Optimizing Multi-level Magic State Factories for Fault-Tolerant Quantum Architectures

We propose a novel technique for optimizing a modular fault-tolerant quantum computing architecture, taking into account any desired space-time trade-offs between the number of physical qubits and the fault-tolerant execution time of a quantum algorithm. We consider a concept architecture comprising a dedicated zone as a multi-level magic state factory and a core processor for efficient logical operations, forming a supply chain network for production and consumption of magic states. Using a heuristic algorithm, we solve the multi-objective optimization problem of minimizing space and time subject to a user-defined error budget for the success of the computation, taking the performance of various fault-tolerant protocols into account. As an application, we show that physical quantum resource estimation reduces to a simple model involving a small number of key parameters, namely, the circuit volume, the error prefactors ($\mu$) and error suppression rates ($\Lambda$) of the fault-tolerant protocols, the reaction time ($\gamma$), and an allowed slowdown factor ($\beta$).