Research Paper#Quantum Computing, Geometric Quantum Computation🔬 ResearchAnalyzed: Jan 3, 2026 16:39
Non-Abelian Geometric Quantum Gates in Triangular Systems
Published:Dec 31, 2025 11:37
•1 min read
•ArXiv
Analysis
This paper proposes a novel method for creating quantum gates using the geometric phases of vibrational modes in a three-body system. The use of shape space and the derivation of an SU(2) holonomy group for single-qubit control is a significant contribution. The paper also outlines a method for creating entangling gates and provides a concrete physical implementation using Rydberg trimers. The focus on experimental verification through interferometric protocols adds to the paper's value.
Key Takeaways
- •Proposes a new method for creating quantum gates using geometric phases in a three-body system.
- •Utilizes shape space and derives an SU(2) holonomy group for single-qubit control.
- •Outlines a method for creating entangling gates (CNOT).
- •Suggests a physically realizable implementation using Rydberg trimers.
- •Includes a Ramsey/echo interferometric protocol for experimental verification.
Reference
“The paper shows that its restricted holonomy group is SU(2), implying universal single-qubit control by closed loops in shape space.”