Curator's Take
This article demonstrates a way to implement truly geometric single‑qubit gates even when the underlying system is lossy, by engineering complex control pulses that close the evolution exactly in the computational subspace despite nonunitary dynamics. It builds on recent advances in nonadiabatic holonomic computation and extends them into the realistic “no‑jump” regime of open quantum systems, addressing a long‑standing gap where decoherence would otherwise erode gate fidelity. If experimental platforms such as superconducting qutrits or trapped‑ion three‑level schemes can deliver the required pulse precision, the approach could provide a hardware‑efficient path to error‑resilient gates without the overhead of full error correction, though it remains contingent on post‑selecting successful no‑jump trajectories.
— Mark Eatherly
Summary
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.