Zinc

Zinc has the ability to kill H. pylori, specifically liquid zinc in the form of zinc sulphate.  This is a great place to start.  A company called BodyBio makes a liquid zinc that I like a lot.  I’ve seen people use 15 drops twice a day with pretty good success.  Zinc is also believed to be one of the minerals needed to produce your own HCL, so that can be a nice bonus.  If you’re using HCL supplementation, including zinc in your protocol may be a good idea because doing so will give your body an additional tool it can use to make its own HCL.  Empirical Labs makes a digestive enzyme called HCL-Zyme that includes a little bit of zinc.  This is a great formula to use when you’re trying to increase HCL production.
http://growyouthful.com/remedy/zinc-sulphate.php
Along with zinc, it is also popular to use an amino acid, L-Carnosine, for this issue.  You can even find “zinc carnosine” manufactured by many companies.  I still like to use the liquid zinc even if I’m going to use zinc carnosine.  If I use plain L-Carnosine capsules with the liquid zinc, one L-Carnosine, capsule twice a day seems to be effective.

HCL

Since H. pylori are happier in an alkaline environment, increasing stomach acid is always an important step.  Not only can H. pylori scarf up all your hydrogen so the body can’t make much HCL, they also pee ammonia.  Ammonia is an alkaline substance and can alkalize the stomach even further, totally pimping out their pad to optimize life for H. pylori.
http://kickitinthenuts.com/h-pylori-and-natural-protocols/