Related papers: Quantum Computation as Geometry
In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
Quantum computing holds the potential to solve problems that are practically unsolvable by classical computers due to its ability to significantly reduce time complexity. We aim to harness this potential to enhance ray casting, a pivotal…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Quantum neural networks are promising for a wide range of applications in the Noisy Intermediate-Scale Quantum era. As such, there is an increasing demand for automatic quantum neural architecture search. We tackle this challenge by…
The discovery of an algorithm for factoring which runs in polynomial time on a quantum computer has given rise to a concerted effort to understand the principles, advantages, and limitations of quantum computing. At the same time, many…
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.…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
Quantum computing has the potential to revolutionize multiple fields by solving complex problems that can not be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its…
The design and performance of computer vision algorithms are greatly influenced by the hardware on which they are implemented. CPUs, multi-core CPUs, FPGAs and GPUs have inspired new algorithms and enabled existing ideas to be realized.…
We establish an isomorphism between quantum circuits and a subspace of polyatomic molecules, which suggests that molecules can be used as descriptors of quantum circuits for quantum machine learning. Our numerical results show that the…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the…
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on…