Nonadiabatic holonomic multiqubit controlled gates

Abstract

Previous schemes of nonadiabatic holonomic quantum computation were focused mainly on realizing a universal set of elementary gates. Multiqubit controlled gates could be built by decomposing them into a series of the universal gates. In this article, we propose an approach for realizing nonadiabatic holonomic multiqubit controlled gates in which a $(n+1)$-qubit controlled-$(\mathrm{n}\cdot \sigma )$ gate is realized by $(2n-1)$ basic operations instead of decomposing it into the universal gates, whereas an $(n+1)$-qubit controlled arbitrary rotation gate can be obtained by combining only two such controlled-$(\mathrm{n}\cdot \sigma )$ gates. Our scheme greatly reduces the operations of nonadiabatic holonomic quantum computation.

6 pages, 2 figures

References in corpus (13)

• Towards fault-tolerant quantum computing with trapped ions
• Effective Hamiltonian Theory and Its Applications in Quantum Information
• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• Optical holonomic single quantum gates with a geometric spin under a zero field
• Robustness of non-adiabatic holonomic gates
• Rydberg-atom-based scheme of nonadiabatic geometric quantum computation
• Single-loop multiple-pulse nonadiabatic holonomic quantum gates
• Single-shot realization of nonadiabatic holonomic quantum gates in decoherence-free subspaces
• Composite nonadiabatic holonomic quantum computation
• Implementation of three-qubit Grover search in cavity QED
• Robust paths to realize nonadiabatic holonomic gates
• Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases
• Shortcut Scheme for One-Step Implementation of a Three-Qubit Nonadiabatic Holonomic Gate

Cited by in corpus (2)

• General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation
• Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade