A Cryogenic Memristive Neural Decoder for Fault-tolerant Quantum Error Correction

TL;DR

This paper presents a cryogenic memristive neural decoder for quantum error correction, leveraging in-memory computation to enable scalable, fast, and low-power fault-tolerant quantum decoding with mitigated device non-idealities.

Contribution

It introduces a novel cryogenic IMC-based neural decoder architecture using resistive memory devices and develops hardware-aware training methods to improve decoding fidelity.

Findings

Simulations show memristive device non-idealities impact decoding fidelity.

Hardware-aware re-training restores pseudo-threshold performance.

Proposes a pathway for scalable cryogenic quantum error correction hardware.

Abstract

Neural decoders for quantum error correction (QEC) rely on neural networks to classify syndromes extracted from error correction codes and find appropriate recovery operators to protect logical information against errors. Its ability to adapt to hardware noise and long-term drifts make neural decoders a promising candidate for inclusion in a fault-tolerant quantum architecture. However, given their limited scalability, it is prudent that small-scale (local) neural decoders are treated as first stages of multi-stage decoding schemes for fault-tolerant quantum computers with millions of qubits. In this case, minimizing the decoding time to match the stabilization measurements frequency and a tight co-integration with the QPUs is highly desired. Cryogenic realizations of neural decoders can not only improve the performance of higher stage decoders, but they can minimize communication delays, and alleviate wiring bottlenecks. In this work, we design and analyze a neural decoder based on an in-memory computation (IMC) architecture, where crossbar arrays of resistive memory devices are employed to both store the synaptic weights of the neural decoder and perform analog matrix-vector multiplications. In simulations supported by experimental measurements, we investigate the impact of TiOx-based memristive devices' non-idealities on decoding fidelity. We develop hardware-aware re-training methods to mitigate the fidelity loss, restoring the ideal decoder's pseudo-threshold for the distance-3 surface code. This work provides a pathway to scalable, fast, and low-power cryogenic IMC hardware for integrated fault-tolerant QEC.