Related papers: Categorical computation
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated operators corresponding to areas of 2-surfaces…
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation…
We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a…
With the development of topological field theory, the mathematical tool of the tensor category was also introduced into physics. Traditional group theory corresponds to a special category,group category. Tensor categories can describe…
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…
If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical…
Quantum computing is rapidly emerging as a promising technology for solving complex optimization problems that arise in various engineering fields. Therefore, it holds significant promise to transform the computational foundations of power…
From the philosopher's perspective, the interest in quantum computation stems primarily from the way that it combines fundamental concepts from two distinct sciences: physics (especially quantum mechanics) and computer science, each long a…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
This paper presents a novel semantics for a quantum programming language by operator algebras, which are known to give a formulation for quantum theory that is alternative to the one by Hilbert spaces. We show that the opposite category of…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
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…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…
We develop a general theory of jump operators, which is intended to provide an abstraction of the notion of "limit-computability" on represented spaces. Jump operators also provide a framework with a strong categorical flavor for…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
We consider the issue of computability at the most fundamental level of physical reality: the Planck scale. To this aim, we consider the theoretical model of a quantum computer on a non commutative space background, which is a computational…