  Cross-lingual open domain question answering (CLQA) is a complex problem,
comprising cross-lingual retrieval from a multilingual knowledge base, followed
by answer generation in the query language. Both steps are usually tackled by
separate models, requiring substantial annotated datasets, and typically
auxiliary resources, like machine translation systems to bridge between
languages. In this paper, we show that CLQA can be addressed using a single
encoder-decoder model. To effectively train this model, we propose a
self-supervised method based on exploiting the cross-lingual link structure
within Wikipedia. We demonstrate how linked Wikipedia pages can be used to
synthesise supervisory signals for cross-lingual retrieval, through a form of
cloze query, and generate more natural questions to supervise answer
generation. Together, we show our approach, \texttt{CLASS}, outperforms
comparable methods on both supervised and zero-shot language adaptation
settings, including those using machine translation.
