Related papers: Classical and Quantum Algorithms for Tensor Princi…
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…
In this paper, we propose a quantum version of the differential cryptanalysis which offers a quadratic speedup over the existing classical one and show the quantum circuit implementing it. The quantum differential cryptanalysis is based on…
Current quantum systems have significant limitations affecting the processing of large datasets with high dimensionality, typical of high energy physics. In the present paper, feature and data prototype selection techniques were studied to…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We discuss the performance of the Search and Fourier Transform algorithms on a hybrid computer constituted of classical and quantum processors working together. We show that this semi-quantum computer would be an improvement over a pure…
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…
The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used…
The recent advent of commercially available quantum annealing hardware (QAH) has expanded opportunities for research into quantum annealing-based algorithms. In the domain of power systems, this advancement has driven increased interest in…
Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to…
Quantum principal component analysis (QPCA) ignited a new development toward quantum machine learning algorithms. Initially showcasing as an active way for analyzing a quantum system using the quantum state itself, QPCA also found potential…
Feedback-based quantum optimization is a quantum approach to combinatorial optimization. In this paper, we introduce the classical counterpart of feedback-based quantum optimization by using the quantum-classical correspondence of spin…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Recent advancements have highlighted the limitations of current quantum systems, particularly the restricted number of qubits available on near-term quantum devices. This constraint greatly inhibits the range of applications that can…
Despite significant effort, the quantum machine learning community has only demonstrated quantum learning advantages for artificial cryptography-inspired datasets when dealing with classical data. In this paper we address the challenge of…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
We present a quantum Viterbi algorithm (QVA) with better than classical performance under certain conditions. In this paper the proposed algorithm is applied to decoding classical convolutional codes, for instance; large constraint length…
Linear regression is one of the most fundamental linear algebra problems. Given a dense matrix $A \in \mathbb{R}^{n \times d}$ and a vector $b$, the goal is to find $x'$ such that $ \| Ax' - b \|_2^2 \leq (1+\epsilon) \min_{x} \| A x - b…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…