Related papers: Translationally invariant universal classical Hami…
Recent work has characterised 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…
In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open…
Spin models are used in many studies of complex systems---be it condensed matter physics, neural networks, or economics---as they exhibit rich macroscopic behaviour despite their microscopic simplicity. Here we prove that all the physics of…
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…
In this paper, we consider spin systems in three spatial dimensions, and prove that the local Hamiltonian problem for 3D lattices with face-centered cubic unit cells, 4-local translationally-invariant interactions between spin-3/2 particles…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
We consider random translation-invariant frustration-free quantum spin Hamiltonians on $\mathbb Z^D$ in which the nearest-neighbor interaction in every direction is randomly sampled and then distributed across the lattice. Our main result…
We study translation-invariant quantum spin Hamiltonians on general graphs with non-commuting interactions either given by (i) a random rank-$1$ projection or (ii) Haar projectors. For (i), we prove that the Hamiltonian is gapped on any…
Classical spin Hamiltonians are a powerful tool to model complex systems, characterised by a local structure given by the local Hamiltonians. One of the best understood local structures is the grammar of formal languages, which are central…
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…
One of the theoretical pillars that sustain certain machine learning models are universal approximation theorems, which prove that they can approximate all functions from a function class to arbitrary precision. Independently, classical…
We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling…
We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses.…
In the spirit of multi-scale modeling, we develop a theoretical framework for spin-lattice coupling that connects, on the one hand, to ab initio calculations of spin-lattice coupling parameters and, on the other hand, to the magneto-elastic…
It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the 2-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions…
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…
The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel…
We present a systematic derivation of effective lattice spin Hamiltonians derived from a rotationally invariant multi-orbital Hubbard model including a term ensuring Hund's rule coupling. The Hamiltonians are derived down-folding the…