Fault-Tolerant Quantum Computing

Fault-tolerant quantum computing uses quantum error correction codes to protect logical qubits from the noise and decoherence that plague current hardware. By encoding information redundantly across multiple physical qubits and continuously correcting errors, fault-tolerant systems can in principle run arbitrarily long computations. This is the threshold required for practically useful quantum algorithms like Shor's factoring algorithm or quantum chemistry simulations. Current estimates suggest fault-tolerant systems will require thousands to millions of physical qubits per logical qubit, depending on the error correction scheme.