Variational quantum eigensolvers based approximation of quantum Gaussian filters

Abstract

Quantum computation attracts much attention in the last decades. However, useful quantum algorithms are very limited and need more exploration. In recent years, we see more and more work in the field of quantum algorithm, which is good. Currently, we are in the stage that physical devices are of the so called Noisy Intermediate-Scale Quantum nature, this poses challenge in designing practical quantum algorithms. Our groundbreaking quantum algorithm stands as a paradigm-shifting solution tailored for the intricate task of approximating the ground state in quantum many-body systems, with a particular emphasis on its relevance to Noisy Intermediate-Scale Quantum devices. At its core, our innovative approach seamlessly integrates two powerful quantum computing methodologies: Variational Quantum Eigensolver and Quantum Gaussian Filter. The key feature of our algorithm lies in its iterative strategy, strategically discretizing the application of the Quantum Gaussian Filter operator into small, optimized steps using the versatility of Variational Quantum Eigensolver. In each iterative step, the state undergoes parameterization, and the modifications introduced through Variational Quantum Eigensolver progressively refine it, bringing it closer to the desired state post-Gaussian Filter application. Our algorithm's efficacy is demonstrated when applied to Transverse Field Ising models, showcasing unparalleled improvements in both convergence speed and accuracy, particularly within noisy environments. This notable outperformance compared to traditional Variational Quantum Eigensolver methods highlights the algorithm's potential in addressing the complexities of complex quantum simulations. This groundbreaking achievement signifies a significant stride in the realm of quantum computing applications within the Noisy Intermediate-Scale Quantum era.