Could a quantum computer recover files from ransomware if the attacker doubly encrypted them with RSA-4096? How would a quantum computer decrypt a file (or find the keys to such a file) if it were encrypted with standard RSA 4096 encryption, but encrypted two times with different keys? The keys are known by only one party. They could be different lengths and complexities. 

And theoretically, how long would it take (with a general estimated Quantum PC's amount of power)?

Note: The incompetent fools at geek squad 'accidentally' ran a ransomware on my clients computer while trying to restore the files from a ransomware. Then, they did a faulty windows backup and charged him a thousand bucks. He won't take "it's just gone" for an answer, so I need numbers and proof that it's completely unrecoverable. Also, this is a very good question in regards to the future of computer encryption if you can't afford to switch to quantum right away...
Ask your friend:


Do you even have the RSA moduli used by the ransomware?


If not, even Shor's alogrithm on a real honest-to-goodness large quantum computer is not going to help.  And there's no reason for the ransomware to share the RSA moduli with you.
While RSA ciphertexts/signatures can be deanonymized by the German tank problem, there's not enough information to reconstruct enough of the modulus to apply Shor.

Do you have a billion euros rattling around in your pocket?


If not, you can't afford the research and construction for a quantum computer.

Do you have a couple decades to wait?


If not, you are too impatient and quantum computers won't be developed in time.

Do you feel lucky?


If not, you might have gambled your billion euros and decades of lifetime on a coin coming up heads when actually it's tails and quantum computers can't actually be made to work.



If the answer to any of these questions is ‘no’, your friend's data are hopelessly lost.  Advise that your friend invest in solid backups, and specifically in backups that cannot be deleted from the computer they are backing up—if you simply back up to an external USB drive, or simply back up to an S3 bucket with an access key that has authority to create and delete archives, then you are not protected.

Also advise your friend that Geek Squad is not their friend: the FBI cultivates informants at Geek Squad to actively search for material at the FBI's request on any computers they work on and forward their data to the FBI[1][2][3][4].



All that said, using RSA twice doesn't really matter: if you had the RSA moduli, then if made a Shor-capable quantum computer could factor the moduli in only twice the time, and the size of the quantum computer needed is linear in the number of bits in the modulus.