Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators

Samuel Godwood, Doga Murat Kurkcuoglu, Gabriel N. Perdue, et al. · 2026 · arXiv

| 编号 QE033 | 主题 基础理论 | 链接 arXiv:2604.26792 |

摘要

摘要保留原文（英文）

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Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Cliford cost of implementing quadratic diagonal evolutions, exemplified by $U=e^{-it{\varphi }_x^2}$ in a uniform field-amplitude discretization of a real scalar field, using either one logical d-level qudit or $n_b=\lceil {\log }_{2}d\rceil$ logical qubits. We analyze two standard settings: productformula simulation and LCU/block encoding, taking the resource metric to be the number of non-Cliford gates after synthesis into a discrete logical gate set. Because tight synthesis bounds for general single-qudit rotations are not known, we express the qudit constructions in terms of embedded two-level SU(2) rotations and derive explicit finite-d break-even conditions for their synthesis cost; these serve as compiler targets for when qudit encodings can outperform the qubit baseline. Within the constructive models studied here, product-formula implementations would require an exponentially stronger per-primitive synthesis advantage for qudits to win asymptotically, while in the LCU setting the qubit encoding is asymptotically cheaper in d. Nevertheless, the finite-d threshold analysis identifies low dimensional regions in which qudits

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