Training quantum neural networks using the quantum information bottleneck method

Çatlı, Ahmet Burak; Wiebe, Nathan

doi:10.1088/1751-8121/ad6daf

Title: Training quantum neural networks using the quantum information bottleneck method

Journal Article · 27 August 2024 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/ad6daf · OSTI ID:2438134

; Wiebe, Nathan

Abstract We provide in this paper a concrete method for training a quantum neural network to maximize the relevant information about a property that is transmitted through the network. This is significant because it gives an operationally well founded quantity to optimize when training autoencoders for problems where the inputs and outputs are fully quantum. We provide a rigorous algorithm for computing the value of the quantum information bottleneck quantity within error ε that requires $O (\log^{2} (1 / ϵ) + 1 / δ^{2})$ queries to a purification of the input density operator if its spectrum is supported on ${0} ⋃ [δ, 1 - δ]$ for δ > 0 and the kernels of the relevant density matrices are disjoint. We further provide algorithms for estimating the derivatives of the QIB function, showing that quantum neural networks can be trained efficiently using the QIB quantity given that the number of gradient steps required is polynomial.

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: NONE; SC0012704

OSTI ID:: 2438134

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 37 Vol. 57; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (30)

On variational expressions for quantum relative entropies Berta, Mario; Fawzi, Omar; Tomamichel, Marco Letters in Mathematical Physics, Vol. 107, Issue 12 https://doi.org/10.1007/s11005-017-0990-7	journal	September 2017
Quantum particle swarm optimization algorithm with the truncated mean stabilization strategy Zhou, Nan-Run; Xia, Shu-Hua; Ma, Yan Quantum Information Processing, Vol. 21, Issue 2 https://doi.org/10.1007/s11128-021-03380-x	journal	January 2022
QuTiP 2: A Python framework for the dynamics of open quantum systems Johansson, J. R.; Nation, P. D.; Nori, Franco Computer Physics Communications, Vol. 184, Issue 4 https://doi.org/10.1016/j.cpc.2012.11.019	journal	April 2013
Hybrid quantum–classical generative adversarial networks for image generation via learning discrete distribution Zhou, Nan-Run; Zhang, Tian-Feng; Xie, Xin-Wen Signal Processing: Image Communication, Vol. 110 https://doi.org/10.1016/j.image.2022.116891	journal	January 2023
Quantum convolutional neural network based on variational quantum circuits Gong, Li-Hua; Pei, Jun-Jie; Zhang, Tian-Feng Optics Communications, Vol. 550 https://doi.org/10.1016/j.optcom.2023.129993	journal	January 2024
Quantum SUSAN edge detection based on double chains quantum genetic algorithm Wu, Chenyi; Huang, Fei; Dai, Jingyi Physica A: Statistical Mechanics and its Applications, Vol. 605 https://doi.org/10.1016/j.physa.2022.128017	journal	November 2022
Quantum machine learning Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola Nature, Vol. 549, Issue 7671 https://doi.org/10.1038/nature23474	journal	September 2017
Quantum algorithms for topological and geometric analysis of data Lloyd, Seth; Garnerone, Silvano; Zanardi, Paolo Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10138	journal	January 2016
Barren plateaus in quantum neural network training landscapes McClean, Jarrod R.; Boixo, Sergio; Smelyanskiy, Vadim N. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07090-4	journal	November 2018
Training deep quantum neural networks Beer, Kerstin; Bondarenko, Dmytro; Farrelly, Terry Nature Communications, Vol. 11, Issue 1 https://doi.org/10.1038/s41467-020-14454-2	journal	February 2020
Noise-induced barren plateaus in variational quantum algorithms Wang, Samson; Fontana, Enrico; Cerezo, M. Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-27045-6	journal	November 2021
