Static and adaptive quantum circuits for VQE ansatz in hypergraphic partitioning

As quantum computing advances, there is a growing need for sophisticated computational methods that efficiently leverage quantum resources. This paper investigates the integration of adaptive quantum circuits with the Variational Quantum Eigensolver (VQE) algorithm, proposing Adaptive VQE as an enhanced approach for dynamically constructing quantum ansätze. We explore the impact of adaptive quantum circuits in multi-Quantum Processing Unit (QPU) environments and address the challenges associated with implementing adaptive VQE in distributed settings. While VQE is a promising algorithm for solving eigenvalue problems on Noisy Intermediate-Scale Quantum (NISQ) devices, it faces limitations such as circuit depth and noise sensitivity inherent in static circuit designs. By employing adaptive quantum circuit templates, our approach dynamically adjusts the quantum ansatz based on real-time feedback, significantly reducing circuit complexity and improving convergence rates compared to traditional static VQE implementations. Furthermore, anticipating the future context of multi-QPU architectures, we present a novel algorithm for circuit partitioning of adaptive quantum circuits. This method creates manageable subcircuits through a hypergraph partitioning approach, considering specific features and patterns from adaptive circuits. It enables parallel processing and enhances scalability for large-scale quantum applications. To support experimentation and further research, we provide a dataset containing files created for experiments with adaptive VQE ansätze, utilizing the adaptive quantum circuits approach. Through a series of comparative experiments with static and adaptive circuits, we explore the advantages of Adaptive VQE over static VQE in terms of circuit dimensions, resource utilization, and flexibility. This research offers comprehensive insights and guidelines for transitioning from static VQE to Adaptive VQE, emphasizing the benefits of adaptive circuits and the critical role of multi-QPU environments in optimizing quantum computations.