A Continuous Topological Interpretation of Quantum Circuits and Entanglement Geometry

We introduce a continuous topological interpretation of quantum circuits that extends the usual discrete gate-based model. In this view, a circuit is not only a finite sequence of unitary operations, but a continuous landscape embedded in a larger parameter space. The standard unitary description appears as a constrained submanifold of this space. Within this framework, entanglement naturally shows up as an enlargement of the accessible parameter manifold, which helps explain why entangled circuits are significantly more expressive than collections of unentangled qubits.