Towards Provably Efficient Quantum Algorithms for Large-Scale Machine-Learning Models - Research Article Summary

Aug 3, 2026

Large-scale machine learning models require substantial computation, energy, and time during both pre-training and fine-tuning, creating pressure to improve efficiency and reduce environmental impact. The work shows that fault-tolerant quantum computing can achieve provably efficient resolutions for generic (stochastic) gradient descent under conditions such as sufficient dissipation, sparsity, and small learning rates. Using related algorithms for dissipative differential equations, the authors prove scaling with model size and training iterations, and benchmark sparse-training regimes to motivate a practical sparse download and re-upload scheme.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages6

Reading Time15 min

AccessFree to download

Introduction

Quantum speedups for (stochastic) gradient descent

Conditions for provable efficiency

Relationship to quantum algorithms for dissipative dynamics

Benchmarking on large model instances

Sparse training and early-stage enhancement

Proposed sparse parameter download and re-upload scheme

Outlook for state-of-the-art large-scale machine learning

Article [https://doi.org/10.1038/s41467-023-43957-x](https://doi.org/10.1038/s41467-023-43957-x) Towards provably efﬁcient quantum algorithms for large-scale machinelearning models Received: 25 April 2023 | Accepted: 24 November 2023 | | --- | | | | Check for updates | Junyu Liu 1,2,3,4,5,6, Minzhao Liu 7,8, Jin-Peng Liu 9,10,11, Ziyu Ye2, Yunfei Wang12, Yuri Alexeev2,3,8, Jens Eisert 13 & Liang Jiang 1,3 Large machine learning models are revolutionary technologies of artiﬁcial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and ﬁne-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efﬁcient resolutions for generic (stochastic) gradient descent algorithms, scaling as OðT2 × polylogðnÞÞ, where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufﬁciently dissipative and sparse, with small learning rates. Based on earlier efﬁcient quantum algorithms for dissipative differential equations, we ﬁnd and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We ﬁnd that, in the context of sparse training, a quantum enhancement is possible atthe early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems. It is widely believed that large-scale machine learning might be one of the most revolutionary technologies beneﬁting society1, including already important breakthroughs in digital arts2, conversation like GPT-33,4, and mathematical problem solving5. However, training such models with considerable parameters is costly and has high carbon emissions. For instance, twelve million dollars and over ﬁve-hundred tons of CO2 equivalent emissions have been produced to train GPT-36. Thus, on the one hand, it is important to make large-scale machinelearning models (like large language models, LLM) sustainable andefﬁcient. On the other hand, machine learning might possibly be one of the ﬂag applications of quantum technology. Running machine learning algorithms on quantum devices, implementing readings of so-called quantum machine learning, is widely seen as a potentially very fruitful application of quantum algorithms7. Speciﬁcally, many quantum approaches are proposed to enhance the capability of classical machine learning and hopefully ﬁnd some useful applications, like8,9. Despite rapid development and signiﬁcant progress, current quantum machine learning algorithms feature substantial limitations both in theory and practice. First, practical applications of quantum machine 1Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA. 2Department of Computer Science, The University of Chicago, Chicago, IL60637, USA. 3Chicago Quantum Exchange, Chicago, IL60637, USA. 4Kadanoff Center for Theoretical Physics, The University of Chicago, Chicago, IL 60637, USA. 5qBraid Co., Chicago, IL 60615, USA. 6SeQure, Chicago, IL 60615, USA. 7Department of Physics, The University of Chicago, Chicago, IL 60637, USA. 8Computational Science Division, Argonne National Laboratory, Lemont, IL 60439, USA. 9Simons Institute for the Theory of Computing, University of California, Berkeley, CA 94720, USA. 10Department of Mathematics, University of California, Berkeley, CA 94720, USA. 11Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. 12Martin A. Fisher School of Physics, Brandeis University, Waltham, MA 02453, USA. 13Dahlem Center for Complex Quantum Systems, Free University Berlin, Berlin 14195, Germany. [e-mail: jense@zedat.fu-

FAQs

What computational bottlenecks motivate this research on large-scale machine learning models?

The paper highlights high computational expenses, energy, and time costs in both pre-training and fine-tuning, along with substantial carbon emissions.

What quantum setting and assumptions are used to obtain provably efficient performance?

It relies on fault-tolerant quantum computing and requires models to be sufficiently dissipative and sparse, together with small learning rates.

How does the proposed approach relate to earlier efficient quantum algorithms?

The work builds on quantum algorithms for dissipative differential equations and adapts similar methods to (stochastic) gradient descent, the core learning algorithm in machine learning.

Aug 3, 2026

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