. This imprints a phase $2\alpha(t) = 2\int_0^t \delta\omega f(t') dt'$ on the XY exchange term.

The effective first-order error becomes: $$\varepsilon^{(1)}_{\rm FM} = \Big|(J/T)\int_0^T e^{i(\Delta t + 2\alpha(t))} dt\Big| + \Big|(J/T)\int_0^T e^{-i(\Delta t + 2\alpha(t))} dt\Big|$$ Scanning $\delta\omega$ numerically reveals "sweet-spot" values $\gamma_N^{\text{opt}}$ for which the above error vanishes for generic $T$. This mechanism is robust, as the cancellation is independent of $J$, depending only on the detuning $\Delta$ and the FM parameters.

3. Dynamical Decoupling (DD) Extension and Integration

An alternative pulse-level suppression utilizes periodic $\pi$-pulses (Z gates) as dynamical decoupling (DD) on the spectator qubit. For $S$ even pulses spaced by $\tau = T/S$, the toggling-frame analysis yields: $$\overline{H}_{\rm XY}^{(1)} = (J/i\Delta T) \sum_{s=1}^{S} (-1)^{s-1}\left[e^{i\Delta s \tau} - e^{i\Delta (s-1)\tau}\right]\sigma_1^+\sigma_2^- + \mathrm{h.c.}$$ This sum can be made to vanish for appropriate $S$ and $\tau$ (e.g., $S=4$, $\tau=2\pi/|S\Delta|$), achieving exact first-order decoupling. The second-order term scales as $J^2/\Delta$ with sequence-dependent prefactor.

FM and DD protocols can be merged for enhanced robustness or adapted to multi-qubit and multi-path scenarios by choosing synchronous modulation patterns or DD pulse schedules across a coupled network.

4. Coupling-Independent Operation and Multi-Qubit Scalability

Both FM and DD pulse-level schemes are explicitly independent of the XY coupling $J$, requiring only knowledge (or calibration) of detuning $\Delta$ and pulse parameters. This enables simultaneous suppression of exchange-type crosstalk for a central qubit coupled to multiple neighbors—all with a single FM or DD pattern, provided the relevant detunings $\Delta_j$ are matched (or grouped). For a five-qubit star topology with a central qubit and four neighbors at equal detuning, the same FM or DD sequence suppresses all direct XY crosstalk paths (Chen et al., 8 Jan 2026).

Calibration overhead is minimal: for each unique detuning class, one calibrates only the FM/sequence duration and amplitude, or the DD pulse schedule. These parameters are reusable across all pairs in that class, ensuring that framework complexity scales with the number of frequency classes, not the total qubit count.

5. Performance Metrics and Numerical Results

Extensive numerical simulations demonstrate orders-of-magnitude suppression, summarized as follows for a pair of coupled qubits with $J/2\pi=5$ MHz and $\Delta/2\pi=50$ MHz, $T=20$ ns:

• Unprotected (CD) idle infidelity: $\sim10^{-3}$
• FM (N=4): $\sim5\times10^{-7}$ (4 order reduction)
• FM (N=8): $\sim3\times10^{-8}$
• DD-$Z_4$: $\sim3\times10^{-4}$ (1 order reduction)

For single-qubit $X_1$ gates:

• CD: $\sim3\times10^{-4}$
• FM (N=4): $\sim2\times10^{-6}$
• DD-$Z_4$: $\sim2\times10^{-5}$

Similar relative improvements are observed in five-qubit topologies, albeit with additive contributions from multiple neighbors. These results are robust over a range of $J/|\Delta|$ and operation times, provided pulse timing is properly matched.

6. Practical Implementation and Hardware Considerations

FM-based suppression provides maximal reduction by averaging out the XY interaction via engineered detuning sweeps but places the modulated qubit off its static flux sweet-spot—implicating potential increases in dephasing and heating rates. DD-based suppression requires rapid high-fidelity $\pi$ pulses, yielding modest improvements while maintaining sweet-spot bias. Both methods are applicable to fixed-frequency transmons, do not require tunable couplers, and entail only O(1) added calibration parameters per detuning group.

Constraints include the achievable modulation bandwidth and pulse widths, accurate timing to match the spectral conditions for cancellation, and phase stability of the control system. The framework is compatible with extant single-qubit gate optimization and DRAG correction stacks, with the FM/DD overlay introduced via pulse-scheduler modifications.

7. Significance for Dense Quantum Architecture and Scalability

The pulse-level XY crosstalk suppression framework fundamentally breaks existing trade-offs imposed by hardware-level detuning, enabling qubit placements and frequency allocation unconstrained by crosstalk-limited error accumulation. By eliminating the need for large static detunings, the protocol supports dense interconnectivity and modular scaling in superconducting quantum processors—addressing a primary bottleneck to error-corrected, large-scale quantum computing. Numerical evidence establishes the protocol's superior suppression over traditional static schemes for both idle and active gates, with substantial resilience to moderate parameter variations (Chen et al., 8 Jan 2026). Extensions to entangling gate protocols and systems with variable coupling topology remain active directions.

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References:

• Scalable Suppression of XY Crosstalk by Pulse-Level Control in Superconducting Quantum Processors (Chen et al., 8 Jan 2026)