Implementing perceptron models with qubits

@article{Wiersema2019ImplementingPM,
  title={Implementing perceptron models with qubits},
  author={Roeland Wiersema and Hilbert J. Kappen},
  journal={Physical Review A},
  year={2019}
}
We propose a method for learning a quantum probabilistic model of a perceptron. By considering a cross entropy between two density matrices we can learn a model that takes noisy output labels into account while learning. A multitude of proposals already exist that aim to utilize the curious properties of quantum systems to build a quantum perceptron, but these proposals rely on a classical cost function for the optimization procedure. We demonstrate the usage of a quantum equivalent of the… 

Figures from this paper

Learning quantum models from quantum or classical data

  • H. Kappen
  • Computer Science, Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2020
The proposed method is to learn the quantum Hamiltonian, that is such that its ground state approximates the given classical distribution, that can be significantly more accurate than the classical maximum likelihood approach, both for unsupervised learning and for classification.

A Leap among Entanglement and Neural Networks: A Quantum Survey

This work introduces basic concepts related to quantum computations, and then the core functionalities of technologies that implement the Gate Model and Adiabatic Quantum Computing paradigms are explained.

A Leap among Quantum Computing and Quantum Neural Networks: A Survey

First, basic concepts related to quantum computations are introduced, and then the core functionalities of technologies that implement the Gate Model and Adiabatic Quantum Computing paradigms are explained.

Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning

This work establishes the parametrized version of Quantum Complexity and Quantum Chaos in terms of physically relevant quantities, which are not only essential in determining the stability, but also essential in providing a very significant lower bound to the generalization capability of QNN.

References

SHOWING 1-10 OF 33 REFERENCES

Learning quantum models from quantum or classical data

  • H. Kappen
  • Computer Science, Physics
    Journal of Physics A: Mathematical and Theoretical
  • 2020
The proposed method is to learn the quantum Hamiltonian, that is such that its ground state approximates the given classical distribution, that can be significantly more accurate than the classical maximum likelihood approach, both for unsupervised learning and for classification.

Quantum generalisation of feedforward neural networks

It is demonstrated numerically that the proposed quantum generalisation of a classical neural network can compress quantum states onto a minimal number of qubits, create a quantum autoencoder, and discover quantum communication protocols such as teleportation.

Quantum Machine Learning in Feature Hilbert Spaces.

This Letter interprets the process of encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space and shows how it opens up a new avenue for the design of quantum machine learning algorithms.

Quantum Boltzmann Machine

This work proposes a new machine learning approach based on quantum Boltzmann distribution of a transverse-field Ising Hamiltonian that allows the QBM efficiently by sampling and discusses the possibility of using quantum annealing processors like D-Wave for QBM training and application.

Qubit neural network and its learning efficiency

Simulations have shown that the Qubit model solves learning problems with significantly improved efficiency as compared to the classical model, and it is suggested that the improved performance is due to the use of superposition of neural states and theUse of probability interpretation in the observation of the output states of the model.

The quest for a Quantum Neural Network

This article presents a systematic approach to QNN research, concentrating on Hopfield-type networks and the task of associative memory, and outlines the challenge of combining the nonlinear, dissipative dynamics of neural computing and the linear, unitary dynamics of quantum computing.

Quantum-Inspired Neural Network with Quantum Weights and Real Weights

To enhance the approximation ability of neural networks, by introducing quantum rotation gates to the traditional BP networks, a novel quantum-inspired neural network model is proposed in this paper.

Quantum extension of conditional probability

We analyze properties of the quantum conditional amplitude operator @Phys. Rev. Lett. 79, 5194 ~1997!#, which plays a role similar to that of the conditional probability in classical information

Quantum M-P Neural Network

This paper validates that this quantum M-P network can realize some network functions, such as “XOR”, but also verifies the feasibility and validity of its weight learning algorithm by some simple examples.