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Quantum phase estimation (QPE) plays a pivotal role in many quantum algorithms, offering provable speedups in applications such as Shor's factoring algorithm. While fault-tolerant quantum algorithms for combinatorial and Hamiltonian…
Variational quantum eigensolvers (VQEs) are one of the most important and effective applications of quantum computing, especially in the current noisy intermediate-scale quantum (NISQ) era. There are mainly two ways for VQEs:…
Quantum computing holds great promise for solving classically intractable problems such as linear systems and partial differential equations (PDEs). While fully fault-tolerant quantum computers remain out of reach, current noisy…
Quantum computing is expected to transform a range of computational tasks beyond the reach of classical algorithms. In this work, we examine the application of variational quantum algorithms (VQAs) for unsupervised image segmentation to…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
Simulating differential equations on classical computers becomes an intractable problem if the grid size is extremely large. Quantum computers are believed to achieve a possibly exponential speedup in the matrix operation. In this paper, we…
While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
Understanding strongly correlated systems is essential for advancing quantum chemistry and materials science, yet conventional methods like Density Functional Theory (DFT) often fail to capture their complex electronic behavior. To address…
Variational quantum algorithms hold great promise for unlocking the power of near-term quantum processors, yet high measurement costs, barren plateaus, and challenging optimization landscapes frequently hinder them. Here, we introduce…
Variational quantum eigensolver (VQE), aiming at determining the ground state energy of a quantum system described by a Hamiltonian on noisy intermediate scale quantum (NISQ) devices, is among the most significant applications of…
Efficient ground state search is fundamental to advancing combinatorial optimization problems and quantum chemistry. While the Variational Imaginary Time Evolution (VITE) method offers a useful alternative to Variational Quantum Eigensolver…
Quantum algorithms offer an exponential speedup over classical algorithms for a range of computational problems. The fundamental mechanisms underlying quantum computation required the development and construction of quantum computers. These…
The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE…
The electronic structure problem is one of the main problems in modern theoretical chemistry. While there are many already-established methods both for the problem itself and its applications like semi-classical or quantum dynamics, it…
This paper introduces an efficient and generic framework for finite-element simulations under an implicit time integration scheme. Being compatible with generic constitutive models, a fast matrix assembly method exploits the fact that…
Recent advances in quantum computing and their increased availability has led to a growing interest in possible applications. Among those is the solution of partial differential equations (PDEs) for, e.g., material or flow simulation.…
We assess the use of variational quantum imaginary time evolution for solving partial differential equations. Our results demonstrate that real-amplitude ansaetze with full circular entangling layers lead to higher-fidelity solutions…
Quantum computers have the potential to deliver speed-ups for solving certain important problems that are intractable for classical counterparts, making them a promising avenue for advancing modern computation. However, many quantum…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…