Related papers: Vector computation
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…
Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems, their dynamics, and interaction. Since the inception of quantum theory, it has been…
What resources are universal for quantum computation? In the standard model, a quantum computer consists of a sequence of unitary gates acting coherently on the qubits making up the computer. This paper shows that a very different model…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
This paper initiates a systematic study of quantum functions, which are (partial) functions defined in terms of quantum mechanical computations. Of all quantum functions, we focus on resource-bounded quantum functions whose inputs are…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
Contextuality - the obstruction to describing quantum mechanics in a classical statistical way - has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality…
Physical processes are computations only when we use them to externalize thought. Computation is the performance of one or more fixed processes within a contingent environment. We reformulate the Church-Turing thesis so that it applies to…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
The concurrent rise of artificial intelligence and quantum information poses opportunity for creating interdisciplinary technologies like quantum neural networks. Quantum reservoir processing, introduced here, is a platform for quantum…
Photonic quantum computation refers to quantum computation that uses photons as the physical system for doing the quantum computation. The field is largely divided between discrete-variable (DV) and continuous-variable (CV) photonic quantum…
The subject of this work is quantum predicative programming -- the study of developing of programs intended for execution on a quantum computer. We look at programming in the context of formal methods of program development, or programming…
A quantum processor is a programmable quantum circuit in which both the data and the program, which specifies the operation that is carried out on the data, are quantum states. We study the situation in which we want to use such a processor…
In this note we point out the fact that the proper conceptual setting of quantum computation is the theory of Linear Time Invariant systems. To convince readers of the utility of the approach, we introduce a new model of computation based…
Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…
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…
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be…