Magic state distillation is the process of consuming many low-fidelity magic states to produce fewer high-fidelity magic states suitable for fault-tolerant T gate implementation. The standard distillation protocol takes 15 noisy T states and produces 1 T state with quadratically reduced error — if the input error rate is p, the output error rate is approximately 35p³. Multiple rounds of distillation can achieve arbitrarily low error rates, with each round further suppressing the error at the cost of consuming more raw magic states.
Magic state distillation dominates the resource budget of fault-tolerant quantum computing. Estimates for running Shor's algorithm to factor 2,048-bit RSA numbers suggest that 70-90% of the physical qubits in the processor would be dedicated to magic state distillation factories, with the remaining 10-30% performing the actual logical computation. A single T gate might require a distillation factory occupying thousands of physical qubits and running for multiple QEC code cycles.
Reducing the cost of magic state distillation is one of the most active research areas in quantum computing theory. Approaches include improved distillation protocols with better yield ratios, more efficient codes that reduce the overhead per distillation round, direct injection techniques that bypass distillation entirely (at the cost of lower fidelity), and alternative qubit architectures (like cat qubits) where certain error types are inherently suppressed, reducing the need for distillation. Amazon's cat qubit approach, for example, claims potential 90% reduction in distillation overhead by exploiting the inherent bias of cat qubit errors.