Astronomical. You could convert every computer into existence into hunting for used private keys, and run them for the lifetime of the universe, and you’d be unlikely to find even one used key.

What is the expected speed up if using quantum techniques?

Can quantum techniques allow one to more effectively search for a specific private key to a BTC account?

Quantum computers can be used to crack public keys for a bitcoin account yes, but an addresses public keys are only published when a transaction is made

Best practice for secure bitcoin accounts is to always send the entire balance when making a transaction, and have the "change" go back to a new address

Not anymore. With taproot the key used is published on the blockchain when the output is created.

That doesn't make sense.

I haven't published the public key to my bitcoin wallet. If someone sends to my address how do they publish the public key?

There are new output formats with taproot but they aren't mandatory and you can still send to addresses with no published public key

Well, theoretically, instantly. But that’s kind of like asking what if I had this potion that instantly cured every disease known to man and then some, what would happen. What sort of quantum computer are you talking about? How many qubits?

not exactly true

BTC addresses that have never sent BTC are not vulnerable to quantum computers as the public key is only sent when a transaction is made. The address you send to is a hash of the public key and irreversible even with quantum computers

This is no longer the case with Taproot, btw.

The more you know. Thankyou

I think it's square root of classical computing time, using Grover's algorithm.

How do the units work there? The dimensions would be time^(1/2)... That isn't a physical time.

It's it the number of operations which is the square root? (Presumably the different types of computer don't take the same amount of time per operation)

That’s reversing hashes. Finding the private key for a given public key would be basically instant if your quantum computer was large enough.