Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, non-adiabatic holonomic quantum computation in decoherence-free subspaces, which avoids long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize non-adiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.
@article{arxiv.1210.6782,
title = {Non-Adiabatic Holonomic Quantum Computation in Decoherence-Free Subspaces},
author = {G. F. Xu and J. Zhang and D. M. Tong and Erik Sjoqvist and L. C. Kwek},
journal= {arXiv preprint arXiv:1210.6782},
year = {2015}
}