Universal Quantum Hamiltonians
Abstract
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We first characterise precisely what it means for one quantum many-body system to replicate the entire physics of another. We then show that certain very simple spin-lattice models are universal in this very strong sense. Examples include the Heisenberg and XY models on a 2D square lattice (with non-uniform coupling strengths). We go on to fully classify all two-qubit interactions, determining which are universal and which can only simulate more restricted classes of models. Our results put the practical field of analogue Hamiltonian simulation on a rigorous footing and take a significant step towards justifying why error correction may not be required for this application of quantum information technology.
Cite
@article{arxiv.1701.05182,
title = {Universal Quantum Hamiltonians},
author = {Toby Cubitt and Ashley Montanaro and Stephen Piddock},
journal= {arXiv preprint arXiv:1701.05182},
year = {2019}
}
Comments
78 pages, 9 figures, 44 theorems etc. v2: Trivial fixes. v3: updated and simplified proof of Thm. 9; 82 pages, 47 theorems etc. v3: Small fix in proof of time-evolution lemma (this fix not in published version)