Fast non-Abelian geometric gates via transitionless quantum driving

Area of Science:

• Quantum Information Science
• Quantum Computing
• Condensed Matter Physics

Background:

• Practical quantum computation requires high-fidelity quantum gates on qubits.
• Noise presents significant challenges to realizing these gates.
• Geometric phases offer intrinsic noise tolerance for robust quantum computation.

Purpose of the Study:

• To propose a method for speeding up adiabatic holonomic gates.
• To achieve a universal set of fast geometric quantum gates.
• To implement these gates in a superconducting circuit architecture.

Main Methods:

• Utilizing transitionless driving techniques to accelerate adiabatic holonomic gate implementation.
• Developing an all-geometric approach for gate construction.
• Employing superconducting circuit architectures.

Main Results:

• Demonstrated a general approach to speed up adiabatic holonomic gates.
• Achieved fast geometric quantum gates with potential for universality.
• The proposed holonomies asymptotically approach adiabatic ones in the long run-time limit.

Conclusions:

• The developed technique offers a way to implement fast, robust geometric quantum gates.
• This approach may overcome limitations of slow adiabatic evolution in quantum computation.
• It opens new possibilities for building practical quantum computers.