The preparation of high-fidelity logical magic states has remained as a necessary but daunting step towards building a large-scale fault-tolerant quantum computer. One possible approach consists of fault-tolerantly preparing a magic state in an error-correcting code and then switching to another code with complementary properties, a technique known as code-switching. I will present a protocol that modifies the standard code-switching technique between color codes by employing (i) a recently discovered transversal gate between 2D and 3D color codes and (ii) a judicious use of flag-based post-selection. This protocol is analyzed with a numerical method akin to an extended stabilizer simulator, which effectively incorporates the action of a transversal logical non-Clifford gate and avoids the use of a resource-intensive state-vector simulation. In addition, I will show preliminary results that extend this numerical method to encompass other logical magic state preparation protocols that rely on the measurement of a logical Clifford gate. Furthermore, I will describe recent experiments performed on a trapped-ion quantum processor, in which the code-switching protocol yielded a logical magic state with state-of-the-art fidelity. The findings provide experimental evidence that the cost of magic states is less than previously thought and highlight the importance of post-selection in designing fault-tolerant protocols for quantum computers.

Based on: https://arxiv.org/pdf/2506.14169 and https://arxiv.org/pdf/2410.07327

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