Title: Exact Quantum Algorithms to Recognize Quantum Phases of Matter

 

Abstract: In  this talk, we explore the relationship between renormalization group  (RG) flow and error correction by constructing quantum algorithms that  exactly recognize 1D symmetry-protected topological (SPT) phases protected by finite internal Abelian symmetries. For each SPT phase, our algorithm runs  a quantum circuit which emulates RG flow: an arbitrary input ground  state wavefunction in the phase is mapped to a unique  minimally-entangled reference state, thereby allowing for efficient  phase identification. This construction is enabled by viewing a generic  input state in the phase as a collection of coherent `errors' applied to  the reference state, and engineering a quantum circuit to efficiently  detect and correct such errors. Importantly, the error correction  threshold is proven to coincide exactly with the phase boundary. We  discuss the implications of our results in the context of condensed  matter physics, machine learning, and near-term quantum algorithms.