Code-switching revisited: high-fidelity logical magic state preparation using color codes
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 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. To certify the magic state in a sample-efficient way, the experiments employed a logical Bell basis measurement which required storing two copies of the logical magic state in the same quantum processor. 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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