Cultivating T states on the surface code with only two-qubit gates (2509.05232v1)

Abstract: High-fidelity T magic states are a key requirement for fault-tolerant quantum computing in 2D. It has generally been assumed that preparing high-fidelity T states requires noisy injection of T states followed by lengthy distillation routines. This assumption has been recently challenged by the introduction of cultivation, in which careful state injection and postselection alone are used to prepare T states close to the fidelity required for quantum algorithms. Cultivation was originally proposed for the color code, but can also be done on the $RP^2$ code, a code similar to the surface code. In this work, we demonstrate how to cultivate T states directly on the surface code. Besides its simplicity compared to color or $RP^2$ cultivation, surface code cultivation offers a number of advantages, including: (1) It is more directly compatible with neutral atom architectures than ${RP}^2$ cultivation (2) Cultivated surface code states can be used in transversal CNOT gates with other surface codes, unlike color code states (3) Surface code cultivation can be done at any distance, unlike color and ${RP}^2$ cultivation which requires odd distances. Under a standard depolarizing error model, our $d=3,\ (4),\ (5)$ cultivation circuit reaches an error rate of $1\cdot 10^{-6},\ (1\cdot10^{-8}),\ (2\cdot10^{-9})$ and an acceptance rate of $34\%,\ (6\%),\ (1\%)$, meeting or exceeding the fidelity of color and $RP^2$ cultivation with comparable acceptance rates.