## RQC Seminar

### 166th RQC Seminar

#### Speaker

Prof. Masaya Nakagawa

( The University of Tokyo, Japan )#### Date

4:00-5:00 p.m. (16:00-17:00), October 23, 2024 (Wednesday)

#### Venue

Hybrid(ZOOM・ Wako Main Research 3F 345-347 Seminar Room/ 研究本館3階 セミナー室(345-347) C01）

#### Title

Topology of discrete quantum feedback control

#### Inquiries

rqc_info[at]ml.riken.jp

**Abstract**

Symmetry and topology are guiding principles for the classification of quantum phases of matter. For instance, unique gapped ground states of quantum many-body systems are classified into symmetry-protected topological phases, where different phases cannot be continuously connected with each other while preserving symmetry and an energy gap [1]. One can also utilize symmetry and topology to classify nonequilibrium dynamics. Examples include Floquet topological phases with topological unitary operators [2] and non-Hermitian topological phases in open systems [3]. In this seminar, we develop a framework of a topological classification of quantum channels that describe discrete quantum feedback control [4]. We construct a topological Maxwell's demon that achieves robust feedback-assisted chiral transport due to its topological nature. Furthermore, we provide a symmetry classification of quantum feedback control and show that only ten symmetry classes out of the 38-fold Bernard-LeClair classes are consistent with projective measurement. Building on the symmetry classification, we construct symmetry-protected topological feedback control which exhibits helical spin transport due to nontrivial point-gap topology.

[1] X. Chen, Z. C. Gu, Z. X. Liu, and X. G. Wen, Phys. Rev. B 87, 155114 (2013).

[2] T. Kitagawa, E. Berg, M. Rudner, and E. Demler, Phys. Rev. B 82, 235114 (2010).

[3] Z. Gong, Y. Ashida, K. Kawabata, K. Takasan, S. Higashikawa, and M. Ueda, Phys. Rev. X 8, 031079 (2018).

[4] M. Nakagawa and M. Ueda, arXiv:2403.08406.