Academia.eduAcademia.edu

Outline

Title
Abstract
Introduction
Results
Example: Autoencoder for Data Compression
Discussion
Methods
References

Quantum generalisation of feedforward neural networks

Profile image of Hlér KristjánssonHlér Kristjánsson

npj Quantum Information

https://doi.org/10.1038/S41534-017-0032-4
visibility

…

description

8 pages

link

1 file

Abstract

We propose a quantum generalisation of a classical neural network. The classical neurons are firstly rendered reversible by adding ancillary bits. Then they are generalised to being quantum reversible, i.e., unitary (the classical networks we generalise are called feedforward, and have step-function activation functions). The quantum network can be trained efficiently using gradient descent on a cost function to perform quantum generalisations of classical tasks. We demonstrate numerically that it can: (i) compress quantum states onto a minimal number of qubits, creating a quantum autoencoder, and (ii) discover quantum communication protocols such as teleportation. Our general recipe is theoretical and implementation-independent. The quantum neuron module can naturally be implemented photonically.

Related papers

Training deep quantum neural networks
daniel scheiermann

Nature Communications, 2020

Neural networks enjoy widespread success in both research and industry and, with the advent of quantum technology, it is a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function, providing both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing deep-network optimisation. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

View PDFchevron_right
New quantum neural network designs
Felix Petitzon

2022

Quantum computers promise improving machine learning. We investigated the performance of new quantum neural network designs. Quantum neural networks currently employed rely on a feature map to encode the input into a quantum state. This state is then evolved via a parameterized variational circuit. Finally, a measurement is performed and post-processed on a classical computer to extract the prediction of the quantum model. We develop a new technique, where we merge feature map and variational circuit into a single parameterized circuit and post-process the results using a classical neural network. On a variety of real and generated datasets, we show that the new, combined approach outperforms the separated feature map & variational circuit method. We achieve lower loss, better accuracy, and faster convergence.

View PDFchevron_right
Quantum artificial neural network architectures and components
Tamaryn Menneer

Information Sciences

It is shown by classical simulation and experimentation that quantum artificial neural networks (QUANNs) are more efficient and in some cases more powerful than classical artificial neural networks (CLANNs) for a variety of experimental tasks. This effect is particularly noticeable with larger and more complex domains. The gain in efficiency is achieved with no generalisation loss in most cases. QUANNs are also more powerful than CLANNs, again for some of the tasks examined, in terms of what the network can learn. What is more, it appears that not all components of a QUANN architecture need to to be quantum for these advantages to surface. It is demonstrated that a fully quantum neural network has no advantage over a partly quantum network and may in fact produce worse results. Overall, this work provides a first insight into the expected behaviour of individual components of QUANNs, if and when quantum hardware is ever built, and raises questions about the interface between quantum...

View PDFchevron_right
Variational Learning for Quantum Artificial Neural Networks
Stefano Mangini

IEEE Transactions on Quantum Engineering

In the past few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of quantum machine learning aims at bringing together these two ongoing revolutions. Here, we first review a series of recent works describing the implementation of artificial neurons and feedforward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. We investigate different learning strategies involving global and local layerwise cost functions, and we assess their performances also in the presence of statistical measurement noise. While keeping full compatibility with the overall memory-efficient feedforward architecture, our constructions effectively reduce the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach toward the use of quantum neural networks for pattern classification on near-term quantum hardware. INDEX TERMS Artificial neural networks, supervised learning, quantum computing, quantum algorithm.

View PDFchevron_right
N E ] 1 5 D ec 2 01 3 Autonomous Quantum Perceptron Neural Network
Alaa Sagheer

2018

Abstract:Recently, with the rapid development of technology, there are a lot of applications require to achieve low-cost learning. However the computational power of classical artificial neural networks, they are not capable to provide low-cost learning. In contrast, quantum neural networks may be representing a good computational alternate to classical neural network approaches, based on the computational power of quantum bit (qubit) over the classical bit. In this paper we present a new computational approach to the quantum perceptron neural network can achieve learning in low-cost computation. The proposed approach has only one neuron can construct self-adaptive activation operators capable to accomplish the learning process in a limited number of iterations and, thereby, reduce the overall computational cost. The proposed approach is capable to construct its own set of activation operators to be applied widely in both quantum and classical applications to overcome the linearity ...

