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Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
by Shiyu Zhou, Zhi-Cheng Yang, Alioscia Hamma, Claudio Chamon
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Submission summary
| Authors (as registered SciPost users): | Alioscia Hamma · Shiyu Zhou |
| Submission information | |
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| Preprint Link: | scipost_202004_00048v3 (pdf) |
| Date accepted: | 2020-12-09 |
| Date submitted: | 2020-12-02 17:18 |
| Submitted by: | Zhou, Shiyu |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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 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.
Author comments upon resubmission
Published as SciPost Phys. 9, 087 (2020)