Error-structure-tailored early fault-tolerant quantum computing

• URL: http://arxiv.org/abs/2511.19983v1
• Date: Tue, 25 Nov 2025 06:51:46 GMT
• Title: Error-structure-tailored early fault-tolerant quantum computing
• Authors: Pei Zeng, Guo Zheng, Qian Xu, Liang Jiang,
• Abstract summary: In quantum algorithms, logical rotation gates $R_Z_L(varphi)$ serve as essential components.<n>In this work, we consider error-structure-tailored fault tolerance, where fault-tolerance conditions are analyzed.<n>We design 1-fault-tolerant continuous-angle rotation gates in stabilizer codes, implemented via dispersive-coupling Hamiltonians.
• Score: 2.824800547988445
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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