Active interference suppression in frequency-division-multiplexed quantum gates via off-resonant microwave tones

TL;DR

This work tackles wiring bottlenecks in scalable quantum processors by employing frequency-division multiplexing (FDM) and introduces active interference suppression (AIS) that intentionally uses off-resonant tones to suppress crosstalk during simultaneous single-qubit gates. Through a Magnus-expansion analysis and numerical simulations, AIS reduces gate infidelity approximately as $1/N_d^{2}$ and reveals that fast-oscillating terms beyond the rotating wave approximation can degrade fidelity unless the drive-tone centroid is shifted to compensate. The key contributions are analytical insight into AIS via $\lambda_x,\lambda_y,\lambda_z$ coefficients and empirical validation showing robust fidelity gains as the number of drive tones increases, with practical constraints from pulse width and spectral spacing. Overall, AIS offers a simple, scalable route to higher-fidelity FDM-based quantum gates and can be extended to related control problems such as selective excitation and microwave crosstalk mitigation.

Abstract

An increase in the number of control lines between the quantum processors and the external electronics constitutes a major bottleneck in the realization of large-scale quantum computers. Frequency-division multiplexing is expected to enable multiple qubits to be controlled through a single microwave cable; however, interference from off-resonant microwave tones hinders precise qubit control. Here, we propose an active interference suppression method for frequency-division-multiplexed simultaneous gate operations. We demonstrate that deliberate incorporation of off-resonant microwave tones improves the accuracy of single-qubit gates. Specifically, we find that by incorporating off-resonant orthogonal or quasi-orthogonal microwave tones, the gate infidelity decreases proportionally to the inverse square of the number of microwave tones. Furthermore, we show that fast oscillations neglected under the rotating wave approximation degrade gate fidelity, and that this degradation can be mitigated through optimized frequency allocation. Our approach is simple yet effective for improving the performance of frequency-division-multiplexed quantum gates.

Figures (8)

• Figure 1: Conceptual illustration of a model consisting of $N_{\mathrm{q}}$ independent qubits with frequencies $\omega_{\mathrm{q}, k_{\mathrm{q}}}$ driven by microwaves via a shared control line. The controller produces $N_{\mathrm{d}}$ microwave tones at distinct frequencies $\omega_{\mathrm{d}, k_{\mathrm{d}}}$, which are then combined and routed to a quantum processor via the shared line. The combined signal is applied uniformly to all qubits. In this figure, $N_{\mathrm{q}}=5$ and $N_{\mathrm{d}} = 7$.
• Figure 2: Illustration of the set $K_{\mathrm{q}}$ and $K_{\mathrm{d}}$. (a) Set of qubit indices $K_{\mathrm{q}}$ for $N_{\mathrm{q}} = 5$, $l_{\mathrm{q}} = -2$, and $r_{\mathrm{q}} = 2$. (b), (c) Set of indices of drive microwave tones $K_{\mathrm{d}}$ for $N_{\mathrm{d}} = 9$. The set $K_{\mathrm{d}}$ shown in (b) corresponds to symmetric allocation, namely, $l_{\mathrm{d}} = -\lfloor N_{\mathrm{d}} / 2\rfloor$ and $r_{\mathrm{d}} = \lfloor \left(N_{\mathrm{d}} - 1\right) / 2\rfloor$. The set shown in (c) corresponds to weakly asymmetric allocation, namely, $l_{\mathrm{d}} = -\lfloor N_{\mathrm{d}} / 2\rfloor + S_{\mathrm{d}}$ and $r_{\mathrm{d}} = \lfloor \left(N_{\mathrm{d}} - 1\right) / 2\rfloor + S_{\mathrm{d}}$ with $S_{\mathrm{d}} = -1$. The shift parameter $S_{\mathrm{d}}$ is introduced to allow asymmetric allocation.
• Figure 3: Absolute values of the normalized spectra of $s\left(t\right) \sin\left(\omega_{\mathrm{d}, k_{\mathrm{d}}} t\right)$ for $k_{\mathrm{d}} \in \left\{-2, -1, 0, 1, 2\right\}$ with $\tau = \tau_0$. Each drive frequency $\omega_{\mathrm{d}, k_{\mathrm{d}}}$ is located at a zero crossing of the spectral components of all other microwave tones.
• Figure 4: Illustration of $\gamma$, which represents the set of indices of drive microwave tones lacking a corresponding element with respect to $k_{\mathrm{d}} = k_{\mathrm{q}}$. The orange and blue arrows denote the driving microwaves that correspond and do not correspond to the set $\gamma$, respectively. In this figure, $k_{\mathrm{q}} = 1$, $l_\mathrm{d} = -3$, and $r_\mathrm{d} = 3$, yielding $\gamma = \left\{ k_{\mathrm{q}}-3,k_{\mathrm{q}}-4 \right\} = \left\{ -2,-3 \right\}$. These indices have no counterpart related to $k_{\mathrm{q}}$, i.e., there are no arrows at $k_{\mathrm{q}}+3 = 4$ and $k_{\mathrm{q}}+4 = 5$.
• Figure 5: Average gate infidelity $1 - F\left(U_{\text{ideal}}, U\right)$ as a function of the number of drive microwave tones $N_{\mathrm{d}}$ for $\tau = \tau_0$. Parameters are set as $N_{\mathrm{q}} = 7$, $l_{\mathrm{q}} = -3$, $r_{\mathrm{q}} =3$, $l_{\mathrm{d}} = -\lfloor N_{\mathrm{d}} / 2\rfloor$, $r_{\mathrm{d}} = \lfloor \left(N_{\mathrm{d}} - 1\right) / 2\rfloor$, $\omega_{\mathrm{q}, 0} / 2\pi = 5 \,\mathrm{GHz}$, $\Delta/2\pi = 10 \,\mathrm{MHz}$, $\phi = \pi / 2$, and $\alpha = -\phi/\tau$. The black dotted line indicates $1 - F_{\text{mean}}\left(U_{\text{ideal}}, U\right)$, which is the mean value of $1 - F\left(U_{\text{ideal}}, U\right)$ over $k_{\mathrm{q}}\in K_{\mathrm{q}} = \left\{-3, -2, -1, 0, 1, 2, 3\right\}$. The operator $U$ is obtained numerically from the Hamiltonian in Eq. \ref{['eq:H']}.