High-yield integration design of fixed-frequency superconducting qubit systems using siZZle-CZ gates

Abstract

Fixed-frequency transmon qubits, characterized by simple architectures and long coherence times, are promising platforms for large-scale quantum computing. However, the rapidly increasing frequency collisions, which directly reduce the fabrication yield, hinder scaling, especially in cross-resonance (CR) gate-based architectures, wherein the restricted drive frequency severely limits the available design space. We investigate the Stark-induced ZZ by level excursions (siZZle) gate, which relaxes this limitation by allowing arbitrary drive-frequency choices. Extensive numerical analyses across a broad parameter range -- including the far-detuned regime that has received negligible prior attention -- reveal wide operating windows that support controlled-Z (CZ) fidelities >99.6%. Leveraging these windows, we design lattice architectures containing >1000 qubits, showing that even under 0.25% fabrication-induced frequency dispersion, the zero-collision yields in square and heavy-hexagonal lattices reach 80% and 100%, respectively. Thus, the siZZle-CZ gate is a scalable and collision-robust alternative to the CR gate, offering a viable route toward high-yield fixed-frequency transmon quantum processors.

Figures (14)

• Figure 1: (a) Schematic of frequency collisions in integrated arrays of fixed-frequency transmon qubits. In practice, the qubit resonance frequencies exhibit stochastic dispersion from their design values owing to fabrication imperfections, probabilistically leading to static collisions, in which resonance transition frequencies of nearby qubits become closely spaced, as well as to dynamical collisions, in which microwave-drive crosstalk induces excitations of neighboring qubits. (b) siZZle drive applied to two qubits in an integrated qubit array. An effective ZZ interaction is induced by simultaneously driving two neighboring qubits with a microwave tone at the same frequency $\omega_{\mathrm{d}}$. (c), (d) Relative configuration of the qubit resonance frequencies ($\omega_0$ and $\omega_1$) and the siZZle drive frequency ($\omega_{\mathrm{d}}$). The qubit detuning $\varDelta_{10} = \omega_1 - \omega_0$ can be classified into the straddling regime, where $|\varDelta_{10}|$ is smaller than the anharmonicities $|\alpha_0|$ and $|\alpha_1|$, and the far-detuned regime, where $|\varDelta_{10}|$ exceeds the anharmonicities. The siZZle drive frequency $\omega_{\mathrm{d}}$ can be chosen to a certain extent, and the resulting strength of the ZZ interaction depends on this choice.
• Figure 2: (a) Parameters used in the numerical simulations of the siZZle dynamics (see the main text and Table \ref{['tab:1']} for detailed numerical values). (b) Arrangement of the resonance frequencies of the two qubits and siZZle drive frequency. The swept parameters are the drive detuning relative to the g-e transition of Q0, $\varDelta_{\rm d0} := \omega_{\rm d} - \omega_0$, and the qubit--qubit detuning, $\varDelta_{10} := \omega_1 - \omega_0$, where the g-e resonance frequency of Q0 is fixed to $\omega_0 = 2\pi \times 5000~{\rm MHz}$. In the straddling regime, either $\omega_1 + \alpha_1 < \omega_0 < \omega_1$ or $\omega_0 + \alpha_0 < \omega_1 < \omega_0$ is satisfied, whereas in the far-detuned regime either $\omega_0 < \omega_1 + \alpha_1$ or $\omega_1 < \omega_0 + \alpha_0$ holds. (c) Numerically calculated fidelity of the siZZle-CZ gate as a function of the qubit detuning $\varDelta_{10}$ and drive detuning $\varDelta_{\rm d0}$. The red solid and dashed lines indicate the g-e and e-f resonance frequencies of Q0, respectively, and the blue solid and dashed lines denote the corresponding transitions of Q1.
• Figure 3: (a), (b) Square and heavy-hexagonal lattices considered in this study. Qubits labeled H1--H4 and L1--L4 denote relatively high- and low-frequency qubits, respectively, which are arranged in a checkerboard pattern such that the frequency detuning between nearest-neighbor (NN) qubits lies in the far-detuned regime. (c), (d) Specific assignments of the H1--H4 and L1--L4 qubit frequencies for the square and heavy-hexagonal lattices, respectively. In both cases, the lowest frequency L1 is fixed to $5000\,\mathrm{MHz}$. (e), (f) Numerically calculated zero-collision yield (vertical axis) as a function of the ratio of fabrication-induced frequency dispersion to the designed qubit frequency (horizontal axis), for the square and heavy-hexagonal lattices, respectively. The dashed line indicates the minimum achievable frequency dispersion ratio of $0.25\%$ reported in a previous study hertzberg2021laser. The red circles, green triangles, and blue squares represent yield evaluation results for square and heavy-hexagonal lattices with code distances $d=5, 11,$ and $23$, respectively. The solid curves represent the fitting results obtained using an error-function-based model. At the minimum achievable frequency dispersion ratio of $0.25\%$, the zero-collision yields for square and heavy-hexagonal lattices, with a code distance $d=23$, reach $80\%$ and $100\%$, respectively indicating that collision-free operation can be achieved with a realistic number of chip fabrication runs.
• Figure 4: Position of our results relative to previous estimates of zero-collision yield for integrated qubit systems based on CR gates hertzberg2021laser and siZZle-CZ gates in the straddling regime morvan2022optimizing. The present approach achieves higher zero-collision yields under conditions involving both larger system sizes and more stringent target gate errors.
• Figure 5: Hierarchical framework for the design of integrated qubit systems based on the siZZle-CZ gate and for the evaluation of the zero-collision yield. (a) For each individual siZZle-CZ gate, optimal siZZle pulse waveforms are defined, such that multiple pulse parameters are treated as dependent variables. (b) The siZZle-CZ gate fidelity is evaluated as a function of the qubit detuning $\varDelta_{10}$ and the drive detuning $\varDelta_{\mathrm{d0}}$, yielding a gate-fidelity function $F(\varDelta_{10}, \varDelta_{\mathrm{d0}})$. (c) For a given frequency allocation across a lattice, the fidelity function $F(\varDelta_{10}, \varDelta_{\mathrm{d0}})$ is used to construct an evaluation function $C(\{\omega_0, \omega_1, \cdots\})$ that determines the presence of frequency collisions. (d) The collision-evaluation function $C(\{\omega_0, \omega_1, \cdots\})$ is applied to various frequency allocations generated under stochastic frequency variations, from which the zero-collision yield is estimated.