Nonadiabatic Holonomic Quantum Computation Research Articles

Nonadiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

Non-adiabatic holonomic quantum computation

We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level Λ configuration. Our scheme opens up the possibility of realizing universal holonomic quantum computation on qubits characterized by short coherence time.

Robustness of optimal working points for nonadiabatic holonomic quantum computation

Geometric phases are an interesting resource for quantum computation, also in view of their robustness against decoherence effects. We study here the effects of the environment on a class of one-qubit holonomic gates that have been recently shown to be characterized by "optimal" working times. We numerically analyze the behavior of these optimal points and focus on their robustness against noise.