The time-dependent pseudo-Hermitian formulation of quantum mechanics allows one to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of holonomic quantum computation can equally be formulated for pseudo-Hermitian systems. Starting from a degenerate pseudo-Hermitian Hamiltonian we show that, in the adiabatic limit, a non-Abelian geometric phase emerges which realizes a pseudounitary quantum gate. We illustrate our findings by studying a pseudo-Hermitian gain-loss system which can be written in the form of a tripod Hamiltonian by using the biorthogonal representation. It is shown that this system allows for arbitrary pseudo- $U(2)$ transformations acting on the dark subspace of the system.The time-dependent pseudo-Hermitian formulation of quantum mechanics allows one to study open system dynamics in analogy to Hermitian quantum systems. In this setting, we show that the notion of holonomic quantum computation can equally be formulated for pseudo-Hermitian systems. Starting from a degenerate pseudo-Hermitian Hamiltonian we show that, in the adiabatic limit, a non-Abelian geometric phase emerges which realizes a pseudounitary quantum gate. We illustrate our findings by studying a pseudo-Hermitian gain-loss system which can be written in the form of a tripod Hamiltonian by using the biorthogonal representation. It is shown that this system allows for arbitrary pseudo-$U(2)$ transformations acting on the dark subspace of the system.

arXiv:1906.12058Physical Review AOct 16, 201912 citations

Nonadiabatic Holonomic Single-Qubit Gates in Non-Hermitian Systems

Wei Li, Yue Zhang, Yu Kun Chen +1 more

Holonomic quantum computation offers a promising route to robust quantum gates, but decoherence remains a central obstacle in realistic implementations. Here we develop a nonadiabatic holonomic scheme for a driven three-level system in the no-jump regime described by an effective non-Hermitian Hamiltonian. Within a biorthogonal framework, tailored complex pulses enforce exact closure of the computational-subspace evolution at the final time despite the underlying nonunitary dynamics, enabling arbitrary single-qubit holonomic gates without requiring cyclic evolution in its orthogonal complement. In contrast to existing non-Hermitian treatments, which either neglect the overall exponential prefactor or, in adiabatic settings, include dissipation only on the auxiliary excited level, our scheme incorporates decay and dephasing of all bare eigenstates directly into the pulse design, so that dissipation does not reduce the no-jump gate fidelity.Holonomic quantum computation offers a promising route to robust quantum gates, but decoherence remains a central obstacle in realistic implementations. Here we develop a nonadiabatic holonomic scheme for a driven three-level system in the no-jump regime described by an effective non-Hermitian Hamiltonian. Within a biorthogonal framework, tailored complex pulses enforce exact closure of the computational-subspace evolution at the final time despite the underlying nonunitary dynamics, enabling arbitrary single-qubit holonomic gates without requiring cyclic evolution in its orthogonal complement. In contrast to existing non-Hermitian treatments, which either neglect the overall exponential prefactor or, in adiabatic settings, include dissipation only on the auxiliary excited level, our scheme incorporates decay and dephasing of all bare eigenstates directly into the pulse design, so that dissipation does not reduce the no-jump gate fidelity.

quant-pharXiv:2606.26798Jun 26, 20260 citations

Three-qubit Phase Gate in a Five-level Tripod Atomic System

李蓬勃, 古英, Kai Wang +2 more

量子光学学报Jan 1, 20060 citations

Entangling power of holonomic gates in atom-based systems

Vahid Azimi Mousolou, Erik Sjöqvist

Abstract Entanglement is one of the main resources of quantum computation, and entangling power of a quantum system is a crucial element in the universality and efficiency of a proposed architecture for realization of quantum processing. Our goal here is to study the entangling power of holonomic gates in some particular systems. We explore the holonomy-induced entanglement, by means of nonadiabatic quantum holonomies, through different types of interactions in atom-based systems, namely, the tripod-type interaction induced by the quantum Zeno effect between three-level atoms, as well as the Λ-type interaction arising from dipole–dipole or van der Waals forces between high-lying states of two-level atoms in systems consisting of N optically trapped identical atoms. Our analysis shows that although the two schemes provide completely separate classes of entangling gates, both schemes permit for full entangling power and also in the sense of quantum efficiency both families of entanglers consist of holonomic gates that have the same efficiency in quantum algorithms. Besides, we observe that holonomy-induced entanglement characteristics remarkably depend on the interaction configuration of the system.Abstract Entanglement is one of the main resources of quantum computation, and entangling power of a quantum system is a crucial element in the universality and efficiency of a proposed architecture for realization of quantum processing. Our goal here is to study the entangling power of holonomic gates in some particular systems. We explore the holonomy-induced entanglement, by means of nonadiabatic quantum holonomies, through different types of interactions in atom-based systems, namely, the tripod-type interaction induced by the quantum Zeno effect between three-level atoms, as well as the Λ-type interaction arising from dipole–dipole or van der Waals forces between high-lying states of two-level atoms in systems consisting of N optically trapped identical atoms. Our analysis shows that although the two schemes provide completely separate classes of entangling gates, both schemes permit for full entangling power and also in the sense of quantum efficiency both families of entanglers consist of holonomic gates that have the same efficiency in quantum algorithms. Besides, we observe that holonomy-induced entanglement characteristics remarkably depend on the interaction configuration of the system.

arXiv:1803.00308Journal of Physics A Mathematical and TheoreticalOct 11, 20183 citations

Realization of a holonomic quantum computer in a chain of three-level systems

Zeynep Nilhan Gürkan, Erik Sjöqvist

arXiv:1404.2102Physics Letters AOct 25, 201513 citations

U(2)

transformations acting on the dark subspace of the system.