A real-time, scalable, fast and highly resource efficient decoder for a quantum computer

Abstract: To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to large qubit counts and cryogenic operation. Additionally, they must operate at speed, to avoid an exponential slowdown in the logical clock rate of the quantum computer. To overcome such challenges, we introduce the Collision Clustering decoder and implement it on FPGA and ASIC hardware. We simulate logical memory experiments using the leading quantum error correction scheme, the surface code, and demonstrate MHz decoding speed - matching the requirements of fast-operating modalities such as superconducting qubits - up to an 881 and 1057 qubits surface code with the FPGA and ASIC, respectively. The ASIC design occupies 0.06 mm$^2$ and consumes only 8 mW of power. Our decoder is both highly performant and resource efficient, unlocking a viable path to practically realising fault-tolerant quantum computers.