Single-loop multiple-pulse nonadiabatic holonomic quantum gates

Abstract

Nonadiabatic holonomic quantum computation provides the means to perform fast and robust quantum gates by utilizing the resilience of non-Abelian geometric phases to fluctuations of the path in state space. While the original scheme [New J. Phys. {\bf 14}, 103035 (2012)] needs two loops in the Grassmann manifold (i.e., the space of computational subspaces of the full state space) to generate an arbitrary holonomic one-qubit gate, we propose single-loop one-qubit gates that constitute an efficient universal set of holonomic gates when combined with an entangling holonomic two-qubit gate. Our one-qubit gate is realized by dividing the loop into path segments, each of which is generated by a $\Lambda$-type Hamiltonian. We demonstrate that two path segments are sufficient to realize arbitrary single-loop holonomic one-qubit gates. We describe how our scheme can be implemented experimentally in a generic atomic system exhibiting a three-level $\Lambda$-coupling structure, by utilizing carefully chosen laser pulses.

Some amendments; journal reference added

References in corpus (6)

• Experimental Realization of Universal Geometric Quantum Gates with Solid-State Spins
• An experimental observation of geometric phases for mixed states using NMR interferometry
• Robustness of non-adiabatic holonomic gates
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Cited by in corpus (3)

• Rydberg-atom-based scheme of nonadiabatic geometric quantum computation
• Composite nonadiabatic holonomic quantum computation
• Robust paths to realize nonadiabatic holonomic gates