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.Comment: 10 pages + appendices v2: extended discussion on RG convergence;
added ref