Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device

Area of Science:

• Quantum Computing
• Condensed Matter Physics
• Computational Physics

Background:

• Quantum annealing is a metaheuristic optimization algorithm.
• The transverse-field Ising model is a fundamental model in statistical mechanics and quantum computing.
• D-Wave systems are specialized quantum processors designed for quantum annealing.

Purpose of the Study:

• To investigate the optimal annealing rate for the 2D transverse-field Ising model on a D-Wave quantum annealer.
• To understand the interplay between quantum fluctuations and noise during the annealing process.
• To develop a model that explains the observed scaling of performance with annealing rate and lattice size.

Main Methods:

• Quantum annealing simulations on a D-Wave device with L×L lattices (L≤32).
• Analysis of residual energy and deviation from maximal magnetization in the final classical state.
• Development and validation of a phenomenological model to describe the results.
• Numerical solutions of the transverse-field Ising model with noise sources.

Main Results:

• An optimal annealing rate (v) was identified, dependent on lattice size (L), that minimizes residual energy and magnetization deviation.
• The optimal rate balances reduced quantum fluctuations (Kibble-Zurek mechanism evidence) against increasing noise impact at lower rates.
• A phenomenological model with specific power-law dependencies on v and L-dependent prefactors accurately describes the experimental and numerical results.
• The optimal annealing time exceeds individual qubit coherence times, explained by the model.

Conclusions:

• The performance of quantum annealing on the 2D transverse-field Ising model is sensitive to the annealing rate.
• A balance between quantum effects and noise is crucial for optimal performance.
• The observed scaling phenomena can be explained by a model incorporating competing effects and noise.
• The study provides insights into optimizing quantum annealing protocols and understanding their limitations.