# How fast can one route quantum states

### APA

Yin, C. (2024). How fast can one route quantum states. Perimeter Institute. https://pirsa.org/24030122

### MLA

Yin, Chao. How fast can one route quantum states. Perimeter Institute, Mar. 20, 2024, https://pirsa.org/24030122

### BibTex

@misc{ pirsa_PIRSA:24030122, doi = {10.48660/24030122}, url = {https://pirsa.org/24030122}, author = {Yin, Chao}, keywords = {Quantum Information}, language = {en}, title = {How fast can one route quantum states}, publisher = {Perimeter Institute}, year = {2024}, month = {mar}, note = {PIRSA:24030122 see, \url{https://pirsa.org}} }

Chao Yin University of Colorado Boulder

## Abstract

Many quantum platforms naturally host Hamiltonians with power-law or even all-to-all connectivity, which may potentially process quantum information in a way much faster than conventional gate-based models. For such non-geometrically-local Hamiltonians, it is then important to both come up with fast protocols and understand the ultimate limit for realizing various information processing tasks. In this talk, I will first overview this quantum speed limit topic, and then dive into the particular task of quantum routing, i.e. permuting unknown quantum states on the qubits. I aim to show [1] a provably optimal Hamiltonian routing protocol on the star graph that is asymptotically faster than gate-based routing; [2] a lower bound on the time to realize the shift unitary using 1d power-law interactions which, perhaps surprisingly, can be much slower than the time for the conventional Lieb-Robinson light cone to spread across the whole system. The latter result shares interesting connections to the classification of 1d quantum cellular automata and symmetry-protected topological order.

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