Qtum Wallet staking feature coming to mobile devices
Qtum team has confirmed on their twitter account that they are working to enable staking feature on mobile wallets. When enabled, it will allow you to earn stakes in form of Qtum coins by simply having Qtum in your mobile wallet.
Right now, it is not enabled. In the future, offline staking may provide this option.
Qtum Proof of Stake wallets require minimal computer/CPU resources and can run on simple computers like a Raspberry Pi. Staking wallets should be running 24/7 to validate blocks, but if they go offline they do not lose maturity of their coins or lose past block rewards.