title: Fast non-Abelian geometric gates via transitionless quantum driving.
abstract: A practical quantum computer must be capable of performing high fidelity quantum gates on a set of quantum bits (qubits). In the presence of noise, the realization of such gates poses daunting challenges. Geometric phases, which possess intrinsic noise-tolerant features, hold the promise for performing robust quantum computation. In particular, quantum holonomies, i.e., non-Abelian geometric phases, naturally lead to universal quantum computation due to their non-commutativity. Although quantum gates based on adiabatic holonomies have already been proposed, the slow evolution eventually compromises qubit coherence and computational power. Here, we propose a general approach to speed up an implementation of adiabatic holonomic gates by using transitionless driving techniques and show how such a universal set of fast geometric quantum gates in a superconducting circuit architecture can be obtained in an all-geometric approach. Compared with standard non-adiabatic holonomic quantum computation, the holonomies obtained in our approach tends asymptotically to those of the adiabatic approach in the long run-time limit and thus might open up a new horizon for realizing a practical quantum computer.
authors.affiliation: Department of Physics, Shandong University, Jinan 250100, China.|Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
authors.forename: J
authors.initials: J
authors.lastname: Zhang
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
authors.forename: Thi Ha
authors.initials: TH
authors.lastname: Kyaw
authors.affiliation: Department of Physics, Shandong University, Jinan 250100, China.
authors.forename: D M
authors.initials: DM
authors.lastname: Tong
authors.affiliation: Department of Quantum Chemistry, Uppsala University, Box 518, Se-751 20 Uppsala, Sweden.|Department of Physics and Astronomy, Uppsala University, Box 516, Se-751 20 Uppsala, Sweden.
authors.forename: Erik
authors.initials: E
authors.lastname: Sjöqvist
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.|MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore.|Institute of Advanced Studies, Nanyang Technological University, 60 Nanyang View, Singapore 639673, Singapore.|National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore.
authors.forename: Leong-Chuan
authors.initials: LC
authors.lastname: Kwek