# Complexity of Entanglement in Quantum Computation and Macroscopic Quantum Orders

Akimasa Miyake

University of New Mexico

Quantum entanglement, which Einstein, Podolsky, and Rosen were concerned about due to its unconventional nonlocal correlation, has been realized by now to be a useful resource for quantum information processing such as quantum computation and communication. Furthermore, the concept of entanglement turns out to be helpful in several research fields of physics in order to capture the complexity of quantum many-body systems. For example, topological orders that exhibit spin liquid behaviors of frustrated quantum antiferromagnets can be well understood in terms of the interplay of entanglement and symmetry. In this talk, I will address the roles of entanglement in two seemingly distant subjects: quantum computation and symmetry-protected topological orders. An unexpected connection between them suggests that entanglement underlies a common hierarchical structure of complexity in both cases.