You can simulate any quantum computer on a Turing machine, though it generally takes exponentially more time than with a real QC. Whether this means they are the same thing or not is a matter of semantics.

But what is clear is that there is no computation that can be done on a QC that can't be done on a TM.

The role of non-determinism in computation is more debatable. There is even a notable MIT professor (who coined the term Actor model) who claims that real computers, like the Android phone I'm writing this on, are in fact not Turing machines, because of non-determinism / parallelism. He also claims that Godel's incompleteness theorem doesn't apply to actual mathematics, so I would take his words with a huge spoonful of salt.

they are they just dont work in binary bits they work with qbits which simply have behavior rules diffrent from digital but can be simulated by one just inefficiently. much like a binary computer can be approximated by a balanced trianay computer or analog computer or by pumps valves and flowing water like in MONIAC. they are all turring complete and can simulate each other just not efficiently. they dont have any magical logic gates they are just able to do a task that would need require lot of time or many parrelel computaions or both in less time because a single qbit is in super position of 1 and 0 simaltaniously and we can do mathmatical operations on it without collapsing the superposition until we have observed it. to simulate this on a traditional computer you would need to run it for each 2 time per bit.

so for a 8 bit key for example you would need to run the same operation 256 times 65536 for a 16 bit key and 4,294,967,296 for a 32 bit. so in essence quantum computation just lets you cheat on massively parallel processes but is not a hyper-turring machine or a turring oracle. in fact there are many algorithms that you get no gain from using qubit other than i higher energy bill

not sure why I am being down voted here perhaps someone needs to do some reading

https://en.wikipedia.org/wiki/Quantum_computing#Computabilit...

https://www.smbc-comics.com/comic/the-talk-3

They are not computably non-deterministic, so they are still Turing machines with a random number generator attached.

Qubits aren't magic either and the amount of data they can store is well known, it's just a complex bit instead of a real one.

> they are still Turing machines with a random number generator attached

It's important to note that probabilistic Turing machines are different from quantum Turing machines in terms of efficiency, as far as it is known today. But still, that doesn't change the fact that they can (inefficiently) simulate each other.