QuIRK: Quantum-Inspired Re-uploading KAN

TL;DR

QuIRK introduces a quantum-inspired re-uploading KAN by replacing B-Splines with single-qubit Data Re-Uploading activations, achieving universal univariate approximation with fewer parameters. The architecture preserves KAN interpretability and the possibility of closed-form solutions, while remaining classically simulable with GPUs. On the Feynman regression dataset, QuIRK attains competitive RMSE with significantly reduced parameter counts and even outperforms vanilla KAN on some equations, highlighting its practical impact for efficient, interpretable scientific modeling. Together, these contributions suggest a scalable pathway to compact, quantum-inspired models for complex regression tasks in scientific domains.

Abstract

Kolmogorov-Arnold Networks or KANs have shown the ability to outperform classical Deep Neural Networks, while using far fewer trainable parameters for regression problems on scientific domains. Even more powerful has been their interpretability due to their structure being composed of univariate B-Spline functions. This enables us to derive closed-form equations from trained KANs for a wide range of problems. This paper introduces a quantum-inspired variant of the KAN based on Quantum Data Re-uploading (DR) models. The Quantum-Inspired Re-uploading KAN or QuIRK model replaces B-Splines with single-qubit DR models as the univariate function approximator, allowing them to match or outperform traditional KANs while using even fewer parameters. This is especially apparent in the case of periodic functions. Additionally, since the model utilizes only single-qubit circuits, it remains classically tractable to simulate with straightforward GPU acceleration. Finally, we also demonstrate that QuIRK retains the interpretability advantages and the ability to produce closed-form solutions.

Figures (9)

• Figure 1: QuIRK Macro architecture. Each incoming edge to a QuIRK layer is a single qubit DR circuit. The output of each hidden QuIRK layer ($h^l_u$) is then rescaled to the range $[0,\pi]$ creating node $h^{'l}_u$. The output of the network is a QuIRK layer with a single unit followed by an optional dense layer which scales the output to the desired range.
• Figure 2: Single qubit Data Re-Uploading circuit with '$L$' layers. Each layer consists of a data encoding function $\phi(x)$ following by a trainable unitary $U(\Theta^{i})$. The final measurement is a function of the input '$x$' and the trainable parameters '$\theta = \{\Theta^i | \;\; \forall i \in [0,L]\}$'. Each activation is composed of multiple DR layers.
• Figure 3: Multi qubit (n) Data Re-Uploading layer. The layer consists of a set of trainable gates, an input embedding function and an entanglement pattern.
• Figure 4: Q-batch execution for 4 dimensional data when 'max_qubits'=2. The data is split into 2 batches and 2 circuits are run in parallel.
• Figure 5: Runtime scaling of with increasing number of qubits across different backends using batch 8- 100 dim data on a 32-thread CPU and A6000 GPU. Tensor Network simulations greatly outperform the state-vector simulator for larger qubit counts but are worse for smaller qubit counts.