Noise robustness and threshold of many-body quantum magic
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| Format: | Preprint |
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2024
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| _version_ | 1866909368350408704 |
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| author | Wei, Fuchuan Liu, Zi-Wen |
| author_facet | Wei, Fuchuan Liu, Zi-Wen |
| contents | Understanding quantum magic (i.e., nonstabilizerness) in many-body quantum systems is challenging but essential to the study of quantum computation and many-body physics. We investigate how noise affects magic properties in entangled many-body quantum states by quantitatively examining the magic decay under noise, with a primary aim being to understand the stability of magic associated with different kinds of entanglement structures. As a standard model, we study hypergraph states, a representative class of many-body magic states, subject to depolarizing noise. First, we show that interactions facilitated by high-degree gates are fragile to noise. In particular, the $\mathrm{C}^{n-1}Z$ state family exhibits a vanishing magic threshold of $Θ(1/n)$. Furthermore, we demonstrate efficiently preparable families of hypergraph states without local magic but with a non-vanishing magic threshold which signifies robust magic that is entirely embedded in global entanglement. We also discuss the qudit case based on the discrete Wigner formalism. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_21215 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Noise robustness and threshold of many-body quantum magic Wei, Fuchuan Liu, Zi-Wen Quantum Physics Understanding quantum magic (i.e., nonstabilizerness) in many-body quantum systems is challenging but essential to the study of quantum computation and many-body physics. We investigate how noise affects magic properties in entangled many-body quantum states by quantitatively examining the magic decay under noise, with a primary aim being to understand the stability of magic associated with different kinds of entanglement structures. As a standard model, we study hypergraph states, a representative class of many-body magic states, subject to depolarizing noise. First, we show that interactions facilitated by high-degree gates are fragile to noise. In particular, the $\mathrm{C}^{n-1}Z$ state family exhibits a vanishing magic threshold of $Θ(1/n)$. Furthermore, we demonstrate efficiently preparable families of hypergraph states without local magic but with a non-vanishing magic threshold which signifies robust magic that is entirely embedded in global entanglement. We also discuss the qudit case based on the discrete Wigner formalism. |
| title | Noise robustness and threshold of many-body quantum magic |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.21215 |