Related papers: Quantum computational advantage implies contextual…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for…
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 computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically…
The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
Contextuality is a fundamental non-classical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of…
Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…
The quantum advantage threshold determines when a quantum processing unit (QPU) is more efficient with respect to classical computing hardware in terms of algorithmic complexity. The "green" quantum advantage threshold $-$ based on a…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of…
The quantum information science community has seen a surge in new algorithmic developments across scientific domains. These developments have demonstrated polynomial or better improvements in computational and space complexity,…
Demonstrating quantum advantage in machine learning tasks requires navigating a complex landscape of proposed models and algorithms. To bring clarity to this search, we introduce a framework that connects the structure of parametrized…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
In recent years, many computational tasks have been proposed as candidates for showing a quantum computational advantage, that is an advantage in the time needed to perform the task using a quantum instead of a classical machine.…
Developing a systematic view of where quantum computers will outperform classical ones is important for researchers, policy makers and business leaders. But developing such a view is challenging because quantum advantage analyses depend not…