Related papers: Quantum Weakest Preconditions
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
Quantum computers require quantum logic, something fundamentally different to classical Boolean logic. This difference leads to a greater efficiency of quantum computation over its classical counter-part. In this review we explain the basic…
We introduce a new kind of expectation transformer for a mixed classical-quantum programming language. Our semantic approach relies on a new notion of a cost structure, which we introduce and which can be seen as a specialisation of the…
We develop a characterization of quantum states by means of first order variables and random variables, within a predicative logic with equality, in the framework of basic logic and its definitory equations. We introduce the notion of…
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…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…
Quantum processes with indefinite causal structure emerge when we wonder which are the most general evolutions, allowed by quantum theory, of a set of local systems which are not assumed to be in any particular causal order. These processes…
We propose a quantum programming paradigm where all data are familiar classical data, and the only non-classical element is a random number generator that can return results with negative probability. Currently, the vast majority of quantum…
The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit…
This paper outlines the construction of categorical models of higher-order quantum computation. We construct a concrete denotational semantics of Selinger and Valiron's quantum lambda calculus, which was previously an open problem. We do…
This series of introductory lectures consists of two parts. In the first part, I rapidly review the basic notions of quantum physics and many primitives of quantum information (i.e. notions that one must be somehow familiar with in the…
We explain the properties and clarify the meaning of quantum weak values using only the basic notions of elementary quantum mechanics.
For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the formally stronger finite type property of Ngai and Wang. We…
The time evolution of the two-time conditional probability of the classical stochastic process is described in an analogous form of the quantum mechanical wave equations. By using it, we emulate the same strange behaviors as those of the…
Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…
To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical…
In many domains it is desirable to assess the preferences of users in a qualitative rather than quantitative way. Such representations of qualitative preference orderings form an importnat component of automated decision tools. We propose a…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
We introduce and review briefly the phenomenon of quantum annealing and analog computation. The role of quantum fluctuation (tunneling) in random systems with rugged (free) energy landscapes having macroscopic barriers are discussed to…
Negativity in certain quasiprobability representations is a necessary condition for a quantum computational advantage. Here we define a quasiprobability representation exhibiting this property with respect to quantum computations in the…