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Finding roots of equations is at the heart of most computational science. A well-known and widely used iterative algorithm is the Newton's method. However, its convergence depends heavily on the initial guess, with poor choices often…
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum…
This article introduces a pedagogical method for {\it solving combinatorial problems} that frequently involve structures that are unfamiliar or less familiar. Indeed, an indirect method has been proposed in order to evade any possible…
A simple scheme was proposed by Knuth to generate binary balanced codewords from any information word. However, this method is limited in the sense that its redundancy is twice that of the full sets of balanced codes. The gap between…
Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper,…
Quantum computers offer a new paradigm of computing with the potential to vastly outperform any imagineable classical computer. This has caused a gold rush towards new quantum algorithms and hardware. In light of the growing expectations…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
When one wishes to numerically solve an initial value problem, it is customary to rewrite it as an equivalent first-order system to which a method, usually from the class of Runge-Kutta methods, is applied. Directly treating higher-order…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…
Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new…
We consider whether trainable quantum unitaries can be used to discover quantum speed-ups for classical problems. Using methods recently developed for training quantum neural nets, we consider Simon's problem, for which there is a known…
Due to recent technological advances, actual quantum devices are being constructed and used to perform computations. As a result, many classical problems are being restated so as to be solved on quantum computers. Some examples include…
Quantum computing can enable a variety of breakthroughs in research and industry in the future. Although some quantum algorithms already exist that show a theoretical speedup compared to the best known classical algorithms, the…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
The recent development of quantum computing, which uses entanglement, superposition, and other quantum fundamental concepts, can provide substantial processing advantages over traditional computing. These quantum features help solve many…
Finding feasible points for which the proof succeeds is a critical issue in safe Branch and Bound algorithms which handle continuous problems. In this paper, we introduce a new strategy to compute very accurate approximations of feasible…
We obtain the strongest separation between quantum and classical query complexity known to date -- specifically, we define a black-box problem that requires exponentially many queries in the classical bounded-error case, but can be solved…