Nonstabilizerness in U(1) lattice gauge theory
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917917133635584 |
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| author | Falcão, Pedro R. Nicácio Tarabunga, Poetri Sonya Frau, Martina Tirrito, Emanuele Zakrzewski, Jakub Dalmonte, Marcello |
| author_facet | Falcão, Pedro R. Nicácio Tarabunga, Poetri Sonya Frau, Martina Tirrito, Emanuele Zakrzewski, Jakub Dalmonte, Marcello |
| contents | We present a thorough investigation of nonstabilizerness - a fundamental quantum resource that quantifies state complexity within the framework of quantum computing - in a one-dimensional U(1) lattice gauge theory. We show how nonstabilizerness is always extensive with volume, and has no direct relation to the presence of critical points. However, its derivatives typically display discontinuities across the latter: This indicates that nonstabilizerness is strongly sensitive to criticality, but in a manner that is very different from entanglement (that, typically, is maximal at the critical point). Our results indicate that error-corrected simulations of lattice gauge theories close to the continuum limit have similar computational costs to those at finite correlation length and provide rigorous lower bounds for quantum resources of such quantum computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01789 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonstabilizerness in U(1) lattice gauge theory Falcão, Pedro R. Nicácio Tarabunga, Poetri Sonya Frau, Martina Tirrito, Emanuele Zakrzewski, Jakub Dalmonte, Marcello Quantum Physics Statistical Mechanics High Energy Physics - Lattice We present a thorough investigation of nonstabilizerness - a fundamental quantum resource that quantifies state complexity within the framework of quantum computing - in a one-dimensional U(1) lattice gauge theory. We show how nonstabilizerness is always extensive with volume, and has no direct relation to the presence of critical points. However, its derivatives typically display discontinuities across the latter: This indicates that nonstabilizerness is strongly sensitive to criticality, but in a manner that is very different from entanglement (that, typically, is maximal at the critical point). Our results indicate that error-corrected simulations of lattice gauge theories close to the continuum limit have similar computational costs to those at finite correlation length and provide rigorous lower bounds for quantum resources of such quantum computations. |
| title | Nonstabilizerness in U(1) lattice gauge theory |
| topic | Quantum Physics Statistical Mechanics High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2409.01789 |