Nonadiabatic holonomic quantum computation is a development of the adiabatic geometric quantum computation [Jones et al, Nature 403, 2000], adiabatic holonomic quantum computation [Zanardi et al, PLA264, 1999; Duan et al, Science 292,2001], and nonadiabatic geometric quantum computation [Wang et al, PRL 87,2001; Zhu et al, PRL89,2002]. It shares all the holonomic nature of its adiabatic counterparts and at the same time avoids the long run-time requirement. Due to the merits of both its robustness against control errors and its rapidity without the speed limit of the adiabatic evolution, nonadiabatic holonomic quantum computation has attracted increasing attentions. Since its original proposal, many schemes of its implementation have been put forward based on various physical systems. Various schemes have been experimentally demonstrated with nuclear magnetic resonance, superconducting circuits, and nitrogen-vacancy centers in diamond. In this talk, I would briefly review the development of nonadiabatic holonomic quantum computation and then introduce some of our theoretical studies and physical implementations.
1. E Sjoqvist，D M Tong, L M Andersson, B Hessmo, M Johansson, K Singh
Non-adiabatic holonomic quantum computation
New J phys., 14, 103035, 2012.
2. G F Xu, J Zhang, D M Tong, E Sjoqvist, L C Kwek,
Nonadiabatic holonomic quantum computation in decoherence-free subspaces
Phys. Rev. Lett, 109, 170501, 2012.
3. G F Xu, C L Liu, P Z Zhao, D M Tong
Nonadiabatic holonomic gates realized by a single-shot implementation
Phys. Rev. A 92, 052302, 2015.
4. P Z Zhao, G F Xu, D M Tong
Nonadiabatic holonomic multiqubit controlled gates
Phys. Rev. A 99, 052309, 2019.
5. P Z Zhao, K Z Li, G F Xu, D M Tong
General approach for constructing Hamiltonians for nonadiabatic holonomic quantum computation
Phys. Rev. A 101, 062306, 2020.