Fast non-Abelian geometric gates via transitionless quantum driving

• Main Authors: Zhang, J., Kyaw, Thi Ha, Tong, D. M., Sjöqvist, Erik, Kwek, Leong-Chuan
• Other Authors: Institute of Advanced Studies
• Format: Article
• Language: English
• Published: 2016
• Online Access: https://hdl.handle.net/10356/81699; http://hdl.handle.net/10220/39668
• Institution: Nanyang Technological University

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.