A Scalable Real-Time Decoder for Quantum Error Correction Based on Hyperdimensional Computing

Abstract

Quantum computers require large-scale error correction codes to circumvent the limited fidelity of physical qubits. However, current error decoders are either not scalable to practical code sizes or cannot meet the strict real-time decoding requirements. This work presents a novel decoder for stabilizer error correction codes that exploits hyperdimensional computing to offer an efficient hardware implementation for large-scale codes, thus achieving low latency and high throughput. Next to a universal approach for generating the necessary hypervectors, an efficient method specific to surface codes is devised. In this very first implementation, the proposed decoder outclasses popular graph-based decoders for small surface codes with depolarizing noise and efficiently scales to large codes, thus representing both a suitable solution for near-term real-time error correction and a promising alternative for future large-scale codes.