Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2003.14122

Tunable Quantum Neural Networks for Boolean Functions

Viet Pham Ngoc, Herbert Wiklicky

Published Mar 31, 2020• 4 citations
arXivHTMLPDF

Abstract

In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural networks. Despite this, our proposed architecture is still able to learn any Boolean function. This ability arises from the correspondence that exists between a Boolean function and a particular quantum circuit made out of multi-controlled NOT gates. This correspondence is built via a polynomial representation of the function called the algebraic normal form. We use this construction to introduce the idea of a generic quantum circuit whose gates can be tuned to learn any Boolean functions. In order to perform the learning task, we have devised an algorithm that leverages the absence of measurements. When presented with a superposition of all the binary inputs of length $n$, the network can learn the target function in at most $n+1$ updates.

DOI
10.48550/arxiv.2003.14122

Related papers

Tunable Quantum Neural Networks in the QPAC-Learning Framework

Viet Pham Ngoc, David Tuckey, Herbert Wiklicky

In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By tuning the set of controls these circuits are able to approximate any Boolean functions. This architecture is particularly suited to be used in the QPAC-learning framework as it can handle the superposition produced by the oracle. In order to tune the network so that it can approximate a target concept, we have devised and implemented an algorithm based on amplitude amplification. The numerical results show that this approach can efficiently learn concepts from a simple class.

arXiv:2205.01514•Electronic Proceedings in Theoretical Computer Science•Nov 14, 2023•0 citations

Quantum Neuron: an elementary building block for machine learning on quantum computers

Yudong Cao, Gian Giacomo Guerreschi, Alán Aspuru‐Guzik

Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.

arXiv:1711.11240•Nov 30, 2017•113 citations

The Design and Implementation of Quantum-Inspired Neural Networks

Yang Shu-yu

The approximation ability of neural networks plays an important role to the result when one uses neural networks to resolve problems.Unfortunately there is no ideal way to construct proper networks with strong approximation ability.A novel construction approach based on the multi-qubits controller-not gates is proposed for neural networks model in this paper.The proposed model consists of three layers where the hidden nodes are the quantum neurons and the output nodes are the common neurons.The quantum neuron consists of the quantum rotation gates and the multi-qubits controllednot gates.The overall memory of input sequences is captured from information feedback of target qubit from output to input in the multi-qubits controlled-not gate.The output of quantum neuron is obtained from the controlled relationship of the multi-qubits controlled-not gate.The L-M learning algorithms are designed in detail based on the basic principles of quantum computation.The features of input sequences can be effectively obtained in two ways of breadth and depth.The experimental results of solitaire forecast show that,when the number of input nodes is close to the length of sequences,the training set recognition rate of the proposed model increases about 8% than the common neural networks,which reveals the effectiveness of the quantum computation for enhancing the approximation capability of the common neural networks.

Journal of Signal Processing•Jan 1, 2014•0 citations

Exploiting the equivalence between quantum neural networks and perceptrons

Chris Mingard, Jessica Pointing, London, Charles +2 more

Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the expressivity and inductive bias of QNNs by exploiting an exact mapping from QNNs with inputs $x$ to classical perceptrons acting on $x \otimes x$ (generalised to complex inputs). The simplicity of the perceptron architecture allows us to provide clear examples of the shortcomings of current QNN models, and the many barriers they face to becoming useful general-purpose learning algorithms. For example, a QNN with amplitude encoding cannot express the Boolean parity function for $n\geq 3$, which is but one of an exponential number of data structures that such a QNN is unable to express. Mapping a QNN to a classical perceptron simplifies training, allowing us to systematically study the inductive biases of other, more expressive embeddings on Boolean data. Several popular embeddings primarily produce an inductive bias towards functions with low class balance, reducing their generalisation performance compared to deep neural network architectures which exhibit much richer inductive biases. We explore two alternate strategies that move beyond standard QNNs. In the first, we use a QNN to help generate a classical DNN-inspired kernel. In the second we draw an analogy to the hierarchical structure of deep neural networks and construct a layered non-linear QNN that is provably fully expressive on Boolean data, while also exhibiting a richer inductive bias than simple QNNs. Finally, we discuss characteristics of the QNN literature that may obscure how hard it is to achieve quantum advantage over deep learning algorithms on classical data.

arXiv:2407.04371•Jul 5, 2024•0 citations

Quantum activation functions for quantum neural networks

Marco Maronese, C. Destri, Enrico Prati

Abstract The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here, we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement–based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik’s theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.

arXiv:2201.03700•Quantum Information Processing•Mar 30, 2022•49 citations

Neural networks with quantum architecture and quantum learning

Massimo Panella, Giuseppe Martinelli

Abstract A method is proposed for solving the two key problems facing quantum neural networks: introduction of nonlinearity in the neuron operation and efficient use of quantum superposition in the learning algorithm. The former is indirectly solved by using suitable Boolean functions. The latter is based on the use of a suitable nonlinear quantum circuit. The resulting learning procedure does not apply any optimization method. The optimal neural network is obtained by applying an exhaustive search among all the possible solutions. The exhaustive search is carried out by the proposed quantum circuit composed of both linear and nonlinear components. Copyright © 2009 John Wiley & Sons, Ltd.