A framework for demonstrating practical quantum advantage: comparing quantum against classical generative models Hibat-Allah, Mohamed; Mauri, Marta; Carrasquilla, Juan Communications Physics, Vol. 7, Issue 1 https://doi.org/10.1038/s42005-024-01552-6	journal	February 2024
On quantum Rényi entropies: A new generalization and some properties Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg Journal of Mathematical Physics, Vol. 54, Issue 12 https://doi.org/10.1063/1.4838856	journal	December 2013
Elucidating reaction mechanisms on quantum computers Reiher, Markus; Wiebe, Nathan; Svore, Krysta M. Proceedings of the National Academy of Sciences, Vol. 114, Issue 29 https://doi.org/10.1073/pnas.1619152114	journal	July 2017
Quantum autoencoders for efficient compression of quantum data Romero, Jonathan; Olson, Jonathan P.; Aspuru-Guzik, Alan Quantum Science and Technology, Vol. 2, Issue 4 https://doi.org/10.1088/2058-9565/aa8072	journal	August 2017
Quantum variational autoencoder Khoshaman, Amir; Vinci, Walter; Denis, Brandon Quantum Science and Technology, Vol. 4, Issue 1 https://doi.org/10.1088/2058-9565/aada1f	journal	September 2018
Entanglement-Induced Barren Plateaus Ortiz Marrero, Carlos; Kieferová, Mária; Wiebe, Nathan PRX Quantum, Vol. 2, Issue 4 https://doi.org/10.1103/PRXQuantum.2.040316	journal	October 2021
Circuit-centric quantum classifiers Schuld, Maria; Bocharov, Alex; Svore, Krysta M. Physical Review A, Vol. 101, Issue 3 https://doi.org/10.1103/PhysRevA.101.032308	journal	March 2020
Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference Leifer, M. S.; Spekkens, Robert W. Physical Review A, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevA.88.052130	journal	November 2013
Tomography and generative training with quantum Boltzmann machines Kieferová, Mária; Wiebe, Nathan Physical Review A, Vol. 96, Issue 6 https://doi.org/10.1103/PhysRevA.96.062327	journal	December 2017
Quantum Algorithm for Linear Systems of Equations Harrow, Aram W.; Hassidim, Avinatan; Lloyd, Seth Physical Review Letters, Vol. 103, Issue 15 https://doi.org/10.1103/PhysRevLett.103.150502	journal	October 2009
Quantum Boltzmann Machine Amin, Mohammad H.; Andriyash, Evgeny; Rolfe, Jason Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021050	journal	May 2018
Using mutual information for selecting features in supervised neural net learning Battiti, R. IEEE Transactions on Neural Networks, Vol. 5, Issue 4 https://doi.org/10.1109/72.298224	journal	July 1994
Convexity and Operational Interpretation of the Quantum Information Bottleneck Function Datta, Nilanjana; Hirche, Christoph; Winter, Andreas 2019 IEEE International Symposium on Information Theory (ISIT) https://doi.org/10.1109/ISIT.2019.8849518	conference	July 2019
The MNIST Database of Handwritten Digit Images for Machine Learning Research [Best of the Web] Deng, Li IEEE Signal Processing Magazine, Vol. 29, Issue 6, p. 141-142 https://doi.org/10.1109/MSP.2012.2211477	journal	October 2012
Rényi Divergence and Kullback-Leibler Divergence van Erven, Tim; Harremoes, Peter IEEE Transactions on Information Theory, Vol. 60, Issue 7 https://doi.org/10.1109/TIT.2014.2320500	journal	July 2014
Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision Childs, Andrew M.; Kothari, Robin; Somma, Rolando D. SIAM Journal on Computing, Vol. 46, Issue 6 https://doi.org/10.1137/16M1087072	journal	January 2017
Hamiltonian Simulation by Qubitization Low, Guang Hao; Chuang, Isaac L. Quantum, Vol. 3 https://doi.org/10.22331/q-2019-07-12-163	journal	July 2019
Quantum SDP-Solvers: Better upper and lower bounds van Apeldoorn, Joran; Gilyén, András; Gribling, Sander Quantum, Vol. 4 https://doi.org/10.22331/q-2020-02-14-230	journal	February 2020
Computable Rényi mutual information: Area laws and correlations Scalet, Samuel O.; Alhambra, Álvaro M.; Styliaris, Georgios Quantum, Vol. 5 https://doi.org/10.22331/q-2021-09-14-541	journal	September 2021