  Blind quantum computation (BQC) allows a client (Alice), who only possesses
relatively poor quantum devices, to delegate universal quantum computation to a
server (Bob) in such a way that Bob cannot know Alice's inputs, algorithm, and
outputs. The quantum channel between Alice and Bob is noisy, and the loss over
the long-distance quantum communication should also be taken into account. Here
we propose to use decoherence-free subspace (DFS) to overcome the collective
noise in the quantum channel for BQC, which we call DFS-BQC. We propose three
variations of DFS-BQC protocols. One of them, a coherent-light-assisted DFS-BQC
protocol, allows Alice to faithfully send the signal photons with a probability
proportional to a transmission rate of the quantum channel. In all cases, we
combine the ideas based on DFS and the Broadbent-Fitzsimons-Kashefi protocol,
which is one of the BQC protocols, without degrading unconditional security.
The proposed DFS-based schemes are generic and hence can be applied to other
BQC protocols where Alice sends quantum states to Bob.
