An Efficient Quantum Algorithm for Portbased Teleportation
APA
Fei, J. & Timmerman, S. (2024). An Efficient Quantum Algorithm for Portbased Teleportation. Perimeter Institute. https://pirsa.org/24040076
MLA
Fei, Jiani, and Sydney Timmerman. An Efficient Quantum Algorithm for Portbased Teleportation. Perimeter Institute, Apr. 03, 2024, https://pirsa.org/24040076
BibTex
@misc{ pirsa_PIRSA:24040076, doi = {10.48660/24040076}, url = {https://pirsa.org/24040076}, author = {Fei, Jiani and Timmerman, Sydney}, keywords = {Quantum Information}, language = {en}, title = {An Efficient Quantum Algorithm for Portbased Teleportation}, publisher = {Perimeter Institute}, year = {2024}, month = {apr}, note = {PIRSA:24040076 see, \url{https://pirsa.org}} }

Jiani Fei Stanford University

Sydney Timmerman Stanford University
Abstract
In this talk, we will outline an efficient algorithm for portbased teleportation, a unitarily equivariant version of teleportation useful for constructing programmable quantum processors and performing instantaneous nonlocal computation (NLQC). The latter connection is important in AdS/CFT, where bulk computations are realized as boundary NLQC. Our algorithm yields an exponential improvement to the known relationship between the amount of entanglement available and the complexity of the nonlocal part of any unitary that can be implemented usin NLQC. Similarly, our algorithm provides the first nontrivial efficient algorithm for an approximate universal programmable quantum processor.
The key to our approach is a general quantum algorithm we develop for block diagonalizing socalled generalized induced representations, a novel type of representation that arises from lifting a representation of a subgroup to one for the whole group while relaxing a linear independence condition from the standard definition. Generalized induced representations appear naturally in quantum information, notably in generalizations of SchurWeyl duality. For the case of portbased teleportation, we apply this framework to develop an efficient twisted Schur transform for transforming to a subgroupreduced irrep basis of the partially transposed permutation algebra, whose dual is the U⊗n−k ⊗ (U∗) ⊗k representation of the unitary group.
