Fidelity sweet spot in transmon qubit rings under strong connectivity noise

TL;DR

This work addresses fidelity losses for SWAP and general quantum operations in fully connected transmon-qubit rings subjected to connectivity noise. It combines a physically grounded model with quasi-static Gaussian noise, shows a robust fidelity sweet spot in the intermediate regime $10 \lesssim J/\lambda_0 \lesssim 100$, and demonstrates that circuit duration can be tuned to maximize fidelity, sometimes reaching near quantum-error-correction levels. The study reveals that initial-state symmetry strongly influences performance and that the sweet-spot position is largely circuit-independent, allowing transfer of optimal timings across different unitaries. A supervised neural-network is then trained on device parameters to predict the sweet-spot location and its fidelity, enabling rapid optimization of circuit durations across varying CPW couplings and noise distributions. These results offer practical guidelines for designing higher-fidelity transmon processors and provide a scalable pathway to optimize gate performance in near-term quantum devices.

Abstract

We investigate the fidelity of quantum operations in transmon qubit systems, focusing on both SWAP and general gate operations. Our results reveal a distinct fidelity sweet spot that emerges even under strong noise, indicating that optimal circuit depth can enhance gate performance. We further demonstrate that specific initial states, particularly those with favorable symmetry or entanglement structure, yield higher fidelity, reaching levels compatible with quantum error-correction thresholds. Finally, we introduce a supervised machine-learning framework capable of predicting the positions of fidelity sweet spots, enabling efficient optimization of circuit durations across different device configurations.

Figures (14)

• Figure 1: Schematic of transmon-qubit devices with different numbers of qubits $L$. Each node represents a transmon qubit, with solid lines denoting cavity couplings and wavy lines denoting CPW couplings. Panel (a) highlights examples of a nearest-neighbor cavity coupling $J_{12}$ and a remote CPW coupling $K_{13}$.
• Figure 2: Schematic of a two-qubit quantum circuit subject to noise. The circuit consists of a Hadamard gate followed by a CNOT gate, both operating under noisy conditions. In this study, the noise primarily represents connectivity-induced fluctuations in transmon-qubit systems.
• Figure 3: Quantum circuit implementing SWAP operations on a product state $|\Psi\rangle_{1}$. The left side represents the initial state, while the right side shows a sequence of SWAP gates transferring the qubit states along the chain.
• Figure 4: Average infidelity of SWAP operations on the product state $|\Psi\rangle_{1}$ for different system sizes $L$. Horizontal dashed lines mark fidelity benchmarks of $\overline{F}=84\%$, $90\%$, and $99.9\%$. As $J/\lambda_{0}$ increases, the noise level decreases and fidelity improves monotonically. For $L=4$, the optimal performance, comparable to current experimental limits, is achieved near $J/\lambda_{0}\approx10$.
• Figure 5: Schematic of the product state $|\Psi\rangle_{1}$ evolved under a general random quantum circuit $R$. The left side shows the initial state $|\Psi\rangle_{1}$, while the right side represents the randomly generated operation acting on it.