Qtum is taking Bitcoin Core 0.13, integrating the Ethereum Virtual Machine, and adding an “Account Abstraction Layer” so that existing Etheruem contracts will work on Qtum with minimal changes. The exact way we are integrating the EVM is by adding new Bitcoin Script opcodes, and adding special processing conditions so that when these EVM using transactions are added to the blockchain, they are executed immediately (rather than only when attempting to be spent, as is normal).
http://news.8btc.com/how-qtum-makes-ethereum-contracts-run-on-the-utxo-model