Quantum computation builds on the use of correlations. Correlations could also play a central role for artificial intelligence, neuromorphic computing or "biological computing." As a step toward a systematic exploration of "correlated computing" we demonstrate that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and correlations of the Ising spins. We show for a two qubit system that quantum gates can be learned as a change of parameters for neural network dynamics. These changes respect restrictions which ensure the quantum correlations. Our proposal for probabilistic computing goes beyond Markov chains and is not based on transition probabilities. Constraints on classical probability distributions relate changes made in one part of the system to other parts, similar to entangled quantum systems.
Quantum computation builds on the use of correlations. Correlations could also play a central role for artificial intelligence, neuromorphic computing or "biological computing." As a step toward a systematic exploration of "correlated computing" we demonstrate that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and correlations of the Ising spins. We show for a two qubit system that quantum gates can be learned as a change of parameters for neural network dynamics. These changes respect restrictions which ensure the quantum correlations. Our proposal for probabilistic computing goes beyond Markov chains and is not based on transition probabilities. Constraints on classical probability distributions relate changes made in one part of the system to other parts, similar to entangled quantum systems.
This paper explores a novel approach to neuromorphic computing by leveraging the unique properties of quantum entanglement. The core idea is to utilize multi-particle quantum entanglement states as the physical connections between artificial neurons, enabling efficient parallel information processing and mimicking biological neural networks. We propose a quantum neuromorphic chip architecture employing multiple superconducting quantum bits (Qubits) engineered to exhibit entanglement. The design focuses on manipulating the coherence time, topological structure, and combined operation of quantum gates to emulate synaptic transmission and learning within biological neural networks. Specifically, we investigate encoding information through entanglement and explore parallel computation facilitated by this quantum phenomenon. Furthermore, we address the challenges of quantum computation by integrating quantum decoherence and quantum error correction techniques. The potential for achieving high-performance, energy-efficient, and biologically inspired computing is discussed, representing a significant departure from traditional approaches and classical neural networks. The proposed framework offers a pathway towards scalable quantum neuromorphic systems with potential applications in areas such as pattern recognition, machine learning, and complex system modeling.
A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level observables, and the quantum subsystem employs suitable expectation values and correlations. We discuss static memory materials based on Ising spins for which boundary information can be transported through the bulk in a generalized equilibrium state. They can realize quantum operations as the Hadamard or CNOT-gate for the quantum subsystem. Classical probabilistic systems can account for the entanglement of quantum spins. An arbitrary unitary evolution for an arbitrary number of quantum spins can be described by static memory materials for an infinite number of Ising spins which may, in turn, correspond to continuous variables or fields. We discuss discrete subsets of unitary operations realized by a finite number of Ising spins. They may be useful for new computational structures. We suggest that features of quantum computation or more general probabilistic computation may be realized by neural networks, neuromorphic computing or perhaps even the brain. This does neither require small isolated entities nor very low temperature. In these systems the processing of probabilistic information can be more general than for static memory materials. We propose a general formalism for probabilistic computing for which deterministic computing and quantum computing are special limiting cases.
Neuromorphic computing is inspired by the dynamics of biological neural systems - they operate event-driven and enable energy-efficient and real-time learning by Spiking neural networks. Advantages of this approach include faster convergence, improved accuracy, and potential energy efficiency gain, making this approach suitable for edge AI, real-time signal processing, and large-scale cognitive simulations. The convergence of neuromorphic computing and quantum optimization offers a transformative pathway for next-generation AI. By integrating event-driven spiking neural networks with quantum algorithms, hybrid systems can achieve faster learning, enhanced global optimization, and energy-efficient computation beyond classical limits. A comprehensive framework has been presented for designing and analyzing such hybrid quantum-neuromorphic architectures, highlighting their potential for real-time, scalable, and intelligent applications.
The convergence of quantum computing and neuromorphic engineering represents a promising frontier for next-generation artificial intelligence. Hybrid quantum-neuromorphic intelligence is emerging as an alternative to conventional von Neumann computing by combining the strengths of both paradigms. Quantum systems provide powerful capabilities for optimization, simulation, and complex problem solving, while neuromorphic systems enable energy-efficient, event-driven processing inspired by biological neural networks. Their integration offers new opportunities to address challenges related to computational complexity, scalability, energy consumption, and adaptive learning. Quantum machine learning, quantum neural networks, spiking neural networks, hybrid optimization approaches, and applications in healthcare, smart cities, cybersecurity, and autonomous systems. It also highlights explainability, ethical considerations, and future research directions, concluding that quantum-neuromorphic intelligence could become a key enabler of future AI industries and advanced intelligent systems.
We demonstrate, that artificial neural networks (ANN) can be trained to emulate single or multiple basic quantum operations. In order to realize a quantum state, we implement a novel "quantumness gate" that maps an arbitrary matrix to the real representation of a positive hermitean normalized density matrix. We train the CNOT gate, the Hadamard gate and a rotation in Hilbert space as basic building blocks for processing the quantum density matrices of two entangled qubits. During the training process the neural networks learn to represent the complex structure, the hermiticity, the normalization and the positivity of the output matrix. The requirement of successful training allows us to find a critical bottleneck dimension which reflects the relevant quantum information. Chains of individually trained neural quantum gates can be constructed to realize any unitary transformation. For scaling to larger quantum systems, we propose to use correlations of stochastic macroscopic two-level observables or classical bits. This novel concept provides a path for a classical implementation of computationally relevant quantum information processing on classical neural networks, in particular on neuromorphic computing machines featuring stochastic operations.
The approximation of quantum states with artificial neural networks has gained a lot of attention during the last years. Meanwhile, analog neuromorphic chips, inspired by structural and dynamical properties of the biological brain, show a high energy efficiency in running artificial neural-network architectures for the profit of generative applications. This encourages employing such hardware systems as platforms for simulations of quantum systems. Here we report on the realization of a prototype using the latest spike-based BrainScaleS hardware allowing us to represent few-qubit maximally entangled quantum states with high fidelities. Bell correlations of pure and mixed two-qubit states are well captured by the analog hardware, demonstrating an important building block for simulating quantum systems with spiking neuromorphic chips.