# Assessing the quantumness of the annealing dynamics via Leggett Gargs inequalities: a weak measurement approach

## TL;DR

This paper proposes using Leggett-Garg inequalities combined with weak measurements to effectively evaluate the quantum coherence of the annealing process in quantum computation, supported by numerical simulations.

## Contribution

It introduces a novel weak measurement approach to assess the quantumness of quantum annealing, bridging a gap in experimental evidence of quantum coherence.

## Key findings

- Weak measurements of Leggett-Garg inequalities can detect quantum coherence during annealing.
- Numerical simulations confirm the effectiveness of the proposed method.
- Classical and quantum models show distinct behaviors in the assessment.

## Abstract

Adiabatic quantum computation (AQC) is a promising counterpart of universal quantum computation, based on the key concept of quantum annealing (QA). QA is claimed to be at the basis of commercial quantum computers and benefits from the fact that the detrimental role of decoherence and dephasing seems to have poor impact on the annealing towards the ground state. While many papers show interesting optimization results with a sizable number of qubits, a clear evidence of a full quantum coherent behavior during the whole annealing procedure is still lacking. In this paper we show that quantum non-demolition (weak) measurements of Leggett Garg inequalities can be used to efficiently assess the quantumness of the QA procedure. Numerical simulations based on a weak coupling Lindblad approach are compared with classical Langevin simulations to support our statements.