Your off by ~61,545 times. As, you don't want the energy to boil water, you want the energy you get from burning hydrogen.
1 liter of water is 11.19% hydrogen or ~0.1119kg. Hydrogen is 143 MJ/kg so 1 liter of water ~= 143,000,000J * 0.1119 = 16,001,700J.
So, you want a 1,661,715 megawatt laser. Good luck with that.
PS: You might be able to do laser assisted rocketry where you hit the combustion chamber with energy to increase exhaust velocity. But even that would take insane accuracy and a 100+ terawatt laser to be useful.
Ah, I didn't do the calculations myself, just did a couple random Google searches for how many joules it takes to boil off one liter of water (not how much it takes to bring a gallon to boiling point, which is of course much much less). Here's one site I used: https://www.physicsforums.com/threads/energy-required-to-boi..., but I didn't see the "k" in front of joules. Thanks.
Your still confusing a state change (boil) with a chemical change (burn). The reason this is important is how fast stuff comes out the bottom of your rocket is really important and pushing it faster takes more energy. To beat chemical rockets you need to use more energy to push harder.
1 liter of water is 11.19% hydrogen or ~0.1119kg. Hydrogen is 143 MJ/kg so 1 liter of water ~= 143,000,000J * 0.1119 = 16,001,700J.
So, you want a 1,661,715 megawatt laser. Good luck with that.
PS: You might be able to do laser assisted rocketry where you hit the combustion chamber with energy to increase exhaust velocity. But even that would take insane accuracy and a 100+ terawatt laser to be useful.