[Paper Review] Artificial Quantum Neural Network: quantum neurons, logical elements and tests of convolutional nets

V. I. Dorozhinsky, Oleg Pavlovsky|arXiv (Cornell University)|Jun 25, 2018

Neural Networks and Applications3 references3 citations

TL;DR

This paper proposes an artificial quantum neural network (AQNN) using quantum particles in a double-well potential as neurons, simulating spike-like soliton excitations via path integral Monte Carlo. It demonstrates implementation of classical logical gates (AND, OR, NOT), constructs a simple convolutional network for vertical line detection, and transfers trained classical MNIST weights to a quantum network achieving ~91% recognition accuracy, proving feasibility of weight transfer from classical to quantum architectures.

ABSTRACT

We consider a model of an artificial neural network that uses quantum-mechanical particles in a two-humped potential as a neuron. To simulate such a quantum-mechanical system the Monte-Carlo integration method is used. A form of the self-potential of a particle and two potentials (exciting and inhibiting) interaction are proposed. The possibility of implementing the simplest logical elements, (such as AND, OR and NOT) based on introduced quantum particles is shown. Further we show implementation of a simplest convolutional network. Finally we construct a network that recognizes handwritten symbols, which shows that in the case of simple architectures, it is possible to transfer weights from a classical network to a quantum one.

Motivation & Objective

• To develop a quantum neural network model based on quantum particles in a double-well potential as artificial neurons.
• To demonstrate the implementation of basic logical elements (AND, OR, NOT) using quantum neurons and their interactions.
• To construct a simple convolutional network for pattern recognition, specifically detecting vertical lines.
• To apply the quantum network to handwritten digit recognition using transferred weights from a classical MNIST model.
• To evaluate the feasibility of transferring trained classical network weights to a quantum neural network architecture.

Proposed method

• Model quantum neurons as particles in a W-shaped potential $ V_0(\varphi) = \frac{\Lambda}{4}(\varphi^2 - 1)^2 $, representing vacuum and excited states.
• Use path integral Monte Carlo formalism to simulate the quantum dynamics of the system, with Euclidean time paths $ \varphi_i(\tau) $ and action $ S = \int_0^T d\tau \left[ \sum_i \left( \frac{1}{2}\dot{\varphi}_i^2 + V_0(\varphi_i) \right) + \sum_{i>j} V_{\text{int}}(\varphi_i, \varphi_j) \right] $.
• Introduce excitatory and inhibitory interactions via a coupling potential $ V_{\text{int}} $, with connection strengths $ \varepsilon_{ij} $ derived from pre-trained classical network weights.
• Construct a Lagrangian $ \mathcal{L} $ that includes kinetic terms, self-potentials, and interaction terms $ \hat{\varepsilon}_{ij} \varphi_j^2 (\hat{\psi}_i^2 - 1)^2 $, where $ \hat{\psi}_i $ encodes pixel brightness.
• Map grayscale pixel values $ b_i \in [0,1] $ to input neuron paths via $ \hat{\psi}_i = \sqrt{ \sqrt{b_i} \psi^2 - \sqrt{b_i} + 1 } $, enabling continuous input representation.
• Normalize classical network weights $ W \in \mathbb{R}^{M \times 10} $ to $ \hat{\varepsilon}_{ij} \in [0,1] $ using $ \hat{\varepsilon}_{ij} = \frac{W_{ij} - \min(W)}{\max(W) - \min(W)} $ for use in the quantum model.

Experimental results

Research questions

• RQ1 Can quantum particles in a two-humped potential serve as artificial neurons capable of generating spike-like soliton excitations?
• RQ2 Is it possible to implement basic classical logical gates (AND, OR, NOT) using quantum neurons with excitatory and inhibitory couplings?
• RQ3 Can a quantum neural network architecture be constructed to perform simple pattern recognition tasks such as detecting vertical lines?
• RQ4 Can trained classical neural network weights be successfully transferred to a quantum neural network for handwritten digit recognition?
• RQ5 How does the performance of the quantum network compare to the classical network when using transferred weights?

Key findings

• The quantum neural network successfully implements basic logical elements (AND, OR, NOT) using quantum particles in a double-well potential with controlled excitatory and inhibitory interactions.
• A simple convolutional network is constructed that correctly identifies vertical lines using the quantum neuron framework.
• The quantum network achieves a digit recognition accuracy of approximately 91% on the MNIST test set when using transferred weights from a classical fully connected network.
• The transfer of classical network weights to the quantum model is feasible and effective, as demonstrated by the network assigning higher scores to correct digits in the output.
• The Monte Carlo simulation introduces stochasticity, resulting in slightly lower performance than the classical network, but the overall recognition pattern remains consistent and meaningful.