Related papers: L-QLES: Sparse Laplacian generator for evaluating …

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…

Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…

Solving large-scale Partial Differential Equations (PDEs) on complex three-dimensional geometries represents a central challenge in scientific and engineering computing, often impeded by expensive pre-processing stages and substantial…

The Variational Quantum Linear Solver (VQLS), a hybrid quantum-classical algorithm for solving linear systems, faces a practical scalability bottleneck: the Linear Combination of Unitaries (LCU) decomposition requires O(L^2) circuit…

We develop a novel approach for efficiently applying variational quantum linear solver (VQLS) in context of structured sparse matrices. Such matrices frequently arise during numerical solution of partial differential equations which are…

We propose an innovative Parallel Quantum Local Search (PQLS) methodology that leverages the capabilities of small-scale quantum computers to efficiently address complex combinatorial optimization problems. Traditional Quantum Local Search…

Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…

Partial differential equations (PDEs) are central to modeling physical and engineering systems, but repeatedly solving parametric PDEs remains computationally expensive. Operator learning enables fast surrogate inference, yet typically…

Large Language Models (LLMs) show strong capabilities in code generation, motivating their use in automated quantum solver development. However, in quantum computing, successful execution of generated code is not sufficient: correctness…

Lie Algebras are powerful mathematical structures used in physics to describe sets of operators and associated combinations. A central task is to identify a minimal set of generators from which the algebra can be constructed. The classical…

Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…

With the potential of quantum algorithms to solve intractable classical problems, quantum computing is rapidly evolving and more algorithms are being developed and optimized. Expressing these quantum algorithms using a high-level language…

We introduce a parallel algorithm to construct a preconditioner for solving a large, sparse linear system where the coefficient matrix is a Laplacian matrix (a.k.a., graph Laplacian). Such a linear system arises from applications such as…

Quantum Layout Synthesis (QLS) plays a crucial role in optimizing quantum circuit execution on physical quantum devices. As we enter the era where quantum computers have hundreds of qubits, we are faced with scalability issues using optimal…

Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large…

Unlike most classical algorithms that take an input and give the solution directly as an output, quantum algorithms produce a quantum circuit that works as an indirect solution to computationally hard problems. In the full quantum computing…

Quantum Chemistry (QC) is one of the most promising applications of Quantum Computing. However, present quantum processing units (QPUs) are still subject to large errors. Therefore, noisy intermediate-scale quantum (NISQ) hardware is…

Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…

In numerical approaches to solving differential equations on a lattice, a representation of the derivative operator that correctly matches the continuum behaviour of functions of momentum up to the band limit must be non-local. We present…

Near term quantum devices have the potential to outperform classical computing through the use of hybrid classical-quantum algorithms such as Variational Quantum Eigensolvers. These iterative algorithms use a classical optimiser to update a…