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arXiv · 2509.12637

Symmetry and Topology of Successive Quantum Feedback Control

Junxuan Wen·Zongping Gong·Takahiro Sagawa
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Abstract

We establish a symmetry classification for a general class of quantum feedback control. For successive feedback control with a non-adaptive sequence of bare measurements (i.e., with positive Kraus operators), we prove that the symmetry classification collapses to the ten-fold AZ$^\dagger$ classes, specifying the allowed topology of CPTP maps associated with feedback control. We demonstrate that a chiral Maxwell's demon with Gaussian measurement errors exhibits quantized winding numbers. Moreover, for general (non-bare) measurements, we explicitly construct a protocol that falls outside the ten-fold classification. These results broaden and clarify the principles in engineering topological aspects of quantum control robust against disorder and imperfections.

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Junxuan Wen, Zongping Gong, Takahiro Sagawa. 2025-09-16. Symmetry and Topology of Successive Quantum Feedback Control. https://doi.org/10.1103/48k3-tb1j

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