Abstract: It is well known that the long-range entanglement structure of gapped state is preserved by finite-depth quantum circuits. To map between states of different gapped phases, we can use Sequential Quantum Circuits, which apply unitary transformations to sub-regions of a system in a sequential way. The sequential structure of the circuit, on the one hand, preserves entanglement area law of the quantum states, and on the other hand, is capable of changing the long-range correlation and entanglement of quantum states and the phase they belong to. 

In this talk, I will discuss the definition, basic properties, and prototypical examples of sequential quantum circuits that map product states to GHZ states, SPT states, and intrinsic topological states. I will also discuss the physical interpretation of the power of the circuits through connection to Kramers-Wannier duality and condensation. Finally, I will discuss our ongoing work about generating and manipulating line defects within a topological ordered state. With the help of sequential quantum circuit, I will show how to generate, deform and fuse these defects. A more physical understanding of the so called 2-category structure of topological order is therefore provided from the circuit perspective.