# Real-time simulation of flux qubits used for quantum annealing

## TL;DR

This paper uses numerical simulations to analyze flux qubit dynamics during quantum annealing, validating the qubit model and environmental effects by comparing with experimental data from a D-Wave system.

## Contribution

It demonstrates that flux qubits can be accurately modeled during annealing and highlights the importance of environmental coupling for matching experimental results.

## Key findings

- Qubit representation effectively describes flux dynamics.
- Tunable coupling does not impair annealing performance.
- Environmental effects improve simulation-experiment agreement.

## Abstract

The real-time flux dynamics of up to three superconducting quantum interference devices (SQUIDs) are studied by numerically solving the time-dependent Schr\"odinger equation. The numerical results are used to scrutinize the mapping of the flux degrees of freedom onto two-level systems (the qubits) as well as the performance of the intermediate SQUID as a tunable coupling element. It is shown that the qubit representation yields a good description of the flux dynamics during quantum annealing and the presence of the tunable coupling element does not have negative effects on the overall performance. Additionally, data obtained from a simulation of the dynamics of two-level systems during quantum annealing are compared to experimental data produced by the D-Wave 2000Q quantum annealer. The effects of finite temperature are incorporated in the simulation by coupling the qubit system to a bath of two-level systems. It is shown that an environment modeled as non-interacting two-level systems coupled to the qubits can produce data which matches the experimental data much better than the simulation data of the qubits without coupling to an environment and better than data obtained from a simulation of an environment modeled as interacting two-level systems coupling to the qubits.