Orthogonal frequency-division multiplexing for simultaneous gate operations on multiple qubits via a shared control line

TL;DR

The paper presents an FDM-based framework for simultaneous qubit control via a single shared microwave line, addressing scalability challenges in cryogenic quantum processors. Using a second-order Magnus expansion, it derives conditions on pulse length, tone spacing, and rotation angle to suppress interference among off-resonant drive components and achieve high gate fidelity, with orthogonal and quasi-orthogonal drive arrangements showing favorable performance. Key findings include near-unit fidelity for central qubits under orthogonal drives, the viability of half-orthogonal schemes for denser spectra, and a clear advantage of longer pulses in reducing interference, albeit with increasing sensitivity to off-center qubits. The work provides practical design guidelines and highlights limitations such as residual crosstalk from noncommuting Hamiltonians and neglected leakage to higher levels, suggesting directions for future multilevel analysis and leakage mitigation to enable scalable, high-throughput quantum control.

Abstract

The increasing number of qubits in quantum processors necessitates a corresponding increase in the number of control lines between the processor, which is typically operated at cryogenic temperatures, and external electronics. Scaling poses significant challenges in terms of the thermal loads, forming a major bottleneck in the realization of large-scale quantum computers. In this study, we analyze simultaneous gate operations on multiple qubits using microwaves transmitted via a single cable in a frequency-division multiplexing (FDM) scheme. By employing rectangular control microwave pulses, we reveal the contribution of drive frequency spacing to gate fidelity. Through theoretical and numerical analyses, we demonstrate that orthogonal and quasi-orthogonal microwave signals suppress interference in simultaneously driven qubits, thereby ensuring high gate fidelity. Additionally, we provide design guidelines for key parameters, including pulse length, number of multiplexed microwave signals, and rotation angle, to achieve precise qubit operations. Our findings enable a scalable FDM-based microwave control scheme suitable for quantum processors with a large number of qubits.

Figures (7)

• Figure 1: Conceptual illustration of a model comprising $N=5$ independent qubits with frequencies $\omega_{\mathrm{q}, k}$ driven by microwaves via a shared control line. The controller produces $N$ microwave tones at distinct frequencies $\omega_{\mathrm{d}, k}$, which are then combined and routed to a quantum processor via the shared line. The combined signal is applied uniformly to all qubits.
• Figure 2: Illustration of $\gamma$, which represents the set of qubit indices lacking a corresponding element with respect to $k_0$. The orange and blue arrows denote the driving microwaves that correspond and do not correspond to the set $\gamma$, respectively. In this figure, the set $\gamma$ is specifically $\left\{ k_0-3,k_0-4 \right\}$. These indices have no counterpart related to $k_0$, i.e., there are no arrows at $k_0+3$ and $k_0+4$.
• Figure 3: Absolute values of the spectra of $s\left(t\right) \sin\left(\omega_{\mathrm{d}, k} t\right)$ for $N=5$ and $k \in \left\{-2, -1, 0, 1, 2\right\}$, with pulse length (a) $\tau = \tau_0$, (b) $\tau = \tau_0/2$, and (c) $\tau = 2 \tau_0$. In (a) and (c), each drive frequency $\omega_{\mathrm{d}, k}$ is placed at the zero-crossing point of the spectral components of all other microwaves.
• Figure 4: Average gate fidelity $F\left(U_{\text{ideal}}, U_{\text{Magnus}}\left(\tau\right)\right)$ (solid lines) and $F\left(U_{\text{ideal}}, U\right)$ (dots) as a function of the target qubit index $k_0$, for three pulse lengths: (a) $\tau = \tau_0$, (b) $\tau = \tau_0/2$, and (c) $\tau = 2 \tau_0$. Parameters are set as $N = 15$, $-l = r =7$, $\omega_{\mathrm{q}, k_0} / 2\pi = 5 \,\unit{\giga\hertz}$, $\Delta/2\pi = 10 \,\unit{\mega\hertz}$, $\phi = \pi / 2$, and $\alpha = \phi/\tau$.
• Figure 5: Rotation angles $\lambda_{\mathrm{x}}$, $\lambda_{\mathrm{y}}$, and $\lambda_{\mathrm{z}}$ as a function of the target qubit index $k_0$ for (a) orthogonal ($\tau = \tau_{0}$) and (b) quasi-orthogonal ($\tau = \tau_{0}/2$) cases. Parameters are set as $N = 15$, $-l = r =7$, and $\phi = \pi / 2$. Results are obtained using Eqs. \ref{['eq:lambda_x_0']}--\ref{['eq:lambda_z_0']} for (a) and Eqs. \ref{['eq:lambda_x_1']}--\ref{['eq:lambda_z_1']} for (b).