Related papers: Quantum Algorithms for Solving Ordinary Differenti…
We explore how a continuous-variable (CV) quantum computer could solve a classic differential equation, making use of its innate capability to represent real numbers in qumodes. Specifically, we construct variational CV quantum circuits…
Quantum computation is a promising emerging technology, and by utilizing the principles of quantum mechanics, it is expected to achieve faster computations than classical computers for specific problems. There are two distinct architectures…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
Quantum computing is an important developing technology with the potential to revolutionise the landscape of scientific and business problems that can be practically addressed. The widespread excitement derives from the potential for a…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…
Although quantum computing hardware has evolved significantly in recent years, spurred by increasing industrial and government interest, the size limitation of current generation quantum computers remains an obstacle when applying these…
Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that…
Digital-analog quantum computing (DAQC) offers a promising approach to addressing the challenges of building a practical quantum computer. By efficiently allocating resources between digital and analog quantum circuits, DAQC paves the way…
We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to…
This work focuses on quantum methods for cryptanalysis of schemes based on the integer factorization problem and the discrete logarithm problem. We demonstrate how to practically solve the largest instances of the factorization problem by…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
Quantum annealing is a generic algorithm using quantum-mechanical fluctuations to search for the solution of an optimization problem. The present paper first reviews the fundamentals of quantum annealing and then reports on preliminary…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
Quantum optimization has emerged as a promising frontier of quantum computing, providing novel numerical approaches to mathematical optimization problems. The main goal of this paper is to facilitate interdisciplinary research between the…
Quantum computing promises to tackle technological and industrial problems insurmountable for classical computers. However, today's quantum computers still have limited demonstrable functionality, and it is expected that scaling up to…
Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…