Acknowledgement
SL expresses gratitude to Dawoon Choi and Yunkyoung Song for their enlightening discussions during the initial phase of this work. This work was partly supported by the Institute for Information & Communications Technology Promotion (IITP) grant (no. 2019-0-00003, Research and Development of Core Technologies for Programming, Running, Implementing, and Validating of Fault-Tolerant Quantum Computing System) and the National Research Foundation of Korea (NRF) grants (nos. 2024M3K5A1004355, RS-2024-00432214, RS-2023-00281456, and RS-2023-00283771). It is worth noting that this work was partially completed at Samsung Electronics, one of the author's former affiliations.
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