Related papers: A diagrammatic calculus for categorical quantum pr…
We study structures which have arisen in recent work by the present author and Bob Coecke on a categorical axiomatics for Quantum Mechanics; in particular, the notion of strongly compact closed category. We explain how these structures…
The key obstacle to the realization of a scalable quantum computer is overcoming environmental and control errors. Topological quantum computation has attracted great attention because it has emerged as one of the most promising approaches…
We present a stack model for breaking down the complexity of entanglement-based quantum networks. More specifically, we focus on the structures and architectures of quantum networks and not on concrete physical implementations of network…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…
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…
The word problem for categories with free products and coproducts (sums), SP-categories, is directly related to the problem of determining the equivalence of certain processes. Indeed, the maps in these categories may be directly…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these `lattice spacing' weights do not have to be independent of the direction of the arrow. We use this…
Quantum tomography is an important tool for obtaining information about the quantum state from experimental data. In this study, we conduct a comparative analysis of various quantum tomography protocols, including protocols based on highly…
Optically connecting quantum bits can effectively reduce decoherence and facilitate long-distance communication. Optically addressable spin-bearing molecules have been demonstrated to have a good potential for quantum computing. In this…
We study quantization of a class of inhomogeneous Lie bialgebras which are crossproducts in dual sectors with Abelian invariant parts. This class forms a category stable under dualization and the double operations. The quantization turns…
Quantum coherence was recently formalized as a physical resource to measure the strength of superposition. Based on the resource theory, we present a systematic framework that connects a coherence measure to the security of quantum key…
Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of…
Connectedness and bipartiteness are basic properties of classical graphs, and the purpose of this paper is to investigate the case of quantum graphs. We introduce the notion of connectedness and bipartiteness of quantum graphs in terms of…
Blind quantum computation is a secure delegated quantum computing protocol where Alice who does not have sufficient quantum technology at her disposal delegates her computation to Bob who has a fully-fledged quantum computer in such a way…
In this paper we study various convolution-type algebras associated with a locally compact quantum group from cohomological and geometrical points of view. The quantum group duality endows the space of trace class operators over a locally…
We present a complete methodology for testing the performances of quantum tomography protocols. The theory is validated by several numerical examples and by the comparison with experimental results achieved with various protocols for whole…
In topological quantum computation, quantum information is stored in states which are intrinsically protected from decoherence, and quantum gates are carried out by dragging particle-like excitations (quasiparticles) around one another in…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…
Simulating physical systems on near-term quantum computers often requires preparing states within constrained subspaces, like those with fixed particle number or spin. We use Lie algebraic techniques to prove that hardware-efficient gates…