Related papers: A Symmetry-Based Taxonomy of Quantum Algorithms
Quantum machine learning aims to release the prowess of quantum computing to improve machine learning methods. By combining quantum computing methods with classical neural network techniques we aim to foster an increase of performance in…
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and…
A universal quantum computing scheme, with a universal set of logical gates, is proposed based on networks of 1D quantum systems. The encoding of information is in terms of universal features of gapped phases, for which effective field…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
Quantum computing holds the potential to revolutionize various fields by efficiently tackling complex problems. At its core are quantum circuits, sequences of quantum gates manipulating quantum states. The selection of the right quantum…
For quantum search via the continuous-time quantum walk, the evolution of the whole system is usually limited in a small subspace. In this paper, we discuss how the symmetries of the graphs are related to the existence of such an invariant…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. Starting from a specific example, we show how to use pure…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
We propose quantum algorithms, purely quantum in nature, for calculating the determinant and inverse of an $(N-1)\times (N-1)$ matrix (depth is $O(N^2\log N)$) which is a simple modification of the algorithm for calculating the determinant…
We consider the problem of distinguishing two vectors (visualized as images or barcodes) and learning if they are related to one another. For this, we develop a geometric quantum machine learning (GQML) approach with embedded symmetries…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
We formalize a new paradigm for optimality of algorithms, that generalizes worst-case optimality based only on input-size to problem-dependent parameters including implicit ones. We re-visit some existing sorting algorithms from this…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
Quantum computing is an emerging paradigm with the potential to offer significant computational advantage over conventional classical computing by exploiting quantum-mechanical principles such as entanglement and superposition. It is…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
The manipulation of neutral atoms by light is at the heart of countless scientific discoveries in the field of quantum physics in the last three decades. The level of control that has been achieved at the single particle level within arrays…
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…