Abstract
We present a strategy for a single quantum miner with relatively low hashing power, with the same ramifications as a 51% attack. Bitcoin nodes consider the chain with the highest cumulative proof-of-work to be the valid chain. A quantum miner can manipulate the block timestamps to multiply the difficulty by c. The fork-choice rule counts every block with increased difficulty with weight c. By using Grover's algorithm, it is only O(√c) harder for the quantum miner to mine such blocks. By picking a high enough c, the single quantum miner can create a competing chain with fewer blocks, but more cumulative proof-of-work. The time required is O(1/r²) epochs, where r is the fraction of the block rewards that the quantum miner would have received if they mined honestly. Most proof-of-work cryptocurrencies, including Bitcoin, are vulnerable to our attack. However, it will likely be impossible to execute in forthcoming years, as it requires an extremely fast and fault-tolerant quantum computer.