Phase transition in Stabilizer Entropy and efficient purity estimation
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866911788883247104 |
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| author | Leone, Lorenzo Oliviero, Salvatore F. E. Esposito, Gianluca Hamma, Alioscia |
| author_facet | Leone, Lorenzo Oliviero, Salvatore F. E. Esposito, Gianluca Hamma, Alioscia |
| contents | Stabilizer Entropy (SE) quantifies the spread of a state in the basis of Pauli operators. It is a computationally tractable measure of non-stabilizerness and thus a useful resource for quantum computation. SE can be moved around a quantum system, effectively purifying a subsystem from its complex features. We show that there is a phase transition in the residual subsystem SE as a function of the density of non-Clifford resources. This phase transition has important operational consequences: it marks the onset of a subsystem purity estimation protocol that requires $poly(n)exp(t)$ many queries to a circuit containing $t$ non-Clifford gates that prepares the state from a stabilizer state. Then, for $t=O(\log_2 n)$, it estimates the purity with polynomial resources and, for highly entangled states, attains an exponential speed-up over the known state-of-the-art algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_07895 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Phase transition in Stabilizer Entropy and efficient purity estimation Leone, Lorenzo Oliviero, Salvatore F. E. Esposito, Gianluca Hamma, Alioscia Quantum Physics Stabilizer Entropy (SE) quantifies the spread of a state in the basis of Pauli operators. It is a computationally tractable measure of non-stabilizerness and thus a useful resource for quantum computation. SE can be moved around a quantum system, effectively purifying a subsystem from its complex features. We show that there is a phase transition in the residual subsystem SE as a function of the density of non-Clifford resources. This phase transition has important operational consequences: it marks the onset of a subsystem purity estimation protocol that requires $poly(n)exp(t)$ many queries to a circuit containing $t$ non-Clifford gates that prepares the state from a stabilizer state. Then, for $t=O(\log_2 n)$, it estimates the purity with polynomial resources and, for highly entangled states, attains an exponential speed-up over the known state-of-the-art algorithms. |
| title | Phase transition in Stabilizer Entropy and efficient purity estimation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2302.07895 |