ICLR 2026 Papers

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 $\epsilon$ with $O(\text{polylog}(N/\epsilon)^k)$ inference cost.

Quantum reservoir computing uses the dynamics of quantum systems to process temporal data, making it particularly well-suited for machine learning with noisy intermediate-scale quantum devices. Recent developments have introduced feedback-based quantum reservoir systems, which process temporal information with comparatively fewer components and enable real-time computation while preserving the input history. Motivated by their promising empirical performance, in this work, we study the approximation capabilities of feedback-based quantum reservoir computing. More specifically, we are concerned with recurrent quantum neural networks, which are quantum analogues of classical recurrent neural networks. Our results show that regular state-space systems can be approximated using quantum recurrent neural networks without the curse of dimensionality and with the number of qubits only growing logarithmically in the reciprocal of the prescribed approximation accuracy. Notably, our analysis demonstrates that quantum recurrent neural networks are universal with linear readouts, making them both powerful and experimentally accessible. These results pave the way for practical and theoretically grounded quantum reservoir computing with real-time processing capabilities.

In this work, we investigate DR-submodular maximization using stochastic biased gradients, which is a more realistic but challenging setting than stochastic unbiased gradients. We first generalize the Lyapunov framework to incorporate biased stochastic gradients, characterizing the adverse impacts of bias and noise. Leveraging this framework, we consider not only conventional constraints but also a novel constraint class: convex sets with a largest element, which naturally arises in applications such as resource allocations. For this constraint, we propose an $1/e$ approximation algorithm for non-monotone DR-submodular maximization, surpassing the hardness result $1/4$ for general convex constraints. As a direct application of stochastic biased gradients, we consider zero-order DR-submodular maximization and introduce both classical and quantum gradient estimation algorithms. In each constraint we consider, while retaining the same approximation ratio, the iteration complexity of our classical zero-order algorithms is $O(\epsilon^{-3})$, matching that of stochastic unbiased gradients; our quantum zero-order algorithms reach $O(\epsilon^{-1})$ iteration complexity, on par with classical first-order algorithms, demonstrating quantum acceleration and validated in numerical experiments.