Quantum simulations under translational symmetry

Abstract

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 interactions we determine time evolutions which can and those that can not be simulated. Whereas for general spin systems no finite universal set of generating interactions is shown to exist, universality turns out to be generic for quadratic bosonic and fermionic nearest-neighbor interactions when supplemented by all translationally invariant on-site Hamiltonians.

9 pages, 2 figures, references added, minor changes

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Cited by in corpus (11)

• Quantum Simulation
• Using Quantum Computers for Quantum Simulation
• A perspective on scaling up quantum computation with molecular spins
• Symmetry Principles in Quantum Systems Theory
• Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods
• A Dynamic Systems Approach to Fermions and Their Relation to Spins
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Dispersive readout of molecular spin qudits
• An experimental proposal to observe non-abelian statistics of Majorana-Shockley fermions in an optical lattice
• Analyzing the quantum approximate optimization algorithm: ansätze, symmetries, and Lie algebras
• Quantum Computing with Global One-and Two-Qubit Gates