*Efficient quantum algorithms for large-scale machine-learning models.*

**The science**: Researchers at the University of Chicago design end-to-end quantum machine-learning algorithms and show how incorporating quantum computing into the classical machine-learning process can potentially help make machine learning more sustainable and efficient.

**The impact**: Constructing a potential method for training sparse classical neural networks using a quantum computer.

**Summary**: Quantum machine learning (QML) is a promising application of quantum algorithms, but the advantages over classical methods are not fully known. Researchers extended earlier efficient quantum algorithms for dissipative differential equations and proved that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. For a sparse machine learning model with model size *n*, running *T* iterations, this research constructs a quantum algorithm that runs in

O(T× poly(logn, 1𝜖))𝑂(𝑇× poly(log𝑛, 1𝜖))

time with precision ϵ > 0. The scaling in *n* outperforms the scaling of the best known classical algorithms.This method has been tested on large ML models having 7-100 million parameters and suggests that a main application of quantum computers might be the training of classical neural networks.

**Contact**: Liang Jiang, liang.jiang@uchicago.edu

**Focus area**: Quantum computing and emulation

**Institutions**: Argonne National Laboratory, University of Chicago, University of California, Berkeley, MIT, Brandis, Free University, qBraid, SeQure

**Citation**: J. Liu, Minzhao Liu, J.-P. Liu, Z. Ye, Y. Wang, Y. Alexeev, J. Eisert, L. Jiang. “Towards provably efficient quantum algorithms for large-scale machine-learning models.” *Nature Communications* 15. doi.org/10.1038/s41467-023-43957-x

**Funding acknowledgment**: This research used the resources of the Argonne Leadership Computing Facility, which is a U.S. Department of Energy (DOE) Office of Science User Facility supported under Contract DE-AC02-06CH11357. J.L. is supported in part by International Business Machines (IBM) Quantum through the Chicago Quantum Exchange, and the Pritzker School of Molecular Engineering at the University of Chicago through AFOSR MURI (FA9550-21-1-0209). M.L. acknowledges support from DOE Q-NEXT. J.-P.L. acknowledges the support by the NSF (grant CCF-1813814, PHY-1818914), an NSF QISE-NET triplet award (DMR-1747426), an NSF QLCI program (OMA-2016245), a Simons Foundation award (No. 825053), and the Simons Quantum Postdoctoral Fellowship. Y.A. acknowledges support from DOE Q-NEXT and the DOE under contract DE-AC02-06CH11357 at Argonne National Laboratory. J.E. acknowledges funding of the ERC (DebuQC), the BMBF (Hybrid, MuniQC-Atoms), the BMWK (PlanQK, EniQma), the Munich Quantum Valley (K-8), the QuantERA (HQCC), the Quantum Flagship (Millenion, PasQuans2), the DFG (The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689), CRC 183), and the Einstein Research Foundation (Einstein Research Unit on Quantum Devices). L.J. acknowledges support from the ARO (W911NF-23-1-0077), ARO MURI (W911NF-21-1-0325), AFOSR MURI (FA9550-19-1-0399, FA9550-21-1-0209), AFRL (FA8649-21-P-0781), DoE Q-NEXT, NSF (OMA-1936118, ERC-1941583, OMA-2137642), NTT Research, and the Packard Foundation (2020-71479).