# A Modified Depolarization Approach for Efficient Quantum Machine Learning

arXiv: https://arxiv.org/abs/2404.07330 · HTML: https://mlsanity.com/paper/2404.07330/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 40 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 14 of 14)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Quantum Adversarial Machine Learning](https://mlsanity.com/paper/2001.00030/) (2019)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Quantum machine learning of large datasets using randomized measurements](https://mlsanity.com/paper/2108.01039/) (2021)
- [Towards quantum enhanced adversarial robustness in machine learning](https://mlsanity.com/paper/2306.12688/) (2023)
- [Transfer of Adversarial Robustness Between Perturbation Types](https://mlsanity.com/paper/1905.01034/) (2019)
- [Certified Robustness of Quantum Classifiers against Adversarial Examples through Quantum Noise](https://mlsanity.com/paper/2211.00887/) (2022)

## Built on by (most cited first, 2 of 2)

- [Learning Robust Observable to Address Noise in Quantum Machine Learning](https://mlsanity.com/paper/2409.07632/) (2024)
- [Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise](https://mlsanity.com/paper/2412.11451/) (2024)

## Abstract (arXiv)

Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has shown promising applications in machine learning, optimization, and cryptography. Despite the progress, challenges persist due to system noise, errors, and decoherence that complicate the simulation of quantum systems. The depolarization channel is a standard tool for simulating a quantum system's noise. However, modeling such noise for practical applications is computationally expensive when we have limited hardware resources, as is the case in the NISQ era. We propose a modified representation for a single-qubit depolarization channel with two Kraus operators based only on X and Z Pauli matrices. Our approach reduces the computational complexity from six to four matrix multiplications per execution of a channel. Experiments on a Quantum Machine Learning (QML) model on the Iris dataset across various circuit depths and depolarization rates validate that our approach maintains the model's accuracy while improving efficiency. This simplified noise model enables more scalable simulations of quantum circuits under depolarization, advancing capabilities in the NISQ era.