Tolerant Testing of Stabilizer States with Mixed State Inputs

Vishnu Iyer; Daniel Liang

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arXiv · 2411.08765

Tolerant Testing of Stabilizer States with Mixed State Inputs

Vishnu Iyer·Daniel Liang

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Abstract

We study the problem of tolerant testing of stabilizer states. In particular, we give the first such algorithm that accepts mixed state inputs. Formally, given a mixed state $\rho$ that either has fidelity at least $\varepsilon_1$ with some stabilizer pure state or fidelity at most $\varepsilon_2$ with all such states, where $\varepsilon_2 \leq \varepsilon_1^{O(1)}$, our algorithm distinguishes the two cases with sample complexity $\text{poly}(1/\varepsilon_1)$ and time complexity $O(n \cdot \text{poly}(1/\varepsilon_1))$.

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Vishnu Iyer, Daniel Liang. 2024-11-13. Tolerant Testing of Stabilizer States with Mixed State Inputs. https://arxiv.org/abs/2411.08765

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