Modern laundry detergents tend not to produce mountains of bubbles, but there are other good reasons to not substitute laundry detergent for dishwashing detergent. One reason is that you likely void the warranty on the appliance if you use a product not made for dishwashers. You may be exposing yourself to toxins, too. The detergent itself may be the same from one product to the other, but laundry detergents may contain brighteners, fragrances, stain removers, and anti-soiling chemicals that you don't really need volatilized by the heat of your dishwasher so that you breathe them. The ingredients in laundry detergent might not rinse completely from your dishes.
If you are desperate for a way to wash your dishes, you can try cleaning them in the sink using other types of soap or detergent. You could try bar soap, liquid soap, or bath gel. Shampoo might leave a residue on your dishes. Laundry detergent might leave a residue, too, but at least you would have more control over rinsing in the sink compared with the dishwasher.
How Detergent Works | How Soap Cleans