Pei Zeng, Guo Zheng, Qian Xu, Liang Jiang (Nov 26 2025).
Abstract: Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge arises in many quantum algorithms with Clifford +
φ compiling, where logical rotation gates
RZL(φ) serve as essential components. The Eastin-Knill theorem prevents their transversal implementation in quantum error correction codes and necessitating resource-intensive workarounds through T-gate compilation combined with magic state distillation and injection. In this work, we consider error-structure-tailored fault tolerance, where fault-tolerance conditions are analyzed by combining perturbative analysis of realistic dissipative noise processes with the structural properties of stabilizer codes. Based on this framework, we design 1-fault-tolerant continuous-angle rotation gates in stabilizer codes, implemented via dispersive-coupling Hamiltonians. Our approach could circumvent the need for T-gate compilation and distillation, offering a hardware-efficient solution that maintains simplicity, minimizes physical footprint, and requires only nearest-neighbor interactions. Integrating with recent small-angle-state preparation techniques, we can suppress the gate error to
91∣φ∣p2 for small rotation angle (where p denotes the physical error rate). For current achievable hardware parameters (
p=10−3), this enables reliable execution of over
107 small-angle rotations when
∣φ∣≈10−3, meeting the requirements of many near-term quantum applications. Compared to the 15-to-1 magic state distillation and magic state cultivation approaches, our method reduces spacetime resource costs by factors of 1337.5 and 43.6, respectively, for a Heisenberg Hamiltonian simulation task under realistic hardware assumptions.