View PDFchevron_right
On Quantum Computers and Artificial Neural Networks
Co. SEP

Quantum computer science in combination with paradigms from computational neuroscience, specifically those from the field of artificial neural networks, seems to be promising for providing an outlook on a possible future of artificial intelligence. Within this elaboration, a quantum artificial neural network not only apportioning effects from quantum mechanics simulated on a von Neumann computer is proposed, but indeed for being processed on a quantum computer. Sooner or later quantum computers will replace classical von Neumann machines, which has been the motivation for this research. Although the proposed quantum artificial neural network is a classical feed forward one making use of quantum mechanical effects, it has, according to its novelty and otherness, been dedicated an own paper. Training such can only be simulated on von Neumann machines, which is pretty slow and not practically applicable (but nonetheless required for proofing the theorem), although the latter ones may be used to simulate an environment suitable for quantum computation. This is what has been realized during the SHOCID (Neukart, 2010) project for showing and proofing the advantages of quantum computers for processing artificial neural networks.

View PDFchevron_right
Quantum Neural Networks: A Novel Architecture for Hybrid Quantum-Classical Algorithms
Dr. Srinivasa Rao Gundu

Research Square (Research Square), 2024

The capacity of quantum computing to tackle complex problems faster than general computers might lead to industry revolutions. However, actual implementation is problematic due to limited qubit coherence and inherent noise. Using Quantum Neural Networks (QNNs), hybrid quantum-classical algorithms successfully address optimization problems by combining the bene ts of both quantum and traditional computer paradigms. The interface layer, the classical layer, and the quantum layer make up the three fundamental parts of the suggested design. The architecture's performance is contrasted with existing methods to demonstrate its advantages in terms of speed, accuracy, and scalability. With the help of this innovative design, di cult issues that are outside the capabilities of conventional computers can now be tackled, offering a workable solution for issues with nance, logistics, and medication development.

View PDFchevron_right
Quantum learning with noise and decoherence: a robust quantum neural network
Elizabeth Behrman

Quantum Machine Intelligence

Noise and decoherence are two major obstacles to the implementation of large-scale quantum computing. Because of the no-cloning theorem, which says we cannot make an exact copy of an arbitrary quantum state, simple redundancy will not work in a quantum context, and unwanted interactions with the environment can destroy coherence and thus the quantum nature of the computation. Because of the parallel and distributed nature of classical neural networks, they have long been successfully used to deal with incomplete or damaged data. In this work, we show that our model of a quantum neural network (QNN) is similarly robust to noise, and that, in addition, it is robust to decoherence. Moreover, robustness to noise and decoherence is not only maintained but improved as the size of the system is increased. Noise and decoherence may even be of advantage in training, as it helps correct for overfitting. We demonstrate the robustness using entanglement as a means for pattern storage in a qubit array. Our results provide evidence that machine learning approaches can obviate otherwise recalcitrant problems in quantum computing.

View PDFchevron_right
A Variational Algorithm for Quantum Neural Networks
Antonio Macaluso

Lecture Notes in Computer Science, 2020

Quantum Computing leverages the laws of quantum mechanics to build computers endowed with tremendous computing power. The field is attracting ever-increasing attention from both academic and private sectors, as testified by the recent demonstration of quantum supremacy in practice. However, the intrinsic restriction to linear operations significantly limits the range of relevant use cases for the application of Quantum Computing. In this work, we introduce a novel variational algorithm for quantum Single Layer Perceptron. Thanks to the universal approximation theorem, and given that the number of hidden neurons scales exponentially with the number of qubits, our framework opens to the possibility of approximating any function on quantum computers. Thus, the proposed approach produces a model with substantial descriptive power, and widens the horizon of potential applications already in the NISQ era, especially the ones related to Quantum Artificial Intelligence. In particular, we design a quantum circuit to perform linear combinations in superposition and discuss adaptations to classification and regression tasks. After this theoretical investigation, we also provide practical implementations using various simulation environments. Finally, we test the proposed algorithm on synthetic data exploiting both simulators and real quantum devices.

