Interpretability of artificial intelligence (AI) methods, particularly deep neural networks, is of great interest. This heightened focus stems from the widespread use of AI-backed systems. These systems, often relying on intricate neural architectures, can exhibit behavior that is challenging to explain and comprehend. The interpretability of such models is a crucial component of building trusted systems. Many methods exist to approach this problem, but they do not apply straightforwardly to the quantum setting. Here, we explore the interpretability of quantum neural networks using local model-agnostic interpretability measures commonly utilized for classical neural networks. Following this analysis, we generalize a classical technique called LIME, introducing Q-LIME, which produces explanations of quantum neural networks. A feature of our explanations is the delineation of the region in which data samples have been given a random label, likely subjects of inherently random quantum measurements. We view this as a step toward understanding how to build responsible and accountable quantum AI models.
Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic circuits designed for generating approximate solutions to combinatorial optimization problems constructed using two-bit stochastic matrices. Through a numerical study, we investigate the performance of our proposed variational circuits in solving the Max-Cut problem on various graphs of increasing sizes. Our classical algorithm demonstrates improved performance for several graph types to the quantum approximate optimization algorithm. Our findings suggest that evaluating the performance of quantum variational circuits against variational circuits with sub-universal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.
Fault-tolerant Quantum Processing Units (QPUs) promise to deliver exponential speed-ups in select computational tasks, yet their integration into modern deep learning pipelines remains unclear. In this work, we take a step towards bridging this gap by presenting the first fully-coherent quantum implementation of a multilayer neural network with non-linear activation functions. Our constructions mirror widely used deep learning architectures based on ResNet, and consist of residual blocks with multi-filter 2D convolutions, sigmoid activations, skip-connections, and layer normalizations. We analyse the complexity of inference for networks under three quantum data access regimes. Without any assumptions, we establish a quadratic speedup over classical methods for shallow bilinear-style networks. With efficient quantum access to the weights, we obtain a quartic speedup over classical methods. With efficient quantum access to both the inputs and the network weights, we prove that a network with an $N$-dimensional vectorized input, $k$ residual block layers, and a final residual-linear-pooling layer can be implemented with an error of $ε$ with $O(\text{polylog}(N/ε)^k)$ inference cost.
Mathew Vanherreweghe, Lirandë Pira, Patrick Rebentrost
We introduce cumulative polynomial Kolmogorov-Arnold networks (CP-KAN), a neural architecture combining Chebyshev polynomial basis functions and quadratic unconstrained binary optimization (QUBO). Our primary contribution involves reformulating the degree selection problem as a QUBO task, reducing the complexity from $O(D^N)$ to a single optimization step per layer. This approach enables efficient degree selection across neurons while maintaining computational tractability. The architecture performs well in regression tasks with limited data, showing good robustness to input scales and natural regularization properties from its polynomial basis. Additionally, theoretical analysis establishes connections between CP-KAN's performance and properties of financial time series. Our empirical validation across multiple domains demonstrates competitive performance compared to several traditional architectures tested, especially in scenarios where data efficiency and numerical stability are important. Our implementation, including strategies for managing computational overhead in larger networks is available in Ref.~\citep{cpkan_implementation}.
Lirandë Pira, Airin Antony, Nayanthara Prathap et al.
Photonic chip design has seen significant advancements with the adoption of inverse design methodologies, offering flexibility and efficiency in optimizing device performance. However, the black-box nature of the optimization approaches, such as those used in inverse design in order to minimize a loss function or maximize coupling efficiency, poses challenges in understanding the outputs. This challenge is prevalent in machine learning-based optimization methods, which can suffer from the same lack of transparency. To this end, interpretability techniques address the opacity of optimization models. In this work, we apply interpretability techniques from machine learning, with the aim of gaining understanding of inverse design optimization used in designing photonic components, specifically two-mode multiplexers. We base our methodology on the widespread interpretability technique known as local interpretable model-agnostic explanations, or LIME. As a result, LIME-informed insights point us to more effective initial conditions, directly improving device performance. This demonstrates that interpretability methods can do more than explain models -- they can actively guide and enhance the inverse-designed photonic components. Our results demonstrate the ability of interpretable techniques to reveal underlying patterns in the inverse design process, leading to the development of better-performing components.