International Journal of Circuit Theory and Applications•Jul 23, 2009•75 citations
In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural networks. Despite this, our proposed architecture is still able to learn any Boolean function. This ability arises from the correspondence that exists between a Boolean function and a particular quantum circuit made out of multi-controlled NOT gates. This correspondence is built via a polynomial representation of the function called the algebraic normal form. We use this construction to introduce the idea of a generic quantum circuit whose gates can be tuned to learn any Boolean functions. In order to perform the learning task, we have devised an algorithm that leverages the absence of measurements. When presented with a superposition of all the binary inputs of length nnn, the network can learn the target function in at most n+1n+1n+1 updates.
In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By tuning the set of controls these circuits are able to approximate any Boolean functions. This architecture is particularly suited to be used in the QPAC-learning framework as it can handle the superposition produced by the oracle. In order to tune the network so that it can approximate a target concept, we have devised and implemented an algorithm based on amplitude amplification. The numerical results show that this approach can efficiently learn concepts from a simple class.
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.
The approximation ability of neural networks plays an important role to the result when one uses neural networks to resolve problems.Unfortunately there is no ideal way to construct proper networks with strong approximation ability.A novel construction approach based on the multi-qubits controller-not gates is proposed for neural networks model in this paper.The proposed model consists of three layers where the hidden nodes are the quantum neurons and the output nodes are the common neurons.The quantum neuron consists of the quantum rotation gates and the multi-qubits controllednot gates.The overall memory of input sequences is captured from information feedback of target qubit from output to input in the multi-qubits controlled-not gate.The output of quantum neuron is obtained from the controlled relationship of the multi-qubits controlled-not gate.The L-M learning algorithms are designed in detail based on the basic principles of quantum computation.The features of input sequences can be effectively obtained in two ways of breadth and depth.The experimental results of solitaire forecast show that,when the number of input nodes is close to the length of sequences,the training set recognition rate of the proposed model increases about 8% than the common neural networks,which reveals the effectiveness of the quantum computation for enhancing the approximation capability of the common neural networks.
Quantum machine learning models based on parametrized quantum circuits, also called quantum neural networks (QNNs), are considered to be among the most promising candidates for applications on near-term quantum devices. Here we explore the expressivity and inductive bias of QNNs by exploiting an exact mapping from QNNs with inputs xxx to classical perceptrons acting on x⊗xx \otimes xx⊗x (generalised to complex inputs). The simplicity of the perceptron architecture allows us to provide clear examples of the shortcomings of current QNN models, and the many barriers they face to becoming useful general-purpose learning algorithms. For example, a QNN with amplitude encoding cannot express the Boolean parity function for n≥3n\geq 3n≥3, which is but one of an exponential number of data structures that such a QNN is unable to express. Mapping a QNN to a classical perceptron simplifies training, allowing us to systematically study the inductive biases of other, more expressive embeddings on Boolean data. Several popular embeddings primarily produce an inductive bias towards functions with low class balance, reducing their generalisation performance compared to deep neural network architectures which exhibit much richer inductive biases. We explore two alternate strategies that move beyond standard QNNs. In the first, we use a QNN to help generate a classical DNN-inspired kernel. In the second we draw an analogy to the hierarchical structure of deep neural networks and construct a layered non-linear QNN that is provably fully expressive on Boolean data, while also exhibiting a richer inductive bias than simple QNNs. Finally, we discuss characteristics of the QNN literature that may obscure how hard it is to achieve quantum advantage over deep learning algorithms on classical data.
Abstract The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here, we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement–based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik’s theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.
Abstract A method is proposed for solving the two key problems facing quantum neural networks: introduction of nonlinearity in the neuron operation and efficient use of quantum superposition in the learning algorithm. The former is indirectly solved by using suitable Boolean functions. The latter is based on the use of a suitable nonlinear quantum circuit. The resulting learning procedure does not apply any optimization method. The optimal neural network is obtained by applying an exhaustive search among all the possible solutions. The exhaustive search is carried out by the proposed quantum circuit composed of both linear and nonlinear components. Copyright © 2009 John Wiley & Sons, Ltd.