View PDFchevron_right
Neural networks with quantum gated nodes
Fariel Shafee

Engineering Applications of Artificial Intelligence, 2007

We study a quantum neural network with superposed qubits replacing classical neurons with deterministic states, and also with quantum gate operators in place of the classical action potentials observed in biological contexts. With our choice of logic gates interconnecting the neural lattice, we find that the state of the system behaves in ways reflecting both the strength of coupling between neurons as well as the initial conditions, and depending on whether there is a threshold for emission from excited to ground state, the system shows either chaotic oscillations or coherent ones with periodicity that depends on the strength of coupling in a unique way. The spatial pattern of the initial input affects the subsequent dynamic behavior of the system in an interesting unambiguous way, which indicates that it can serve as a dynamic memory system analogous to biological ones, but with an unlimited lifetime.

View PDFchevron_right

References (46)

  1. Nielsen, M. A. Neural Networks and Deep Learning (Determination Press, 2015).
  2. Azoff, E. M. Neural Network Time Series Forecasting of Financial Markets (Wiley, 1994).
  3. LeCunn, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436-444 (2015).
  4. Schuld, M., Sinayskiy, I. & Petruccione, F. An introduction to quantum machine learning. Contemp. Phys. 56, 172-185 (2014).
  5. Biamonte, J. et al. Quantum Machine Learning. Preprint at https://arxiv.org/abs/ 1611.09347 (2016).
  6. Lloyd, S., Mohseni, M. & Rebentrost, P. Quantum algorithms for supervised and unsupervised machine learning. Preprint at https://arxiv.org/abs/1307.0411 (2013).
  7. Lloyd, S., Mohseni, M. & Rebentrost, P. Quantum principal component analysis. Nat Phys 10, 631-633 (2014).
  8. Montanaro, A. Quantum pattern matching fast on average. Algorithmica 10, 16-39 (2017).
  9. Aaronson, S. Read the fine print. Nat. Phys. 11, 291-293 (2015).
  10. Garnerone, S., Zanardi, P. & Lidar, D. A. Adiabatic quantum algorithm for search engine ranking. Phys. Rev. Lett. 108, 230506 (2012).
  11. Harrow, A. W., Hassidim, A. & Lloyd, S. Quantum algorithm for linear systems of equations. Phys. Rev. Lett. 103, 150502 (2009).
  12. Lloyd, S., Garnerone, S. & Zanardi, P. Quantum algorithms for topological and geometric analysis of big data. Nat. Commun. 7, 10138 (2016).
  13. Rebentrost, P., Mohseni, M. & Lloyd, S. Quantum support vector machine for big data classification. Phys. Rev. Lett. 113, 130503 (2014).
  14. Wiebe, N., Braun, D. & Lloyd, S. Quantum algorithm for data fitting. Phys. Rev. Lett. 109, 050505 (2012).
  15. Adcock, J. et al. Advances in quantum machine learning https://arxiv.org/abs/ 1512.02900 (2015).
  16. Heim, B., Rønnow, T. F., Isakov, S. V. & Troyer, M. Quantum versus classical annealing of Ising spin glasses. Science 348, 215-217 (2015).
  17. Gross, D., Liu, Y. K., Flammia, S. T., Becker, S. & Eisert, J. Quantum state tomo- graphy via compressed sensing. Phys. Rev. Lett. 105, 150401 (2010).
  18. Dunjko, V., Taylor, J. M. & Briegel, H. J. Quantum-enhanced machine learning. Phys. Rev. Lett. 117, 130501 (2016).
  19. Wittek, P. (ed.) Quantum Machine Learning (Academic, 2014).
  20. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge University Press, 2000).
  21. Garner, A. J. P., Dahlsten, O. C. O., Nakata, Y., Murao, M. & Vedral, V. A framework for phase and interference in generalized probabilistic theories. New. J. Phys. 15, 093044 (2013).
