Translationally Invariant Universal Quantum Hamiltonians in 1D

Recent work has characterized rigorously what it means for one quantum system to simulate another and demonstrated the existence of universal Hamiltonians—simple spin lattice Hamiltonians that can replicate the entire physics of any other quantum many-body system. Previous universality results have...

Full description

Saved in:
Bibliographic Details
Published in:Annales Henri Poincaré 2022, Vol.23 (1), p.223-254
Main Authors: Kohler, Tamara, Piddock, Stephen, Bausch, Johannes, Cubitt, Toby
Format: Article
Language:English
Subjects:
Chains
Classical and Quantum Gravitation
Complexity
Dynamical Systems and Ergodic Theory
Elementary Particles
Invariants
Mathematical and Computational Physics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Quantum computing
Quantum Field Theory
Quantum Physics
Quantum theory
Relativity Theory
Theoretical
Two dimensional models
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Recent work has characterized rigorously what it means for one quantum system to simulate another and demonstrated the existence of universal Hamiltonians—simple spin lattice Hamiltonians that can replicate the entire physics of any other quantum many-body system. Previous universality results have required proofs involving complicated ‘chains’ of perturbative ‘gadgets.’ In this paper, we derive a significantly simpler and more powerful method of proving universality of Hamiltonians, directly leveraging the ability to encode quantum computation into ground states. This provides new insight into the origins of universal models and suggests a deep connection between universality and complexity. We apply this new approach to show that there are universal models even in translationally invariant spin chains in 1D. This gives as a corollary a new Hamiltonian complexity result that the local Hamiltonian problem for translationally invariant spin chains in one dimension with an exponentially small promise gap is PSPACE-complete. Finally, we use these new universal models to construct the first known toy model of 2D–1D holographic duality between local Hamiltonians.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-021-01111-7