Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
Abstract
Clifford circuits are insufficient for universal quantum computation or creating t -designs with t\ge 4 . While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (\pi/8) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.
- Authors:
-
- Boston University
- University of Massachusetts Boston
- Publication Date:
- Research Org.:
- Northeastern Univ., Boston, MA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1735670
- Alternate Identifier(s):
- OSTI ID: 1853000
- Grant/Contract Number:
- SC0019275
- Resource Type:
- Published Article
- Journal Name:
- SciPost Physics
- Additional Journal Information:
- Journal Name: SciPost Physics Journal Volume: 9 Journal Issue: 6; Journal ID: ISSN 2542-4653
- Publisher:
- Stichting SciPost
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Zhou, Shiyu, Yang, Zhicheng, Hamma, Alioscia, and Chamon, Claudio. Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics. Netherlands: N. p., 2020.
Web. doi:10.21468/SciPostPhys.9.6.087.
Zhou, Shiyu, Yang, Zhicheng, Hamma, Alioscia, & Chamon, Claudio. Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics. Netherlands. https://doi.org/10.21468/SciPostPhys.9.6.087
Zhou, Shiyu, Yang, Zhicheng, Hamma, Alioscia, and Chamon, Claudio. Mon .
"Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics". Netherlands. https://doi.org/10.21468/SciPostPhys.9.6.087.
@article{osti_1735670,
title = {Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics},
author = {Zhou, Shiyu and Yang, Zhicheng and Hamma, Alioscia and Chamon, Claudio},
abstractNote = {Clifford circuits are insufficient for universal quantum computation or creating t t -designs with t\ge 4 t ≥ 4 . While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum of a time evolved random product state is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T (\pi/8) ( π / 8 ) gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution.},
doi = {10.21468/SciPostPhys.9.6.087},
journal = {SciPost Physics},
number = 6,
volume = 9,
place = {Netherlands},
year = {Mon Dec 14 00:00:00 EST 2020},
month = {Mon Dec 14 00:00:00 EST 2020}
}
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