  22. Lechner, W., Hauke, P. & Zoller, P. A quantum annealing architecture with all-to-all connectivity from local interactions. Sci. Adv. 1, e1500838 (2015).
  23. Wiebe, N., Kapoor, A. & Svore, K. M. Quantum deep learning. Preprint at https:// arxiv.org/abs/1303.5904 (2015).
  24. Schuld, M., Sinayskiy, I. & Petruccione, F. The quest for a quantum neural network. Quant. Inf. Process. 13, 25672586 (2014).
  25. Bisio, A., Chiribella, G., D'Ariano, G. M., Facchini, S. & Perinotti, P. Optimal quantum learning of a unitary transformation. Phys. Rev. A 81, 032324 (2010).
  26. Sasaki, M. & Carlini, A. Quantum learning and universal quantum matching machine. Phys. Rev. A 66, 022303 (2002).
  27. Sentís, G., Guţă, M. & Adesso, G. Quantum learning of coherent states. EPJ Quant. Technol. 2, 17 (2015).
  28. Banchi, L., Pancotti, N. & Bose, S. Quantum gate learning in qubit networks: Toffoli gate without time-dependent control. NPJ Quant. Inf. 2, 16019 (2016).
  29. Palittapongarnpim, P., Wittek, P., Zahedinejad, E., Vedaie, S. & Sanders, B. C. Learning in quantum control: high-dimensional global optimization for noisy quantum dynamics. Neurocomputing (in press, available online) doi: 10.1016/j. neucom.2016.12.087 (2016).
  30. Feynman, R. P. Quantum mechanical computers. Found. Phys. 16, 507531 (1986).
  31. Muthukrishnan, A. Classical and Quantum Logic Gates: An Introduction to Quan- tum Computing. Rochester Center for Quantum Information (online seminar notes). Retrieved from http://www.optics.rochester.edu/~stroud/presentations/ muthukrishnan991/LogicGates.pdf (1999).
  32. Curtis, C. W. & Reiner, I. Representation Theory of Finite Groups and Associative Algebras (AMS Chelsea Publishing, 1962).
  33. Bartlett, P. L. & Downs, T. Using random weights to train multilayer networks of hard-limiting units. IEEE Trans. Neural Netw. 3, 202-210 (1992).
  34. Downs, T. & Gaynier, R. J. The use of random weights for the training of multilayer networks of neurons with heaviside characteristics. Math. Comput. Model. 22, 53-61 (1995).
  35. Rowell, D. Computing the Matrix Exponential the Cayley-Hamilton Method. Department of Mechanical Engineering, MIT (online lecture notes). Retrieved from http://web.mit.edu/2.151/www/Handouts/CayleyHamilton.pdf (2004).
  36. Hedemann, S. R. Hyperspherical parameterization of unitary matrices. Preprint at https://arxiv.org/abs/1303.5904 (2013).
  37. Wilde, M. M. Quantum Information Theory (Cambridge University Press, 2013).
  38. Rudolph, T. Why I am optimistic about the silicon-photonic route to quantum computing. Preprint at https://arxiv.org/abs/1607.08535 (2016).
  39. Rojas, R. Neural Networks (Springer, 1996).
  40. Cerf, N. J., Adami, C. & Kwiat, P. G. Optical simulation of quantum logic. Phys. Rev. A. 57, R1477-R1480 (1998).
  41. Reck, M., Zeilinger, A., Bernstein, H. J. & Bertani, P. Experimental realization of any discrete unitary operator. Phys. Rev. Lett. 73, 58-61 (1994).
  42. Clements, W. R., Humphreys, P. C., Metcalf, B. J., Kolthammer, W. S. & Walmsley, I. A. An optimal design for universal multiport interferometers. Preprint at https:// arxiv.org/abs/1603.08788 (2016).
  43. Knill, E., Laamme, R. & Milburn, G. J. A for efficient quantum computation with linear optics. Nature 409, (2001).
  44. Humphreys, P. C. et al. Strain-optic active control for quantum integrated pho- tonics. Opt. Express 22, 21719-21726 (2014).
  45. Sansoni, L. et al. Polarization entangled state measurement on a chip. Phys. Rev. Lett. 105, 200503 (2010).
  46. Bonneau, D. et al. Fast path and polarization manipulation of telecom wave- length single photons in lithium niobate waveguide devices. Phys. Rev. Lett. 108, 053601 (2012).

