Strategies for Powerful Quantum-Enabled Bitcoin Miners

Bitcoin miners equipped with purpose-built quantum computers that execute Grover’s algorithm on classical candidate blocks, measuring the resulting quantum state to yield a potentially valid proof-of-work, pose a threat to Bitcoin’s security against 51% attacks. I aim to assess this threat by employing a game-theoretic framework inspired by the Lee-Ray-Santha quantum races model, extending it to better reflect how quantum miners would behave in practice. These extensions address some of the simplifications of prior works, where quantum miners performed only one quantum measurement (which does not maximise their resources), and were assumed to employ a peaceful strategy, wherein the quantum miners discard the resources already invested into searching upon receiving a broadcast of a newly-mined block (which is not enforceable). I consider a setting in which the quantum miners perform multiple quantum measurements between successive blocks, employ Sattath’s Aggressive Quantum Mining Strategy (AQMS), and must allocate limited quantum resources across these measurements. When employing Sattah’s AQMS, a quantum miner halts their execution of Grover’s algorithm and measures the resulting quantum state upon receiving a broadcast of a newly mined block, attempting to create a temporary fork and thereby decreasing the effective hash rate required for a 51% attack. In this novel setting, I derive the payoff matrices for the quantum miners and compute optimal quantum mining strategies that correspond to Nash equilibria. I simulate the deployment of these optimal quantum mining strategies within the Bitcoin network and estimate their effect on Bitcoin’s security against a 51% attack. I determine how two quantum miners should optimally allocate their quantum resources based on the network difficulty. Overall, I find that even when behaving optimally, two quantum miners cannot create enough temporary forks to render the Bitcoin network vulnerable to this quantum threat, given realistic constraints on their quantum resources. This thesis contributes to the growing body of research on the potential threats posed by scalable quantum computers, using the case of two quantum miners as a step toward understanding how quantum miners in general could affect Proof-of-Work-based cryptocurrencies like Bitcoin.