Researchers have proposed a method for training classical artificial neural networks using a quantum algorithm. The proposed procedure uses quantum walk as a search algorithm in a complete graph to find all synaptic weights of a classical artificial neural network. Each vertex of the graph represents a possible synaptic weight set in the w-dimensional search space. In addition to being able to know the number of iterations required beforehand, the method does not stagnate in local minimums, making it an alternative to the backpropagation algorithm. The researchers used the proposed method to solve an XOR problem with a classical artificial neural network that had nine weights. However, the procedure can be used for any number of dimensions. The results obtained demonstrate the viability of the proposal and contribute to research in machine learning and quantum computing.

The article proposes using quantum walks as an approach to Quantum Neural Networks (QNNs), which replace binary neurons with a qubit for the advantages of quantum computing in neural networks. The authors show that a biased discrete Hadamard walk for the firing states of a QNN does not lead to a unitary walk, but a Stochastic Quantum Walk between the global firing states of a QNN can be constructed and contains the feature of associative memory. The quantum contribution to the walk accounts for modest speed-up in some regimes. Overall, the study suggests that quantum walks can be useful tools in analyzing the dynamic properties of quantum systems and in simulating central properties of classical neural networks such as associative memory.

Researchers have successfully demonstrated the ability of quantum simulation to perform associative memory in Hopfield neural networks through the quantum stochastic walk method. This method relies on well-controlled detunings of the propagation constant in a three-dimensional photonic quantum chip. The experimental results showed a good match rate with the expected results for Hopfield neural networks, demonstrating the potential for using quantum simulation as a powerful tool for optimization and computation tasks in artificial intelligence. The scalability of the approach through low-loss integrated chips and straightforward Hamiltonian engineering further enhances the potential for creating photonic artificial intelligence devices with improved efficiencies. This research represents a significant step forward in the intersection of quantum information and machine learning, offering promising possibilities for future developments in the field.

Graph Neural Networks (GNNs) are often used to predict graph structured data but have remained black boxes for users due to their tight entanglement of input graph into neural network structure. However, a new paper reveals that GNNs can be naturally explained using higher-order expansions by identifying groups of edges that contribute to the prediction. A nested attribution scheme is applied at each step, resulting in a collection of walks into the input graph relevant for the prediction. This method, called GNN-LRP, is applicable to a wide range of GNNs and has yielded insights into sentiment analysis of text data, structure-property relationships in quantum chemistry, and image classification. GNN-LRP provides a practical way to explain the workings of GNNs and make them more transparent for users.

Harmonic functions are frequently found in the natural world, but there have been few attempts to use them within machine learning architectures. With a bias towards harmonic functions, data-driven modelling and solving inverse problems would be significantly easier. Within classical neural networks, inductive biases have already been established to improve performance, but it is still a relatively new concept within quantum machine learning. This study aimed to derive exactly-harmonic conventional and quantum neural networks in two dimensions for simply-connected domains using techniques inspired by domain decomposition in physics-informed neural networks. They were able to provide architectures and training protocols to enforce approximately harmonic constraints in three dimensions and higher, which then allowed for divergence-free network architectures in arbitrary dimensions. These approaches were tested in applications such as heat transfer, electrostatics, and robot navigation, with comparisons to physics-informed neural networks. This work is significant as it shows how harmonic functions can be incorporated into machine learning and indicates potential applications in various fields.

Researchers have developed a new machine-learning algorithm that predicts quantum advantages by simply looking at graphs. Quantum walks are integral to modern quantum technologies and have implications for algorithm design, particularly for designing energy-transfer mechanisms in biophotonics and material science. Quantum walks on graphs are distinctly different from their classical random walk counterparts. However, it remains unknown whether quantum walks offer advantages on arbitrary graphs without explicit symmetries. Such graphs require simulations of both classical and quantum walk dynamics that can take a long computational time. The team’s new methodology views graphs through a convolutional neural network. By observing various simulated examples, the machine recognizes different graphs that elicit quantum advantages. The network learns from graphs, eliminating the need for quantum walk or random walk simulations to identify graphs that offer quantum advantages. Researchers evaluated the performance of the algorithm on line and random graphs. The resulting classifications were better than random guesses even for the most challenging cases. The new approach has potential applications in the automated design of large-scale quantum circuits, and for simulating more efficient energy transfer mechanisms in various fields.

A team of researchers has found that automating the search for conditions under which quantum effects provide an advantage in particle transfer could pave the way for automating scientific discoveries. They show that by using a particular type of convolutional neural network, the process of finding the requirements for such quantum effects can be automated by learning from simulated examples. The researchers applied the machine learning approach to an analysis of noisy quantum walks on cycle graphs of different sizes and found it was possible to predict the existence of quantum advantage for the decoherence parameter range, even for graphs outside of the training set. The study’s results are considered important for demonstrations of quantum advantage in experiments, as well as potentially significant for other fields of research looking for conditions under which quantum effects can help identify advantages.

Researchers have proposed a variational approach to quantize projective simulation (PS), a reinforcement learning model for interpretable artificial intelligence, using variational quantum algorithms. PS models decision-making as a random walk on a graph of an agent's memory. The team proposed using quantum walks of single photons in a lattice of tunable Mach-Zehnder interferometers to implement a quantized model. The study proposed variational algorithms for reinforcement learning tasks, showing an example from transfer learning where the quantized PS learning model can outperform its classical counterpart. The team also discussed the role of quantum interference within training and decision-making in the context of interpretable quantum learning agents. Their study paves the way for the realization of interpretable quantum learning agents.

Quantum computing is seen as a potential solution to complement traditional von Neumann architectures in a time when classical computational infrastructure is becoming limited. Quantum platforms provide scalability, energy efficiency, and 3-D problem modeling. Quantum information science is a multi-disciplinary field, drawing from physics, mathematics, computer science, and photonics. Quantum systems are expressed with the properties of superposition and entanglement, transmitted via quantum teleportation, and evolved indirectly with operators such as neural operators, ladder operators, and master equations. Emerging applications in quantum cryptography, quantum machine learning, quantum finance, quantum neuroscience, quantum networks, and quantum error correction are discussed.

A team of researchers has proposed using a simple discrete-time quantum walk on a cycle graph as an alternative approach to the quantum circuit model. Their model is essentially a quantum neural network that can model an arbitrary unitary operation without the need to decompose it into a sequence of smaller gates. The model is universal and can be updated efficiently via a modified stochastic gradient descent algorithm adapted to the network, and by training the network, approximations to arbitrary desired unitary operations can be found. The DTQW-based neural network can also implement general measurements described by positive-operator-valued measures. The researchers demonstrated the network's capability by numeric simulation, showing that it could implement arbitrary 2-outcome POVM measurements. They further demonstrated that the network could be simplified and made more friendly for laboratory implementations. The research shows the potential of the DTQW-based neural network in quantum computation and laboratory implementations.