Related papers: Circuit pedantry
Cirquent calculus is a proof system manipulating circuit-style constructs rather than formulas. Using it, this article constructs a sound and complete axiomatization CL16 of the propositional fragment of computability logic (the…
A quantum robot is a mobile quantum system including an on bord quantum computer and ancillary systems, that interact with an environment of quantum systems. Quantum robots carry out tasks whose goals include carrying out measurements and…
Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing gate -- commonly chosen to be the…
Circuit diagrams have been used in electrical engineering for decades to describe the wiring of devices and facilities. They depict electrical components in a symbolic and graph-based manner. While the circuit design is usually performed…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX…
Circuit algebras, introduced by Bar-Natan and the first author, are a generalization of Jones's planar algebras, in which one drops the planarity condition on "connection diagrams". They provide a useful language for the study of virtual…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
For quantum computer circuits, it is proposed that they have, besides the presently used compact graphs, an expanded system of subgraphs, in line with the quantum mechanics superposition axiom. The representation of each process by these…
We report on the idea to use colours to distinguish syntax and semantics as an educational tool in logic classes. This distinction gives also reason to reflect on some philosophical issues concerning semantics.
Logic gates can be written in terms of complex differential operators, where the inputs and outputs are holomorphic functions with several variables. Using the polar representation of complex numbers, we arrive at an immediate connection…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
Non-Newtonian calculus naturally unifies various ideas that have occurred over the years in the field of generalized thermostatistics, or in the borderland between classical and quantum information theory. The formalism, being very general,…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
A correlational dialect is introduced within the quantum theory language to give a unified treatment of finite-dimensional informational/operational quantum theories, infinite-dimensional relativistic quantum theories, and quantum gravity.…
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to…
This article exhibits a particular encoding of logic circuits into a sheaf formalism. The central result of this article is that there exists strictly more information available to a circuit designer in this setting than exists in static…
Two classically identical expressions for the mutual information generally differ when the two systems involved are quantum. We investigate this difference -- quantum discord -- and show that it can be used as a criterion for the…
We look into the ontology of quantum theory as distinct from that of the classical theory in the sciences, following a broadly Kantian tradition and distinguishing between the noumenal and phenomenal realities where the former is…
We introduce a formalism that exploits the many-input many-output nature of nodes in quantum circuits. There is a diagrammatic and an algebraic version, the latter similar to the spinor formalism of general relativity. This allows us to…