Comparing quantum complexity and quantum fidelity
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908392167047168 |
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| author | de Buruaga, Nadir Samos Sáenz |
| author_facet | de Buruaga, Nadir Samos Sáenz |
| contents | Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the manifold of Gaussian states, provides the same information as quantum fidelity and is therefore capable of detecting quantum phase transitions. However, it does not offer a more refined analysis than entanglement entropy for a given state. We conclude that incorporating a notion of spatial locality into the computation of complexity is essential to uncover new physics beyond what is accessible through entanglement entropy and fidelity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09364 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparing quantum complexity and quantum fidelity de Buruaga, Nadir Samos Sáenz Quantum Physics Strongly Correlated Electrons Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the manifold of Gaussian states, provides the same information as quantum fidelity and is therefore capable of detecting quantum phase transitions. However, it does not offer a more refined analysis than entanglement entropy for a given state. We conclude that incorporating a notion of spatial locality into the computation of complexity is essential to uncover new physics beyond what is accessible through entanglement entropy and fidelity. |
| title | Comparing quantum complexity and quantum fidelity |
| topic | Quantum Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2503.09364 |