Related papers: The Abstract Structure of Quantum Algorithms
Neutral-atom arrays are a leading platform for quantum technologies, offering a promising route toward large-scale, fault-tolerant quantum computing. We propose a novel quantum processing architecture based on dual-type, dual-element atom…
Encryption schemes often derive their power from the properties of the underlying algebra on the symbols used. Inspired by group theoretic tools, we use the centralizer of a subgroup of operations to present a private-key quantum…
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…
The advent of quantum computing has challenged classical conceptions of which problems are efficiently solvable in our physical world. This motivates the general study of how physical principles bound computational power. In this paper we…
With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
Attempts to find new quantum algorithms that outperform classical computation have focused primarily on the nonabelian hidden subgroup problem, which generalizes the central problem solved by Shor's factoring algorithm. We suggest an…
We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
In this article a notion of information is presented which stresses the contextuality of quantum objects and their measurement. Mathematically this is reached by a quantification of the quantum mechanical surplus knowledge which has been…
Quantum Machine Learning represents a paradigm shift at the intersection of Quantum Computing and Machine Learning, leveraging quantum phenomena such as superposition, entanglement, and quantum parallelism to address the limitations of…
In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we…
If a one-phrase summary of the subject of this thesis were required, it would be something like: miscellaneous large (but finite) dimensional phenomena in quantum information theory. That said, it could nonetheless be helpful to briefly…
In my Montreal lecture notes of 1988, it was suggested that the theory of linear quantum groups can be presented in the framework of the category of {\it quadratic algebras} (imagined as algebras of functions on "quantum linear spaces"),…
As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available…
Quantum information, a field in which great advances have been made in the past decades, now presents opportunities for chemistry. One roadblock to progress, especially for experimental chemical science, is that new concepts and technical…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…