# Hamiltonian simulation meets holographic duality

### APA

Cubitt, T. (2020). Hamiltonian simulation meets holographic duality . Perimeter Institute. https://pirsa.org/20110052

### MLA

Cubitt, Toby. Hamiltonian simulation meets holographic duality . Perimeter Institute, Nov. 11, 2020, https://pirsa.org/20110052

### BibTex

@misc{ pirsa_PIRSA:20110052, doi = {10.48660/20110052}, url = {https://pirsa.org/20110052}, author = {Cubitt, Toby}, keywords = {Quantum Information}, language = {en}, title = {Hamiltonian simulation meets holographic duality }, publisher = {Perimeter Institute}, year = {2020}, month = {nov}, note = {PIRSA:20110052 see, \url{https://pirsa.org}} }

Toby Cubitt University College London

## Abstract

"Analogue" Hamiltonian simulation involves engineering a Hamiltonian of

interest in the laboratory and studying its properties experimentally.

Large-scale Hamiltonian simulation experiments have been carried out in

optical lattices, ion traps and other systems for two decades. Despite

this, the theoretical basis for Hamiltonian simulation is surprisingly

sparse. Even a precise definition of what it means to simulate a

Hamiltonian was lacking.

AdS/CFT duality postulates that quantum gravity in a d-dimensional

anti-de-Sitter bulk space is equivalent to a strongly interacting field

theory on its d-1 dimensional boundary. Recently, connections between

AdS/CFT duality and quantum error-correcting codes have led (amongst

other things) to tensor network toy models that capture important aspects

of this holographic duality. However, these toy models struggle to

encompass dualities between bulk and boundary energy scales and dynamics.

On the face of it, these two topics seem to have nothing whatsoever to do

with one another.

In my talk, I will explain how we put analogue Hamiltonian simulation on

a rigorous theoretical footing, by drawing on techniques from Hamiltonian

complexity theory and Jordan algebras. I will show how this proved far

more fruitful than a mere mathematical tidying-up exercise, leading to

the discovery of universal quantum Hamiltonians [Science, 351:6 278,

p.1180, 2016], [Proc. Natl. Acad. Sci. 115:38 p.9497, 2018]. And I will

explain how this new Hamiltonian simulation formalism, together with

hyperbolic Coxeter groups, allowed us to extend the toy models of AdS/CFT

to encompass energy scales, dynamics, and even (toy models of) black hole

formation [arXiv:1810.08992].