Work

Efficient Benchmarking of Logical Magic State

Year: 2026

Type: article

Abstract: High-fidelity logical magic states are a critical resource for fault-tolerant quantum computation, enabling non-Clifford logical operations through state injection. However, benchmarking these states presents significant challenges: one must estimate the infidelity ε with multiplicative precision, while many quantum error-correcting codes only permit Clifford operations to be implemented fault-tolerantly. Consequently, conventional state tomography requires ∼1/ε^{2} samples, making benchmarking impractical for high-fidelity states. In this Letter, we show that any benchmarking scheme measuring one copy of the magic state per round necessarily requires Ω(1/ε^{2}) samples for single-qubit magic states. We then propose two approaches to overcome this limitation: (i) Bell measurements on two copies of the twirled state and (ii) single-copy schemes leveraging twirled multiqubit magic states. Both benchmarking schemes utilize measurements with stabilizer states orthogonal to the ideal magic state and we show that O(1/ε) sample complexity is achieved, which we prove to be optimal. Finally, we demonstrate the robustness of our protocols through numerical simulations under realistic noise models, confirming that their advantage persists even at the moderate error rates currently achievable in state-of-the-art experiments.

Source: Physical Review Letters

DOI: 10.1103/fwjt-mw2c

Authors: Su-un Lee, Ming Yuan, Senrui Chen, Kento Tsubouchi, Liang Jiang

Institutions: University of Chicago, The University of Tokyo

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green