Curator's Take
This article shows that truly low‑overhead quantum LDPC codes can be realized on the same planar superconducting chips that currently host surface‑code experiments, eliminating the need for long‑range couplers that have hampered qLDPC adoption. By introducing “Vine Codes” with open boundaries and routing qubits, the authors demonstrate up to a 28 % reduction in data‑qubit count at distance 7 and an overall ~18 % saving even when routing overhead is included, while still outperforming the surface code in realistic noise simulations at $10^{-3}$ error rates. If these scaling advantages persist at larger distances, Vine Codes could accelerate the transition from prototype devices to fault‑tolerant processors without redesigning existing hardware architectures.
— Mark Eatherly
Summary
The surface code is a promising route towards large-scale quantum computing, requiring only nearest-neighbour gates amenable to superconducting hardware. However, surface codes incur large qubit overheads. Novel quantum low-density parity check (qLDPC) codes promise to reduce overheads but require long-range connections that are difficult to achieve on superconducting platforms. Here, we introduce "Vine Codes" - qLDPC codes that are implementable on a planar square grid through nearest-neighbour, two-qubit gates native to superconducting platforms (iSWAP and CZ). Our approach generalises "Directional Codes" recently introduced by Gehér et. al. (2025) which are constrained to a torus. In contrast, vine codes have open boundary conditions constructed with the aid of routing qubits. We perform extensive numeric searches and find promising candidate vine codes, e.g. [[121,4,6]], [[221,6,7]], and [[234,9,6]] codes. We verify the circuit distances and show that data and measure qubits required can be reduced by up to ~28% relative to the surface code at a circuit distance of 7. Even including routing qubits, vine codes require fewer total qubits than the surface code (e.g. ~18% reduction at circuit distance 10) and benefits are expected to increase at higher distances. We perform circuit-level noise simulations to demonstrate that under a realistic noise model and at a near-term noise rate of $10^{-3}$, vine codes can perform better than the surface code while using fewer qubits. We give an exhaustive list of all unique vine codes up to stabiliser-weight 9. We additionally introduce "Flip-Vine Codes" which possess single-qubit transversal Clifford gates useful for fault-tolerant logic and magic state cultivation. We furthermore construct examples of generalised open boundaries for vine codes that go beyond the familiar X/Z boundaries of the surface and tile codes.