Can anyone expound further on the practical applications of quantum computing? In my limited understanding, I think the following are definitely candidates (presented in no particular order), but I'm sure there are others:<p>1. Shor's algorithm could expose all encryption algorithms that are based on integer factorization.<p>2. Quantum simulation could open new avenues of research into how our universe operates at the quantum level. This could lead to advancements in materials science, for example.<p>3. Quantum computing could open new avenues of research into the P versus NP problem.<p>4. Quantum computing could open the door to the possibility of instantaneous communication via an understanding of action at a distance / quantum entanglement.<p><i>Edit: Thanks for all of the great responses, clarifications and links to further reading.</i>