Symmetry and Topology of Successive Quantum Feedback Control

• URL: http://arxiv.org/abs/2509.12637v2
• Date: Fri, 03 Oct 2025 11:19:48 GMT
• Title: Symmetry and Topology of Successive Quantum Feedback Control
• Authors: Junxuan Wen, Zongping Gong, Takahiro Sagawa,
• Abstract summary: We establish a symmetry classification for a general class of quantum feedback control.<n>We prove that the symmetry classification collapses to the ten-fold AZ$dagger$ classes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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