Consistency of the adiabatic theorem

Area of Science:

• Quantum Physics
• Quantum Computation

Background:

• The adiabatic theorem is foundational for adiabatic quantum computation.
• Recent studies have questioned the conditions under which the adiabatic theorem applies.
• Understanding these conditions is crucial for reliable quantum computation.

Purpose of the Study:

• To investigate the reported violations of the adiabatic theorem.
• To clarify the conditions necessary for the adiabatic theorem to hold.
• To assess the implications for adiabatic quantum computation.

Main Methods:

• Analysis of resonant transitions between energy levels.
• Theoretical examination of the adiabatic theorem under various conditions.
• Comparison with existing literature on adiabatic quantum computation.

Main Results:

• Reported violations of the adiabatic theorem are attributed to resonant transitions.
• The traditional adiabatic theorem is shown to hold in the absence of fast driven oscillations.
• This finding reinforces the validity of the adiabatic model under specific constraints.

Conclusions:

• The adiabatic theorem remains a robust principle for quantum computation when resonant transitions are managed.
• Adiabatic quantum computation is viable when systems are free from rapid, driving oscillations.
• Further research should focus on mitigating resonant effects in quantum computing architectures.