The modern perspective on the classification of phases of matter is given in terms of circuit complexity: two many-body quantum states belong to the same phase of matter if and only if they can be related by a finite-depth quantum circuit. In this talk, I will discuss how quantum circuits can also be used to transform between different phases of matter. First, I will introduce a special class of linear-depth quantum circuits called "sequential circuits" which suffice to transform between a majority of known gapped phases while preserving the entanglement area law. Second, I will show how certain phases can be related using finite-depth circuits if one is allowed to employ long-range interactions. Finally, I will show how highly entangled quantum states can serve as "many-body catalysts" which enable otherwise impossible transformations between phases of matter. The circuits constructed in this talk provide new insights into the entanglement structure and stability of topological phases of matter and also new routes to prepare these phases in quantum devices.
This talk is based on the following works: https://arxiv.org/abs/2212.06844, https://arxiv.org/abs/2307.01267