Related papers: Integrating Quantum Algorithms Into Classical Fram…
Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within…
We present classical sublinear-time algorithms for solving low-rank linear systems of equations. Our algorithms are inspired by the HHL quantum algorithm for solving linear systems and the recent breakthrough by Tang of dequantizing the…
We provide an example of a quantum system which solves a numerical problem more efficiently than a classical computer. The example uses the Aharonov-Bohm effect, and can be integrated into standard quantum mechanics courses. The aim is to…
Implicit methods are attractive for hybrid quantum-classical CFD solvers as the flow equations are combined into a single coupled matrix that is solved on the quantum device, leaving only the CFD discretisation and matrix assembly on the…
Combinatorial optimization is a challenging problem applicable in a wide range of fields from logistics to finance. Recently, quantum computing has been used to attempt to solve these problems using a range of algorithms, including…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all science and engineering. The Harrow-Hassidim-Lloyd algorithm, a…
The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
The Harrow-Hassidim-Lloyd algorithm is intended for solving the system of linear equations on quantum devices. The exponential advantage of the algorithm comes with four caveats. We present a numerical study of the performance of the…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
To date, research in quantum computation promises potential for outperforming classical heuristics in combinatorial optimization. However, when aiming at provable optimality, one has to rely on classical exact methods like integer…
The expectations arising from the latest achievements in the quantum computing field are causing that researchers coming from classical artificial intelligence to be fascinated by this new paradigm. In turn, quantum computing, on the road…
Quantum computers promise exponential speed ups over classical computers for various tasks. This emerging technology is expected to have its first huge impact in High Performance Computing (HPC), as it can solve problems beyond the reach of…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
Quantum machine learning (QML) presents potential for early industrial adoption, yet limited access to quantum hardware remains a significant bottleneck for deployment of QML solutions. This work explores the use of classical surrogates to…
We develop a hybrid classical-quantum method for solving the Lorenz system. We use the forward Euler method to discretize the system in time, transforming it into a system of equations. This set of equations is solved using the Variational…
Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…