Fidelity of adiabatic holonomic quantum gates

Vahid Azimi Mousolou, C. M. Canali, Erik Sjöqvist

Kazuyasu Matsuda, Kodai Nagata, Shiro Tamiya +3 more

Guo Jiang Yang

Daniel Töyrä

Geometric and holonomic quantum gates perform transformations that only dependon the geometry of a loop covered by the parameters controlling the gate. Thesegates require adiabatic time evolution, which is achieved in the limit when the looptakes infinite time to complete. However, it is of interest to also know thetransformation properties of the gates for finite run times. It has been shown [Phys.Rev. A 73, 022327 (2006)] that some holonomic gates for a trapped ion system showrevival structures, i.e., for some finite run time the gate performs the sametransformation as it does in the adiabatic limit. The purpose of this thesis is to investigate if similar revival structures are shown alsofor geometric and holonomic quantum gates for spin systems. To study geometricquantum gates an NMR setup for spin-1/2 particles is used, while an NQR setup forspin-3/2 particles is used to study holonomic quantum gates. Furthermore, for thegeometric quantum gates the impact of some open system effects are examined byusing the quantum jump approach. The non-adiabatic time evolution operators of thesystems are calculated and compared to the corresponding adiabatic time evolutionoperators by computing their operator fidelity. The operator fidelity ranges between0 and 1, where 1 means that the gates are identical up to an unimportant phasefactor. All gates show an oscillating dependency on the run time, and some Abeliangates even show true revivals, i.e., the operator fidelity reaches 1.

Alexander Shalyt-Margolin, В. И. Стражев, A. Ya. Tregubovich

Yingcheng Li, Tao Xin, Chu-Dan Qiu +5 more

Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here, we report a systematic, scalable approach based on dynamical invariants to realize HQGs without using additional Hilbert spaces. While presenting the theoretical framework of our approach, we design and experimentally evaluate single-qubit and two-qubits HQGs for the nuclear magnetic resonance system. The single-qubit gates acquire average fidelity 0.9972 by randomized benchmarking, and the controlled-NOT gate acquires fidelity 0.9782 by quantum process tomography. Our approach is also platform-independent, and thus may open a way to large-scale holonomic quantum computation.