Related papers

Training a Quantum Neural Network
Daniel Lima

2003

Quantum learning holds great promise for the field of machine intelligence. The most studied quantum learning algorithm is the quantum neural network. Many such models have been proposed, yet none has become a standard. In addition, these models usually leave out many details, often excluding how they intend to train their networks. This paper discusses one approach to the problem and what advantages it would have over classical networks.

View PDFchevron_right
A Leap among Entanglement and Neural Networks: A Quantum Survey
Fabrizio Falchi

2021

In recent years, Quantum Computing witnessed massive improvements both in terms of resources availability and algorithms development. The ability to harness quantum phenomena to solve computational problems is a long-standing dream that has drawn the scientific community’s interest since the late ’80s. In such a context, we pose our contribution. First, we introduce basic concepts related to quantum computations, and then we explain the core functionalities of technologies that implement the Gate Model and Adiabatic Quantum Computing paradigms. Finally, we gather, compare and analyze the current state-of-the-art concerning Quantum Perceptrons and Quantum Neural Networks implementations.

View PDFchevron_right
Communication via quantum neural networks
Alaa Sagheer

In this paper, a quantum teleportation protocol based on quantum neural networks is presented. We studied the relation between the network's weight and the fidelity of transferring information among neurons. It has been found that as the network's weight increases the accuracy of the transformed information increases. Preliminary results of a practical example are given in this paper.

View PDFchevron_right
A Leap among Quantum Computing and Quantum Neural Networks: A Survey
Fabrizio Falchi

ACM Computing Surveys

In recent years, Quantum Computing witnessed massive improvements in terms of available resources and algorithms development. The ability to harness quantum phenomena to solve computational problems is a long-standing dream that has drawn the scientific community’s interest since the late 80s. In such a context, we propose our contribution. First, we introduce basic concepts related to quantum computations, and then we explain the core functionalities of technologies that implement the Gate Model and Adiabatic Quantum Computing paradigms. Finally, we gather, compare and analyze the current state-of-the-art concerning Quantum Perceptrons and Quantum Neural Networks implementations.

View PDFchevron_right
"Overview of Quantum Computing in Quantum Neural Network and Artificial Intelligence"
Dr. K A R U N A M U R T H Y . A

“Quing: International Journal of Innovative Research in Science and Engineering, 2023

In recent years, quantum computing has emerged as a potentially gamechanging technology, with applications across various disciplines, including AI and machine learning. In recent years, the combination of quantum computing and neural networks has led to the development of quantum neural networks (QNNs). This paper explores the potential of QNNs and their applications in solving complex problems that are challenging for classical neural networks. This paper explores the fundamental principles of quantum computing, the architecture of QNNs, and their advantages over classical neural networks. Furthermore, this will highlight key research areas and challenges in the development and utilization of QNNs. Through an in-depth analysis, it demonstrates the QNNs hold significant promise for addressing complex computational problems and advancing the field of artificial intelligence.

