Simplifying the simulation of local Hamiltonian dynamics

Abstract

Local Hamiltonians, $H_k$, describe non-trivial $k$-body interactions in quantum many-body systems. Here, we address the dynamical simulatability of a $k$-local Hamiltonian by a simpler one, $H_{k^{\prime }}$, with $k^{\prime }<k$, under the realistic constraint that both Hamiltonians act on the same Hilbert space. When it comes to exact simulation, we build upon known methods to derive examples of $H_k$ and $H_{k^{\prime }}$ that simulate the same physics. We also address the most realistic case of approximate simulation. There, we upper-bound the error up to which a Hamiltonian can simulate another one, regardless of their internal structure, and prove, by means of an example, that the accuracy of a $(k^{\prime }=2)$-local Hamiltonian to simulate $H_k$ with $k>2$ increases with $k$. Finally, we propose a method to search for the $k^{\prime }$-local Hamiltonian that simulates, with the highest possible precision, the short time dynamics of a given $H_k$ Hamiltonian.

13 pages, 6 figures, accepted version for publication

References in corpus (10)

• Quantum Simulation
• Quantum Simulators: Architectures and Opportunities
• Determining a local Hamiltonian from a single eigenstate
• Universal Quantum Hamiltonians
• Classically optimized Hamiltonian simulation
• Distance Bounds on Quantum Dynamics
• Extremal eigenvalues of local Hamiltonians
• Simulating the same physics with two distinct Hamiltonians
• General conditions for universality of Quantum Hamiltonians
• Simulating highly nonlocal Hamiltonians with less nonlocal Hamiltonians

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