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
This Submission thread is now published as
Submission summary
| Submission information |
| 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 |
| 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)
Author comments upon resubmission
We thank Referee 1 for recommending publication of our manuscript. We address comments from Referee 2 in detail in the reply.
