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

arXiv: https://arxiv.org/abs/2307.09463 · HTML: https://mlsanity.com/paper/2307.09463/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 110 references that are in the map.
- First posted on arXiv 18 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Noisy Activation Functions](https://mlsanity.com/paper/1603.00391/) (2016)
- [A flexible and fast PyTorch toolkit for simulating training and inference on analog crossbar arrays](https://mlsanity.com/paper/2104.02184/) (2021)
- [Deep neural decoders for near term fault-tolerant experiments](https://mlsanity.com/paper/1802.06441/) (2018)
- [Assessing requirements to scale to practical quantum advantage](https://mlsanity.com/paper/2211.07629/) (2022)
- [4K-Memristor Analog-Grade Passive Crossbar Circuit](https://mlsanity.com/paper/1906.12045/) (2019)
- [Training LSTM Networks with Resistive Cross-Point Devices](https://mlsanity.com/paper/1806.00166/) (2018)
- [NEO-QEC: Neural Network Enhanced Online Superconducting Decoder for Surface Codes](https://mlsanity.com/paper/2208.05758/) (2022)
- [Scalable Quantum Error Correction for Surface Codes using FPGA](https://mlsanity.com/paper/2301.08419/) (2023)
- [Memristor-based cryogenic programmable DC sources for scalable in-situ quantum-dot control](https://mlsanity.com/paper/2203.07107/) (2022)

## Built on by (most cited first, 1 of 1)

- [Robust quantum dots charge autotuning using neural network uncertainty](https://mlsanity.com/paper/2406.05175/) (2024)

## Abstract (arXiv)

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.