Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions

Abstract

We show how to map a given n-qubit target Hamiltonian with bounded-strength k-body interactions onto a simulator Hamiltonian with two-body interactions, such that the ground-state energy of the target and the simulator Hamiltonians are the same up to an extensive error O(epsilon n) for arbitrary small epsilon. The strength of interactions in the simulator Hamiltonian depends on epsilon and k but does not depend on n. We accomplish this reduction using a new way of deriving an effective low-energy Hamiltonian which relies on the Schrieffer-Wolff transformation of many-body physics.

v1: 8 pages Latex, 1 figure

References in corpus (11)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Measurement-based quantum computation with cluster states
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Spectral Gap and Exponential Decay of Correlations
• The power of quantum systems on a line
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Error correcting codes for adiabatic quantum computation
• Perturbative Gadgets at Arbitrary Orders

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