SciPost Submission Page
Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
by Shiyu Zhou, Zhi-Cheng Yang, Alioscia Hamma, Claudio Chamon
- Published as SciPost Phys. 9, 087 (2020)
Submission summary
| As Contributors: | Alioscia Hamma · Shiyu Zhou |
| Preprint link: | scipost_202004_00048v3 |
| Date accepted: | 2020-12-09 |
| Date submitted: | 2020-12-02 17:18 |
| Submitted by: | Zhou, Shiyu |
| Submitted to: | SciPost Physics |
| Academic field: | Physics |
| Specialties: |
|
| 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.
Published as SciPost Phys. 9, 087 (2020)