Quantum computing as an inevitable technology can revolutionize many aspects of our society. One potential impact is on cryptocurrency such as Bitcoin, which relies on proof-of-work mining to secure the underlying blockchain protocol. Miners empowered by quantum computers will have superior computational power to win the competition. The quantum advantage jeopardizes the security and trustworthy of cryptocurrency and the transaction validation process by taking over a majority of the network’s computing power, known as a \(51\%\) attack. Fraudulent Bitcoin transactions in the form of double spending can happen, and the emerging quantum miner could enable double spending and benefit from it. How much double spending is optimal without causing too much “inflation”? What shall be the optimal strategy of the first quantum miner facing the competition from other quantum miners? What are the implications of having one or multiple quantum miners to the security of the Bitcoin network? We conduct a novel game theoretic and economic analysis to address these questions. Simulation illustrates that quantum miners would have to collude to gain from double spending in a quantum competitive environment. The distribution of cryptocurrency between quantum miners and classical miners and how cost-effective classical miners are can affect the profitability and the sustainability of double spending as well as the collusion of quantum miners. Intensified quantum competition will decrease the chance of collusion and eventually make the Bitcoin network secure again. The critical point of quantum popularity that will eliminate double spending is found.