Holonomic Gates in Pseudo-Hermitian Quantum Systems

Abstract

The time-dependent pseudo-Hermitian formulation of quantum mechanics allows 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-$\mathrm{U}(2)$ transformations acting on the dark subspace of the system.

arXiv comment8 pages, 1 figure

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Cited by in corpus (5)

• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
• Robustness of entanglement in a non-Hermitian cavity-optomechanical system even away from exceptional points
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems