# Superposition of Macroscopically Distinct States in Adiabatic Quantum Computation

## TL;DR

This paper explores how superpositions of macroscopically distinct states relate to the quantum speedup in adiabatic quantum computation, suggesting such superpositions are key indicators of entanglement necessary for speedup.

## Contribution

It introduces an index to quantify superpositions of macroscopically distinct states and links this to the presence of entanglement in adiabatic algorithms exhibiting speedup.

## Key findings

- Superpositions of macroscopically distinct states correlate with quantum speedup.
- The index p effectively measures the degree of such superpositions.
- Superpositions serve as indicators of entanglement crucial for AQC efficiency.

## Abstract

What are the conditions for adiabatic quantum computation (AQC) to outperform classical computation? Although there exist several quantum adiabatic algorithms achieving the strong quantum speedup, the essential keys to their speedups are still unclear. Here, we investigate the connection between superpositions of macroscopically distinct states and known examples of the speedup in AQC. To formalize this notion we consider an index $p$ that quantifies a superposition of macroscopically distinct states from the asymptotic behaviors of fluctuations of additive observables. We determine this index for five examples of adiabatic algorithms exhibiting various degrees of the speedup. The results suggest that the superposition of macroscopically distinct states is an appropriate indicator of entanglement crucial to the strong quantum speedup in AQC.