Related papers: Quantum Theory in Design
This paper introduces a new inequality in algorithmic information theory that can be seen as an extended coding theorem. This inequality has applications in new bounds between quantum complexity measures.
We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
$*$-structures on quantum and braided spaces of the type defined via an R-matrix are studied. These include $q$-Minkowski and $q$-Euclidean spaces as additive braided groups. The duality between the $*$-braided groups of vectors and…
A kei, or 2-quandle, is an algebraic structure one can use to produce a numerical invariant of links, known as coloring invariants. Motivated by Mazur's analogy between prime numbers and knots, we define for every finite kei $\mathcal{K}$…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular…
This paper proposes a general framework for nonperturbatively defining continuum quantum field theories. Unlike most such frameworks, the one offered here is finitary: continuum theories are defined by reducing large but finite quantum…
Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some…
Quantum computing holds the potential to revolutionize various fields by efficiently tackling complex problems. At its core are quantum circuits, sequences of quantum gates manipulating quantum states. The selection of the right quantum…
Virtual knot theory has experienced a lot of nice features that did not appear in classical knot theory, e.g., parity and picture-valued invariants. In the present paper we use virtual knot theory effects to construct new representations of…
This article considers the problem of designing adaption and optimisation techniques for training quantum learning machines. To this end, the division algebra of quaternions is used to derive an effective model for representing computation…
A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…
Quantum computers are expected to give major speed-ups for the simulation of quantum systems. In this work, we present quantum gates that simulate the colour part of the interactions of quarks and gluons in perturbative quantum…
The field of quantum computing is at an exciting time where we are constructing novel hardware, evaluating algorithms, and finding out what works best. As qubit technology grows and matures, we need to be ready to design and program larger…
In these lecture notes I describe the theory of QCD and its application, through perturbation theory, at particle colliders.
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning, specifically the ZX-calculus, to practical…
Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum…
We introduce an addition law for the usual quantum matrices $A(R)$ by means of a coaddition $\underline{\Delta} t=t\otimes 1+1\otimes t$. It supplements the usual comultiplication $\Delta t=t\otimes t$ and together they obey a…