[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119176-en":3,"doc-seo-119176-105":30,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119176,8796095461564,"Liam","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Training-efficient density quantum machine learning","Quantum machine learning relies on models that are both expressive and efficiently trainable on near-term hardware. This work introduces density quantum neural networks, built by randomising over sets of trainable unitaries inside parameterised quantum circuits. The framework enables an explicit trade-off between expressibility and trainability, demonstrating versatility on two recent QNN families. Results show improved training capacity with minimal gradient overhead for commuting-block models, and a quadratic-to-constant gradient query advantage for density orthogonal (Hamming-weight preserving) models. Numerical studies use synthetic translationally invariant data and MNIST with hyperparameter optimisation, and the paper relates the approach to post-variational, measurement-based QML and dropout mechanisms.","arXiv :2405 .20237v1 [ quant-ph] 30 May 2024  \nTraining-efficient density quantum machine learning  \nBrian Coyle 1 , El Amine Cherrat 1 , Nishant Jain 1, 2 , Natansh Mathur 1, 3 , Snehal Raj 1 , Skander  \nKazdaghli 1 , and Iordanis Kerenidis 1, 3  \n1 QC Ware, Palo Alto, USA and Paris France.  \n2 Indian Institute of Technology, Roorkee, India.  \n3 IRIF, CNRS-University of Paris, France.  \nAbstract  \nQuantum machine learning requires powerful, flexible and efficiently trainable models to be successful in solving challenging problems. In this work, we present density quantum neural networks, a learning model incorporating randomisation over a set of trainable unitaries. These models generalise quantum neural networks using parameterised quantum circuits, and allow a trade-off between expressibility and efficient trainability, particularly on quantum hardware. We demonstrate the flexibility of the formalism by applying it to two recently proposed model families. The first are commuting-block quantum neural networks (QNNs) which are efficiently trainable but may be limited in expressibility. The second are orthogonal (Hamming-weight preserving) quantum neural networks which provide well-defined and interpretable transformationson data but are challenging to train at scale on quantum devices. Density commuting QNNs improve capacity with minimal gradient complexity overhead, and density orthogonal neural networks admit a quadratic-to-constant gradient query advantage with minimal to no performance loss. We conduct numerical experiments on synthetic translationally invariant data and MNIST image data with hyperparameter optimisation to support our findings. Finally, we discuss the connection to post-variational quantum neural networks, measurement-based quantum machine learning and the dropout mechanism.  \n1 Introduction  \nModern deep learning owes much of its success to the existence of efficient gradient-based methods to train large and deep neural networks. The backpropagation algorithm [1], and its variants, enable the computation of gradients throughout the entirety of the network, with an overhead not much larger than the evaluation of the network itself. In order to build and train successful models for quantum neural networks in quantum machine learning (QML) problems, we must have training protocols which scale in a similarly efficient fashion to their classical counterparts. Current approaches for evaluating gradients of trainable quantum models such as parameterised quantum circuits (PQCs) [2– 5] (commonly referred to as quantum neural networks (QNNs)) unfortunately do not generally possess such an efficient scaling 1. If the evaluation of gradients of a QNN requires computation which  \n1 Here, we do not refer to ‘non-efficient’ in the complexity theory sense-usually used to mean a super-polynomial scaling in some input parameter, but instead in the practical sense.  \neven scales linearly in the number of parameters, this renders the model effectively untrainable at scale. Unfortunately, such a linear scaling does appear in, for example, the parameter-shift rule for QNNs [6–11], a popular method which enables the computation of exact (i.e., not relying on approximate finite differences) gradients. For example, applying the parameter-shift rule to a QNN with trainable parameters only located in fixed-axis singlequbit Pauli rotations, requires two individual circuits to run per parameter, leading to a O (M) gradient scaling for M parameters. As a second example, recent proposals for orthogonal quantum neural networks [12] (OrthoQNNs) contain O (n2 ) parameters to fully parameterise an orthogonal transformation (i.e. an n × n orthogonal matrix) on an input vector of size n. Using a generalisation of the parametershift rule, training such an orthogonal ‘layer’would require the evaluation of ∼ 40 , 000 separate circuits to operate on vectors of length n = 1002 . Scaling  \n2 Ref. [13] gave an estimate that in a single day of comp","cbCaitgJRdVsfzwq","https://ap.wps.com/l/cbCaitgJRdVsfzwq","pdf",7372010,1,32,"English","en",105,"# Abstract\n# Introduction\n## The search for quantum backpropagation\n## Density quantum neural networks","[{\"question\":\"What are density quantum neural networks in this paper?\",\"answer\":\"They are learning models that generalise quantum neural networks by incorporating randomisation over a set of trainable unitaries within parameterised quantum circuits.\"},{\"question\":\"How does the method address the efficiency of gradient evaluation for quantum models?\",\"answer\":\"It targets training protocols where gradient queries do not scale poorly with the number of parameters, providing efficient trainability particularly on quantum hardware.\"},{\"question\":\"Which two quantum neural network families are used to demonstrate the framework?\",\"answer\":\"The paper applies the formalism to commuting-block quantum neural networks and to orthogonal (Hamming-weight preserving) quantum neural networks.\"}]","Training-efficient density quantum machine learning | 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are density quantum neural networks in this paper?","Question",{"text":76,"@type":77},"They are learning models that generalise quantum neural networks by incorporating randomisation over a set of trainable unitaries within parameterised quantum circuits.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the method address the efficiency of gradient evaluation for quantum models?",{"text":81,"@type":77},"It targets training protocols where gradient queries do not scale poorly with the number of parameters, providing efficient trainability particularly on quantum hardware.",{"name":83,"@type":74,"acceptedAnswer":84},"Which two quantum neural network families are used to demonstrate the framework?",{"text":85,"@type":77},"The paper applies the formalism to commuting-block quantum neural networks and to orthogonal (Hamming-weight preserving) quantum neural 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