Quantum computers use quantum mechanics to compute much faster than traditional computers. Large quantum computers would cause trouble for Bitcoin, though it would not be the end of it.
The cryptography used to secure the Bitcoin network is SHA-256. Designed to be impenetrable for modern computers, but not against quantum computers.
How Would Quantum Computing Effect Bitcoin?
Bitcoin is built upon a blockchain, which serves to record everything that happens on it – in a public and transparent ledger.
The danger quantum computing has against Bitcoin is within the public key encryption system.
Modern computers would have to complete a computation of 2^128 to decrypt the private key associated with the private key – in turn allowing access to the said wallet. A large quantum computer would be able to decipher the private key from the public key with 128^3, a large amount of time but much less than modern computers. [1]https://en.bitcoin.it/wiki/Quantum_computing_and_Bitcoin
The larger the quantum computer the simpler these encryption methods become to solve.
The ledger that holds every transaction of bitcoin would also be at risk. If the ledger were to be attacked, then it could be altered to accommodate fraudulent transactions or as stated above steal coins from wallets.
Scientists from Sussex University published a paper, finding that quantum computing is expected to break the SHA-256 encryption method currently utilized by Bitcoin, within the next decade.[2]https://avs.scitation.org/doi/10.1116/5.0073075
Overcoming The Threat Of Quantum Computing To Bitcoin.
A new public-key algorithm can be added to Bitcoin as a soft fork. From the end-user perspective, this would appear as the creation of a new address type, and everyone would need to send their bitcoins to this new address type to achieve quantum security.[3]https://en.bitcoin.it/wiki/Quantum_computing_and_Bitcoin
Encryption methods would develop in unison with computational power. So despite quantum computing breaking down current encryption methods, it would open the door for quantum encryption. The larger the quantum computer, the more powerful the quantum encryption will be.
Accommodating cryptography to secure a network against quantum computing is a problem that is yet to affect anyone, but if it is left for too long it will affect everyone.
In turn, the developments in quantum computing could speed up progress towards securing Bitcoin for the long term, with this Bitcoin will survive quantum computing.
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