View PDFchevron_right

Cited by

Noise Robustness and Experimental Demonstration of a Quantum Generative Adversarial Network for Continuous Distributions
Jonathan Romero

Advanced Quantum Technologies

The potential advantage of machine learning in quantum computers is a topic of intense discussion in the literature. Theoretical, numerical and experimental explorations will most likely be required to understand its power. There has been different algorithms proposed to exploit the probabilistic nature of variational quantum circuits for generative modelling. In this paper, we employ a hybrid architecture for quantum generative adversarial networks (QGANs) and study their robustness in the presence of noise. We devise a simple way of adding different types of noise to the quantum generator circuit, and numerically simulate the noisy hybrid QGANs to learn continuous probability distributions, and show that the performance of HQGANs remain unaffected. We also investigate the effect of different parameters on the training time to reduce the computational scaling of the algorithm and simplify its deployment on a quantum computer. We then perform the training on Rigetti's Aspen-4-2Q-A quantum processing unit, and present the results from the training. Our results pave the way for experimental exploration of different quantum machine learning algorithms on noisy intermediate scale quantum devices.

View PDFchevron_right
Quantum computing methods for supervised learning
Aniruddha Pant

Quantum Machine Intelligence

The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon semiconductor miniaturization approaches its physics limits, quantum computing is increasingly being considered to cater to these computational needs in the future. Small-scale quantum computers and quantum annealers have been built and are already being sold commercially. Quantum computers can benefit machine learning research and application across all science and engineering domains. However, owing to its roots in quantum mechanics, research in this field has so far been confined within the purview of the physics community, and most work is not easily accessible to researchers from other disciplines. In this paper, we provide a background and summarize key results of quantum computing before exploring its application to supervised machine learning problems. By eschewing results from physics that have little bearing on quantum computation, we hope to make this introduction accessible to data scientists, machine learning practitioners, and researchers from across disciplines.

View PDFchevron_right
The prospects of quantum computing in computational molecular biology
Charlotte Deane

WIREs Computational Molecular Science

Quantum computers can in principle solve certain problems exponentially more quickly than their classical counterparts. We have not yet reached the advent of useful quantum computation, but when we do, it will affect nearly all scientific disciplines. In this review, we examine how current quantum algorithms could revolutionize computational biology and bioinformatics. There are potential benefits across the entire field, from the ability to process vast amounts of information and run machine learning algorithms far more efficiently, to algorithms for quantum simulation that are poised to improve computational calculations in drug discovery, to quantum algorithms for optimization that may advance fields from protein structure prediction to network analysis. However, these exciting prospects are susceptible to "hype," and it is also important to recognize the caveats and challenges in this new technology. Our aim is to introduce the promise and limitations of emerging quantum computing technologies in the areas of computational molecular biology and bioinformatics.

View PDFchevron_right
An optical neural chip for implementing complex-valued neural network
Mile Gu

Nature Communications

Complex-valued neural networks have many advantages over their real-valued counterparts. Conventional digital electronic computing platforms are incapable of executing truly complex-valued representations and operations. In contrast, optical computing platforms that encode information in both phase and magnitude can execute complex arithmetic by optical interference, offering significantly enhanced computational speed and energy efficiency. However, to date, most demonstrations of optical neural networks still only utilize conventional real-valued frameworks that are designed for digital computers, forfeiting many of the advantages of optical computing such as efficient complex-valued operations. In this article, we highlight an optical neural chip (ONC) that implements truly complex-valued neural networks. We benchmark the performance of our complex-valued ONC in four settings: simple Boolean tasks, species classification of an Iris dataset, classifying nonlinear datasets (Circle a...

View PDFchevron_right
Quantum arithmetics via computation with minimized external control: The half-adder
Leonardo Banchi

Physical Review A, 2018

The while-you-wait computing paradigm combines elements of digital and analog quantum computation with the aim of minimizing the need of external control. In this architecture the computer is split into logic units, each continuously implementing a single recurring multigate operation via the unmodulated Hamiltonian evolution of a quantum many-body system. Here we use evolutionary algorithms to engineer such many-body dynamics, and develop logic units capable of continuously implementing a quantum half-adder in a time-independent four-qubit network, where qubits are coupled with either Ising or Heisenberg interactions. Our results provide a step for the development of larger modules for full quantum arithmetics.

View PDFchevron_right
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved