Simulating Sparse Hamiltonians on 2D Lattices

Abstract

Systems with sparse, yet long-range interactions, form a rich class capable of exhibiting various interesting physics, including good error correction. In this Letter we show how to simulate any sparse Pauli Hamiltonian with a 2D nearest neighbor Hamiltonian, using fewer resources than previous techniques. As an application we demonstrate how to simulate a good quantum code Hamiltonian, effectively approximating a [[N,Ω(N),Ω(N)]] code in two dimensions. Published by the American Physical Society 2025