QuickBooks Shopping Cart? (Syncing QuickBooks Data to eCommerce Website)

We have QuickBooks Enterprise 2013 Canadian Edition and we wish to sync our data to our website, and vice versa. When we store inventory in QuickBooks, we want that to be apparent on the website, when we sell on the website we want the data to sync with QuickBooks Enterprise 2013. Is anything like this doable? Our website is built from scratch so perhaps a shopping cart API from QuickBooks is available to work with?

Thanks,