Lovász Meets Lieb-Schultz-Mattis: Complexity in Approximate Quantum Error Correction
Fuente:
arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916990986223616 |
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| author | Yi, Jinmin Liu, Ruizhi Li, Zhi |
| author_facet | Yi, Jinmin Liu, Ruizhi Li, Zhi |
| contents | Approximate quantum error correction (AQEC) provides a versatile framework for both quantum information processing and probing many-body entanglement. We reveal a fundamental tension between the error-correcting power of an AQEC and the hardness of code state preparation. More precisely, through a novel application of the Lovász local lemma, we establish a fundamental trade-off between local indistinguishability and circuit complexity, showing that orthogonal short-range entangled states must be distinguishable via a local operator. These results offer a powerful tool for exploring quantum circuit complexity across diverse settings. As applications, we derive stronger constraints on the complexity of AQEC codes with transversal logical gates and establish strong complexity lower bounds for W state preparation. Our framework also provides a novel perspective for systems with Lieb-Schultz-Mattis type constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lovász Meets Lieb-Schultz-Mattis: Complexity in Approximate Quantum Error Correction Yi, Jinmin Liu, Ruizhi Li, Zhi Quantum Physics Strongly Correlated Electrons Mathematical Physics Approximate quantum error correction (AQEC) provides a versatile framework for both quantum information processing and probing many-body entanglement. We reveal a fundamental tension between the error-correcting power of an AQEC and the hardness of code state preparation. More precisely, through a novel application of the Lovász local lemma, we establish a fundamental trade-off between local indistinguishability and circuit complexity, showing that orthogonal short-range entangled states must be distinguishable via a local operator. These results offer a powerful tool for exploring quantum circuit complexity across diverse settings. As applications, we derive stronger constraints on the complexity of AQEC codes with transversal logical gates and establish strong complexity lower bounds for W state preparation. Our framework also provides a novel perspective for systems with Lieb-Schultz-Mattis type constraints. |
| title | Lovász Meets Lieb-Schultz-Mattis: Complexity in Approximate Quantum Error Correction |
| topic | Quantum Physics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2510.04453 |