Towards logical entanglement creation in trivalent planar architectures

As quantum error correction (QEC) moves toward practical implementation, the connectivity requirements of physical qubits pose a significant engineering challenge. While the surface code is the leading paradigm for fault-tolerant quantum computing, its standard implementation requires a four-valent lattice (each qubit connected to four neighbors). This paper investigates whether a trivalent (degree-three) architecture—which is more compatible with many planar superconducting qubit layouts—can effectively support lattice surgery, the essential operation for entangling logical qubits.

The researchers developed a trivalent circuit construction for the rotated surface code. They mapped this construction to experimentally realistic noise models, specifically targeting fluxonium-based superconducting architectures. By comparing the trivalent measurement scheme against the conventional four-valent approach, they benchmarked logical fidelity across different code distances (d=3, 5, 7). They further introduced a lattice-surgery protocol that eliminates the need for additional data qubits in the intermediate region between logical patches, thereby reducing the overall qubit and gate overhead.

• Resource Efficiency: The trivalent protocol reduces the total qubit count by O(d) and the total two-qubit gate count by O(d) compared to the four-valent scheme.
• Logical Performance: Simulations using an experimentally motivated noise model indicate that the trivalent approach is competitive with, and in some configurations outperforms, the four-valent scheme, showing up to a 25% improvement in logical fidelity for distance-three codes.
• The trivalent layout provides a direct advantage in gate count as system size increases, making it a highly promising candidate for scalable planar quantum processors.