Simulating typical entanglement with many-body Hamiltonian dynamics

TL;DR

This paper investigates how one-dimensional spin-1/2 Ising-type Hamiltonians with many-body interactions can generate entanglement distributions similar to typical entanglement, with implications for quantum simulation efficiency.

Contribution

It demonstrates that certain time-independent Hamiltonians with many-body interactions can replicate the average and variability of typical entanglement distributions.

Findings

Entanglement distributions match typical entanglement when using suitable many-body Hamiltonians.

The time to reach such entanglement distributions scales polynomially with system size.

Hamiltonians with specific many-body interactions effectively simulate typical entanglement properties.

Abstract

We study the time evolution of the amount of entanglement generated by one dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.