High Rate Magic State Cultivation on the Surface Code

Magic state cultivation is a leading approach for generating the resource states required for fault-tolerant quantum computation. Here we present a cultivation protocol that increases the success probability of magic state generation in platforms with flexible and nonlocal connectivity. Our method implements cultivation directly on the surface code, avoiding the detour through alternative, less efficient error-correcting codes used in prior approaches. This both improves the acceptance rate and preserves compatibility with the geometry of the code and the hardware. Numerical simulations show that our protocols improve success probabilities and reduce output error rates compared with protocols tailored to locally connected platforms. Under realistic noise models for cold-atom and trapped-ion systems, we improve the rate of magic state generation by more than a factor of 20. Finally, we study qubit loss and erasure and show that very low error rates can be achieved with minimal overhead, reaching below <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mn>10</a:mn> <a:mrow> <a:mo>−</a:mo> <a:mn>6</a:mn> </a:mrow> </a:msup> </a:math> infidelity using only nine physical erasure qubits.