The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's original paradigm. Here, we develop an algebraic framework for systematically deriving the fusion rules of topological defects in higher-dimensional lattice systems with noninvertible generalized symmetries, and focus on a $(2+1)$-dimensional quantum Ising plaquette model as a concrete illustration. We show that bond-algebraic automorphisms, when combined with the so-called half-gauging procedure, reveal the structure of the noninvertible duality symmetry operators, which can be explicitly represented as a sequential quantum circuit. The resulting duality defects are constrained by the model's rigid higher symmetries (lower-dimensional subsystem symmetries), leading to restricted mobility. We establish the fusion algebra of these defects. Finally, in constructing the noninvertible duality transformation, we explicitly verify that it acts as partial isometry on the physical Hilbert space, thereby satisfying a recent generalization of Wigner's theorem applicable to noninvertible symmetries.

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• Lattice gauge theory
• Quantum measurements
• Topological defects
• Discrete symmetries
• Symmetries
• Gauge symmetries