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 + \varphi compiling, where logical rotation gates R_{Z_L}(\varphi) 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|\varphi| p^2 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 10^7 small-angle rotations when |\varphi|\approx 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.

Personal information

Pei Zeng is currently a tenure-track associate professor at Institute of Natural Science, Shanghai Jiao Tong University. Prior to this, he was a postdoctoral researcher at the University of Chicago from 2021 to 2025 and a visiting scholar at the University of Science and Technology of China in 2021. He completed a Ph.D. and B.Sc. at Tsinghua University (2020) and Nanjing University (2016), respectively. He also serves as an editor for Quantum Journal.

Reference

https://arxiv.org/abs/2511.19983