The notion that quantum computers pose an imminent threat to the security of the bitcoin network has been a topic of increasing concern. However, recent academic research provides a more nuanced perspective, highlighting the significant constraints that limit the potential of quantum computers to compromise the bitcoin blockchain.
Two key areas of concern are the potential for quantum computers to derive a private key from a public key, thereby breaking wallet security, and the possibility of a quantum computer outperforming traditional miners, potentially allowing for a 51% attack. The first threat is based on Shor's algorithm, which could theoretically be used to derive a private key from a public key.
The second threat, based on Grover's algorithm, applies to mining and offers a theoretical speedup on the trial-and-error search miners perform. However, research indicates that the energy required to run Grover's algorithm against the bitcoin blockchain would be physically impossible, with estimates suggesting that a quantum mining fleet would need roughly 10^23 qubits drawing 10^25 watts, approaching the energy output of a star. Another paper highlights that many quantum factoring breakthroughs have been overstated, with some researchers using simplified problems or cheating by picking numbers whose hidden prime factors are easy to guess.
The authors of this paper were able to replicate every major quantum factoring breakthrough using a 1981 VIC-20 home computer, an abacus, and a dog, demonstrating that the underlying science has not advanced as much as claimed. While the quantum threat to bitcoin is real, it is primarily focused on wallet security rather than mining, with millions of bitcoin sitting in older or reused addresses where key information is already exposed on the blockchain. Developers are working on fixes, including ways to reduce key exposure and new types of signatures designed to withstand quantum attacks.