Related papers: The Arrow Calculus as a Quantum Programming Langua…
We define computational atoms named "actions" equipped primarily with three operations: reduction, collection, and inspection. We show how actions can be used for decision-making algorithms from simple axioms. We describe the encodings of…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
A geometrical approach to quantum computation is presented, where a non-abelian connection is introduced in order to rewrite the evolution operator of an energy degenerate system as a holonomic unitary. For a simple geometrical model we…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and…
The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time --- the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
Quantum walks are powerful tools not only to construct the quantum speedup algorithms but also to describe specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various…
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…
The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…
We present a number of quantum computing patterns that build on top of fundamental algorithms, that can be applied to solving concrete, NP-hard problems. In particular, we introduce the concept of a quantum dictionary as a summation of…