Humans are just a collection of protons, neutrons, and electrons. Our brains are operated on a definite algorithm. We think, but since there is no randomness to our thought

What makes you think that? Electrons exhibit random behavior. How can you be sure that neurons don't?

I would think that it's far more plausable that they do:

Neurons communicate with each other by releasing neurotransmitter chemicals to diffuse across the synaptic gap to the next neuron's receptor (ie by random brownian motion), so there is bound to be a certain level of noise in the system.

The next neuron will fire if it detects a certain level of neurotransmitter present (in the simplest case). Given the noise in the system, the time of arrival of the neurotransmiter molecules, and thus the timing of the firing (or in borderline cases, the decision to fire or not), will be affected by the noise.