If you are in the US and a work at will employee, then you can quit without notice, just like they can fire you without notice. The professional thing to do is go in and let them know that this is your last day adn you're leaving. Explain that you have found something that is better suited to your needs.
Thank them for taking the time to train you, and wish them well. Be professional and pleasant. And recognize that they may be upset.
They might be disappointed, they might say something you find off-putting, and they might walk you out the door right then and there. Or, they might say thank you and good luck, and leave it at that. Either way, you need to do what is best for you.
Good luck in your new position.
It is always important to give a minimum of two weeks notice. Quitting, even in the training stage, before 2 weeks notice can cause tension, and bad feelings with the employer that is training you. It is important to realize, that training a new employee doesn't only cost money, but it also costs valuable time with allocating someone to train you.
You always want to give the impression that you are not "quick to be trained, and then to escape". You may think that it is great to jump ship from this current job to your new job, but without two weeks notice, it gives an impression to your new employer as well that you will just train at your new job, until something better comes along, and then you will jump ship again to that next job. You never know when you're going to need a reference from the company that you're currently training with in the future.
My suggestion, is talk with your new employer, and tell them that you need to give 2 weeks notice to your current employer, and they should understand. This way they will be able to find someone else for your current job to fill the space. I hope that that this helps, and it may not be what you wanted to hear, but you don't ever want to burn brdges that might be able to help you in the future.
Hope this helps you.
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