Related papers: A Categorical Model for Classical and Quantum Bloc…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
Quantum machine learning has emerged as a promising application domain for near-term quantum hardware, particularly through hybrid quantum-classical models that leverage both classical and quantum processing. Although numerous hybrid…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. These consist of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose…
In the context of space-time block codes (STBCs), the theory of generalized quaternion and biquaternion algebras (i.e., tensor products of two quaternion algebras) over arbitrary base fields is presented, as well as quadratic form theoretic…
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical…
Block encoding is a successful technique used in several powerful quantum algorithms. In this work we provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure. The proposed methodology is…
We introduce a novel scheme of quantum recursive programming, in which large unitary transformations, i.e. quantum gates, can be recursively defined using quantum case statements, which are quantum counterparts of conditionals and case…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
Programming a quantum computer, i.e., implementing quantum algorithms on a quantum processor-based copmputer architecture, is a task that can be addressed (just as for classical computers) at different levels of abstraction. This paper…
We describe how dagger-Frobenius monoids give the correct categorical description of certain kinds of finite-dimensional 'quantum algebras'. We develop the concept of an involution monoid, and use it to construct a correspondence between…
We describe arithmetic algorithms on a canonical number representation based on the Catalan family of combinatorial objects specified as a Haskell type class. Our algorithms work on a {\em generic} representation that we illustrate on…
Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable…
Classical representations of quantum states and operations as vectors and matrices are plagued by an exponential growth in memory and runtime requirements for increasing system sizes. Based on their use in classical computing, an…
We present a class of hybrid classical systems using quantum co-processors and point out that unlike purely quantum computers, such hybrids can be both universal and Turing complete; we introduce such quantum-classical hybrids as…