Related papers: Birkhoff style proof systems for hybrid-dynamic qu…
This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static)…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
We work out a quantum-theoretic model in complex Hilbert space of a recently performed test on co-occurrencies of two concepts and their combination in retrieval processes on specific corpuses of documents. The test violated the…
Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincar\'e--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number…
In classical two-dimensional pure dilaton gravity, and in particular in spherically symmetric pure gravity in d dimensions, the generalized Birkhoff theorem states that, for a suitable choice of coordinates, the metric coefficients are only…
We give a calculus for reasoning about the first-order fragment of classical logic that is adequate for giving the truth conditions of intuitionistic Kripke frames, and outline a proof-theoretic soundness and completeness proof, which we…
Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…
We study compound systems with a classical sector and a quantum sector. Among other consistency conditions we require a canonical structure, that is, a Lie bracket for the dynamical evolution of hybrid observables in the Heisenberg picture,…
By the method of intense terahertz laser spectroscopy, we provide strong evidence that if an integer quantum Hall (IQH) system has asymmetric confining potential and the external quantizing magnetic field has a nonzero in-plane component,…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
We introduce a quantum analogue of classical first-order logic (FO) and develop a theory of quantum first-order logic as a basis of the productive discussions on the power of logical expressiveness toward quantum computing. The purpose of…
The basic notions of quantum mechanics are formulated in terms of separable infinite dimensional Hilbert space $\mathcal{H}$. In terms of the Hilbert lattice $\mathcal{L}$ of closed linear subspaces of $\mathcal{H}$ the notions of state and…
Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant…
We discuss hybrid master equations of composite systems which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested, its consistency is derived from the consistency of Lindblad…
In this paper, we present a Hoare-style logic for reasoning about quantum programs with classical variables. Our approach offers several improvements over previous work: (1) Enhanced expressivity of the programming language: Our logic…
A holistic extension of classical propositional logic is introduced in the framework of quantum computation with mixed states. The concepts of tautology and contradiction are investigated in this extensions. A special family of quantum…
Necessary and sufficient conditions are given for the construction of a hybrid quantum computer that operates on both continuous and discrete quantum variables. Such hybrid computers are shown to be more efficient than conventional quantum…
We study the problem of constructing a general hybrid quantum-classical bracket from a partial classical limit of a full quantum bracket. Introducing a hybrid composition product, we show that such a bracket is the commutator of that…
When considering a sequent-style proof system for quantum programs, there are certain elements of quantum mechanics that we may wish to capture, such as phase, dynamics of unitary transformations, and measurement probabilities. Traditional…