If you were using Solr's default or Lucene query parser, you can pretty much always put it into a query string query:
POST test/_search
{
"query": {
"query_string": {
"query": "(( name:(+foo +bar) OR info:(+foo +bar) )) AND state:(1) AND (has_image:(0) OR has_image:(1)^100)"
}
}
}
That said, you may want to use a boolean query, like the one you already posted, or even a combination of the two.