# A double-slit proposal for quantum annealing

## TL;DR

This paper proposes a double-slit experiment analogy for quantum annealing, demonstrating interference effects in the ground state probability that reveal coherence and are affected by thermal environments, linking theory to practical hardware tests.

## Contribution

It introduces a novel interference-based test for coherence in quantum annealing and simplifies the analysis of the generalized Landau-Zener problem.

## Key findings

- Oscillations in ground state probability indicate quantum coherence.
- Thermal bath coupling dampens interference oscillations.
- Theoretical tools connect quantum speedup mechanisms to experimental hardware.

## Abstract

We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the final time $t_f$. We demonstrate that for annealing schedules involving two consecutive diabatic transitions, an interference effect is generated akin to a double-slit experiment. The observation of oscillations in the ground state probability as a function of $t_f$ (before the adiabatic limit sets in) then constitutes a sensitive test of coherence between energy eigenstates. This is further illustrated by analyzing the effect of coupling the TLS to a thermal bath: increasing either the bath temperature or the coupling strength results in a damping of these oscillations. The theoretical tools we introduce significantly simplify the analysis of the generalized Landau-Zener problem. Furthermore, our analysis connects quantum annealing algorithms exhibiting speedups via the mechanism of coherent diabatic transitions to near-term experiments with quantum annealing hardware.