| Autor: |
Leone, Lorenzo, Oliviero, Salvatore F. E., Esposito, Gianluca, Hamma, Alioscia |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
Phys. Rev. A 109, 032403 (2024) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1103/PhysRevA.109.032403 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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