Non-Abelian geometric phases in a system of coupled quantum bits
arXiv:1307.5315 · doi:10.1103/PhysRevA.89.022117
Abstract
A common strategy to measure the Abelian geometric phase for a qubit is to let it evolve along an 'orange slice' shaped path connecting two antipodal points on the Bloch sphere by two different semi- great circles. Since the dynamical phases vanish for such paths, this allows for direct measurement of the geometric phase. Here, we generalize the orange slice setting to the non-Abelian case. The proposed method to measure the non-Abelian geometric phase can be implemented in a cyclic chain of four qubits with controllable interactions.
New title, minor revision, journal ref added
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- Composite nonadiabatic holonomic quantum computation
- Fast holonomic quantum computation on superconducting circuits with optimal control
- Doubly geometric quantum control
- Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade
- Fast holonomic quantum computation based on solid-state spins with all-optical control
- Nonadiabatic holonomic quantum computation on coupled transmons with ancillaries
- Nonadiabatic geometric quantum gates that are insensitive to qubit-frequency drifts
- Noncyclic Geometric Quantum Gates with Smooth Paths via Invariant-based Shortcuts
- Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
- Scalable nonadiabatic holonomic quantum computation on a superconducting qubit lattice
- Geometric and holonomic quantum computation