If I buy an AT&T iPhone 5s, can I unlock it to verizon?

I want the iPhone 5s. I was wondering if I could just buy an at&t or t-mobile iPhone 5s and unlock it to verizon.

I know that LTE uses a sim card so when you use verizon on LTE, you are using the GSM bandwidth and you have to use a sim card.

So would I be able to place a verizon sim card into a at&t or t-mobile iPhone 5s?

No you can't.

T-Mobile and AT&T are interchangeable with each other. At least they used to be. Verizon is not. They are on different systems. You can't use a Verizon or Sprint phone on any network but the one it's based on. Not without expensive reprogramming of the phone.

Technically, they don't even need a SIM. Verizon just uses it for their LTE.