Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916634309951488 |
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| author | Turkeshi, Xhek Dymarsky, Anatoly Sierant, Piotr |
| author_facet | Turkeshi, Xhek Dymarsky, Anatoly Sierant, Piotr |
| contents | An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how magic, beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality and then confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. Our results underscore differences between typical and atypical states from the point of view of quantum information. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11631 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States Turkeshi, Xhek Dymarsky, Anatoly Sierant, Piotr Quantum Physics Statistical Mechanics High Energy Physics - Theory An important question of quantum information is to characterize genuinely quantum (beyond-Clifford) resources necessary for universal quantum computing. Here, we use the Pauli spectrum to quantify how magic, beyond Clifford, typical many-qubit states are. We first present a phenomenological picture of the Pauli spectrum based on quantum typicality and then confirm it for Haar random states. We then introduce filtered stabilizer entropy, a magic measure that can resolve the difference between typical and atypical states. We proceed with the numerical study of the Pauli spectrum of states created by random circuits as well as for eigenstates of chaotic Hamiltonians. We find that in both cases the Pauli spectrum approaches the one of Haar random states, up to exponentially suppressed tails. Our results underscore differences between typical and atypical states from the point of view of quantum information. |
| title | Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.11631 |