State of the Art in Fault-Tolerant Quantum Computing

Fault-tolerant quantum computing (FTQC) has the potential to reliably execute complex calculations by overcoming the problems raised from the errors and noise inherent in quantum systems. This paper builds upon a 2025 report issued by the National Academy of Technologies of France. After recalling the principles that underly the so-called "quantum advantage," the use of error-correcting codes in the design of fault-tolerant quantum computers is discussed. Also explored are the five most advanced physical technologies that can be used to build such computers and the challenges of scaling up to a sufficient size to run useful applications. After highlighting the limits of monolithic qubit integration, the focus turns to increasing the number of available physical qubits by interconnecting several quantum processing modules. The paper concludes with a discussion of technical and economic environments, their performance benchmarks, and their future coexistence with other computing technologies and with supercomputers.