Duality as a Feasible Physical Transformation

Abstract

Duality transformations are very important in both classical and quantum physics. They allow one to relate two seemingly different formulations of the same physical realm through clever mathematical manipulations, and offer numerous advantages for the study of many-body physics. In this work, we suggest a method which shall introduce them to the world of quantum simulation too: a feasible scheme for implementing duality transformations as physical operations, mapping between dual quantum states showing the same observable physics, rather than just a mathematical trick. Demonstrating with Abelian lattice models, we show how duality transformations could be implemented in the laboratory as sequences of single- and two-body operations - unitaries and measurements.

16 pages

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• Subsystem Non-Invertible Symmetry Operators and Defects
• Non-invertible symmetries act locally by quantum operations
• Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
• State Preparation in the Heisenberg Model through Adiabatic Spiraling
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Stabilizer Rényi Entropy Encodes Fusion Rules of Topological Defects and Boundaries
• Efficient Preparation of Nonabelian Topological Orders in the Doubled Hilbert Space