Michael Beverland (IBM), QISE Seminar: Real-time decoding for fault-tolerant quantum computers

Abstract: 
Fault-tolerant quantum computers involve running circuits on quantum hardware that sometimes undergo faults in such a way that the faults can be identified and fixed to ensure the quantum computation runs reliably. To do this, information is protected in a quantum error correcting code, and carefully-designed logical operations are carried out on the protected information, with information about the noise that arises during the entire process being generated in a continuous stream of classical output called the syndrome. Decoding is the task of taking the syndrome data and using it to identify what faults occurred so that they can be fixed. This decoding task is run on a classical computer, and is needed to make the quantum computer work – but it is a very challenging unsolved problem to design a decoding algorithm that performs well enough in practice.

Real-time decoding for fault tolerance is a central challenge as we move beyond NISQ. The decoding timescale is set by the QEC cycle time of the hardware, which is microseconds for superconducting platforms. Meeting this constraint likely requires specialized classical hardware such as FPGAs or ASICs, whose high degree of parallelism changes the relative performance of decoding algorithms, for example allowing Gaussian elimination to run in linear parallel time on FPGAs rather than cubic time on CPUs, and therefore motivates hardware-aware redesign rather than direct porting of CPU-based methods.

In this talk, I discuss recent progress toward real-time decoding under these constraints, and argue that message-passing decoders, particularly the Relay-BP algorithm, offer a promising route to real-time decoding. Relay-BP improves on the convergence of standard belief propagation while retaining a lightweight, highly parallel structure suitable for FPGA implementation, and significantly outperforms alternative decoders for quantum LDPC codes.

Beyond average decoding speed, I address the backlog problem that arises from variable decoding latency. I present conditions on decoder latency distributions under which fast average-case decoding and sufficiently light latency tails allow decoding to keep pace with syndrome generation, ensuring bounded computational slowdown in large-scale fault-tolerant computations.