From neural to quantum associative networks: A new quantum “algorithm”

Ri‐Gui Zhou, Hui’an Wang, Qian Hong Wu +1 more

Kathleen E. Hamilton, Jonathan Schrock, Neena Imam +1 more

Yoshihiro Osakabe, Hisanao Akima, Masao Sakuraba +2 more

There is increasing interest in quantum computing, because of its enormous computing potential. A small number of powerful quantum algorithms have been proposed to date; however, the development of new quantum algorithms for practical use remains essential. Parallel computing with a neural network has successfully realized certain unique functions such as learning and recognition; therefore, the introduction of certain neural computing techniques into quantum computing to enlarge the quantum computing application field is worthwhile. In this paper, a novel quantum associative memory (QuAM) is proposed, which is achieved with a quantum neural network by employing adiabatic Hamiltonian evolution. The memorization and retrieval procedures are inspired by the concept of associative memory realized with an artificial neural network. To study the detailed dynamics of our QuAM, we examine two types of Hamiltonians for pattern memorization. The first is a Hamiltonian having diagonal elements, which is known as an Ising Hamiltonian and which is similar to the cost function of a Hopfield network. The second is a Hamiltonian having non-diagonal elements, which is known as a neuro-inspired Hamiltonian and which is based on interactions between qubits. Numerical simulations indicate that the proposed methods for pattern memorization and retrieval work well with both types of Hamiltonians. Further, both Hamiltonians yield almost identical performance, although their retrieval properties differ. The QuAM exhibits new and unique features, such as a large memory capacity, which differs from a conventional neural associative memory.

憲明 幸田

Jincheng Zhang

This paper presents a novel approach to demonstrating the feasibility of universal quantum algorithms using neural simulations. We propose a methodology for decomposing universal quantum algorithms into computational models amenable to neural simulation, leveraging the inherent parallelism of biological neural networks. This work aims to bridge the gap between theoretical quantum algorithms and the potential of neuromorphic computing, offering a new perspective on quantum algorithm design and potentially circumventing hardware limitations associated with traditional quantum computers. Specifically, we outline a framework where quantum circuits are mapped onto neural networks, enabling the exploration of quantum algorithms within a biologically inspired computational paradigm. The core of this approach lies in simplifying the complexity of quantum computation through the parallel processing capabilities of neural networks, ultimately providing a biological foundation for quantum algorithms. This research contributes to a deeper understanding of quantum computation and opens avenues for designing quantum algorithms with enhanced practicality and potentially reduced hardware requirements.

Subhash C. Kak