Training quantum neural networks using the Quantum Information Bottleneck method

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 probl...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Catli, Ahmet Burak, Wiebe, Nathan
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Catli, Ahmet Burak
Wiebe, Nathan
description 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 $\epsilon$ that requires $O(\log^2(1/\epsilon) + 1/\delta^2)$ queries to a purification of the input density operator if its spectrum is supported on $\{0\}~\bigcup ~[\delta,1-\delta]$ for $\delta>0$ 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.
doi_str_mv 10.48550/arxiv.2212.02600
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2212_02600</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2212_02600</sourcerecordid><originalsourceid>FETCH-LOGICAL-a670-92b74e2e88fc2b2dc516bc55d97a40dedfa7c3d837152e64b6e25ba07176d30e3</originalsourceid><addsrcrecordid>eNotj8lOwzAURb1hgQofwAr_QIKH2E6XpWKoVAmQso-e7Zc2amKD4zD8PbR0dRb36kiHkBvOyqpWit1B-u4_SyG4KJnQjF2S1yZBH_qwox8zhDyPNOCcYPhD_orpMNF5Oq55j_Tt_NiELqYRch8DvY85DxjQHeiIeR_9FbnoYJjw-swFaR4fmvVzsX152qxX2wK0YcVSWFOhwLrunLDCO8W1dUr5pYGKefQdGCd9LQ1XAnVlNQplgRlutJcM5YLc_mtPSe176kdIP-0xrT2lyV8eeEri</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Training quantum neural networks using the Quantum Information Bottleneck method</title><source>arXiv.org</source><creator>Catli, Ahmet Burak ; Wiebe, Nathan</creator><creatorcontrib>Catli, Ahmet Burak ; Wiebe, Nathan</creatorcontrib><description>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 $\epsilon$ that requires $O(\log^2(1/\epsilon) + 1/\delta^2)$ queries to a purification of the input density operator if its spectrum is supported on $\{0\}~\bigcup ~[\delta,1-\delta]$ for $\delta&gt;0$ 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.</description><identifier>DOI: 10.48550/arxiv.2212.02600</identifier><language>eng</language><subject>Physics - Quantum Physics</subject><creationdate>2022-12</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2212.02600$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2212.02600$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Catli, Ahmet Burak</creatorcontrib><creatorcontrib>Wiebe, Nathan</creatorcontrib><title>Training quantum neural networks using the Quantum Information Bottleneck method</title><description>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 $\epsilon$ that requires $O(\log^2(1/\epsilon) + 1/\delta^2)$ queries to a purification of the input density operator if its spectrum is supported on $\{0\}~\bigcup ~[\delta,1-\delta]$ for $\delta&gt;0$ 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.</description><subject>Physics - Quantum Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8lOwzAURb1hgQofwAr_QIKH2E6XpWKoVAmQso-e7Zc2amKD4zD8PbR0dRb36kiHkBvOyqpWit1B-u4_SyG4KJnQjF2S1yZBH_qwox8zhDyPNOCcYPhD_orpMNF5Oq55j_Tt_NiELqYRch8DvY85DxjQHeiIeR_9FbnoYJjw-swFaR4fmvVzsX152qxX2wK0YcVSWFOhwLrunLDCO8W1dUr5pYGKefQdGCd9LQ1XAnVlNQplgRlutJcM5YLc_mtPSe176kdIP-0xrT2lyV8eeEri</recordid><startdate>20221205</startdate><enddate>20221205</enddate><creator>Catli, Ahmet Burak</creator><creator>Wiebe, Nathan</creator><scope>GOX</scope></search><sort><creationdate>20221205</creationdate><title>Training quantum neural networks using the Quantum Information Bottleneck method</title><author>Catli, Ahmet Burak ; Wiebe, Nathan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a670-92b74e2e88fc2b2dc516bc55d97a40dedfa7c3d837152e64b6e25ba07176d30e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Physics - Quantum Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Catli, Ahmet Burak</creatorcontrib><creatorcontrib>Wiebe, Nathan</creatorcontrib><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Catli, Ahmet Burak</au><au>Wiebe, Nathan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Training quantum neural networks using the Quantum Information Bottleneck method</atitle><date>2022-12-05</date><risdate>2022</risdate><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 $\epsilon$ that requires $O(\log^2(1/\epsilon) + 1/\delta^2)$ queries to a purification of the input density operator if its spectrum is supported on $\{0\}~\bigcup ~[\delta,1-\delta]$ for $\delta&gt;0$ 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.</abstract><doi>10.48550/arxiv.2212.02600</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2212.02600
ispartof
issn
language eng
recordid cdi_arxiv_primary_2212_02600
source arXiv.org
subjects Physics - Quantum Physics
title Training quantum neural networks using the Quantum Information Bottleneck method
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-23T06%3A40%3A39IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Training%20quantum%20neural%20networks%20using%20the%20Quantum%20Information%20Bottleneck%20method&rft.au=Catli,%20Ahmet%20Burak&rft.date=2022-12-05&rft_id=info:doi/10.48550/arxiv.2212.02600&rft_dat=%3Carxiv_GOX%3E2212_02600%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true