Item-Item similarity based on text
There are methods that approximate Jaccard similarity using hash functions, one of them MinHash. They scale well with the number of dimensions and  evaluate similarity of two items. If you want to do nearest neighbor queries (finding similar items given one item) you should look at locality sensitive hashing (LSH), which essentially maps similar items to the same hash value. There is a nice implementation in scikit-learn called LSHForest. It approximates cosine distance and scales well to large number of items and dimensions.