Code switching revisited: Low-overhead magic state preparation using color codes

We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code-switching protocol with (1) a recently discovered transversal gate between the 2D and the 3D code and (2) a judicious use of flag-based postselection. We numerically demonstrate that these modifications lead to a significant improvement in the fidelity of the magic state. For instance, subjected to a uniform circuit-level noise of 10−3 (excluding idling noise), our code-switching protocol yields a magic state encoded in the distance-3 2D color code with a logical infidelity of 4.6×10−5±1.6×10−5 (quantified by an error-corrected logical state tomography) with an 84% of acceptance rate. Used in conjunction with a postselection approach, extrapolation from a polynomial fit suggests a fidelity improvement to 5.1×10−7 for the same code. Our protocol is aimed for architectures that allow nonlocal connectivity and should be readily implementable in near-term devices. Finally, we also present a simulation technique akin to an extended stabilizer simulator which effectively incorporates the non-Clifford T gate, that permits to simulate the protocol without resorting to a resource intensive state-vector simulation.