# Quantum simulation of long range $XY$ quantum spin glass with strong area-law violation using trapped ions

## TL;DR

This paper demonstrates that a one-dimensional long-range disordered quantum spin glass exhibits strong area-law violation in its ground state, and proposes a trapped ion quantum simulation to study this complex quantum system.

## Contribution

It introduces a quantum simulation method for a long-range disordered spin glass exhibiting strong area-law violation, enabling exploration of large systems beyond numerical limitations.

## Key findings

- Ground state shows more than logarithmic entanglement entropy violation.
- Strong area-law violation occurs even in short-range regime.
- Feasible trapped ion implementation with realistic parameters.

## Abstract

Ground states of local Hamiltonians are known to obey the entanglement entropy area law. While area law violation of a mild kind (logarithmic) is commonly encountered, strong area-law violation (more than logarithmic) is rare. In this paper, we study the long range quantum spin glass in one dimension whose couplings are disordered and fall off with distance as a power-law. We show that this system exhibits more than logarithmic area law violation in its ground state. Strikingly this feature is found to be true even in the short range regime in sharp contrast to the spinless long range disordered fermionic model. This necessitates the study of large systems for the quantum $XY$ spin glass model which is challenging since these numerical methods depend on the validity of the area law. This situation lends itself naturally for the exploration of a quantum simulation approach. We present a proof-of-principle implementation of this non-trivially interacting spin model using trapped ions and provide a detailed study of experimentally realistic parameters.