Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions

• URL: http://arxiv.org/abs/2501.09637v1
• Date: Thu, 16 Jan 2025 16:27:45 GMT
• Title: Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
• Authors: Mladen Pavicic,
• Abstract summary: Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory.<n>This study demonstrates how to generate contextual hypergraphs in any dimension using various methods.<n>We introduce innovative examples of hypergraphs extending to dimension 32.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen--Specker and non-Kochen--Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality of implemented sets. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field.

Related papers

• Many-body quantum resources of graph states [0.0]
  Characterizing the non-classical correlations of a complex many-body system is an important part of quantum technologies. We consider four topologies, namely the star graph states with edges, Tur'an graphs, $r$-ary tree graphs, and square grid cluster states. We characterize many-body entanglement depth in graph states with up to $8$ qubits in $146$ classes non-equivalent under local transformations and graph isomorphisms.
  arXiv  Detail & Related papers  (2024-10-16T12:05:19Z)
• Exploring Quantum Contextuality with the Quantum Moebius-Escher-Penrose hypergraph [0.0]
  This study presents the quantum Moebius-Escher-Penrose hypergraph, drawing inspiration from paradoxical constructs such as the Moeobius strip and Penrose's impossible objects'
  arXiv  Detail & Related papers  (2024-09-16T11:17:53Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Non-Kochen-Specker Contextuality [0.0]
  We show how to generate non-Kochen-Specker hypergraphs in any dimension. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure.
  arXiv  Detail & Related papers  (2023-07-30T23:16:36Z)
• Assessing requirements to scale to practical quantum advantage [56.22441723982983]
  We develop a framework for quantum resource estimation, abstracting the layers of the stack, to estimate resources required for large-scale quantum applications. We assess three scaled quantum applications and find that hundreds of thousands to millions of physical qubits are needed to achieve practical quantum advantage. A goal of our work is to accelerate progress towards practical quantum advantage by enabling the broader community to explore design choices across the stack.
  arXiv  Detail & Related papers  (2022-11-14T18:50:27Z)
• From Quantum Graph Computing to Quantum Graph Learning: A Survey [86.8206129053725]
  We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research.
  arXiv  Detail & Related papers  (2022-02-19T02:56:47Z)
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding [58.720142291102135]
  We define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. Our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation.
  arXiv  Detail & Related papers  (2021-09-27T12:56:01Z)
• Quantum verification and estimation with few copies [63.669642197519934]
  The verification and estimation of large entangled systems represents one of the main challenges in the employment of such systems for reliable quantum information processing. This review article presents novel techniques focusing on a fixed number of resources (sampling complexity) and thus prove suitable for systems of arbitrary dimension. Specifically, a probabilistic framework requiring at best only a single copy for entanglement detection is reviewed, together with the concept of selective quantum state tomography.
  arXiv  Detail & Related papers  (2021-09-08T18:20:07Z)
• Quantum Contextuality [0.0]
  Quantum contextual sets are resources for universal quantum computation, quantum steering and quantum communication. Discriminators considered are inequalities defined for hypergraphs whose structure and generation are determined by their basic properties. Results are obtained by making use of universal automated algorithms which generate hypergraphs with both odd and even numbers of hyperedges in any odd and even dimensional space.
  arXiv  Detail & Related papers  (2021-08-02T15:11:53Z)
• Graph-theoretic approach to dimension witnessing [0.0]
  We present a novel approach to quantum dimension witnessing for scenarios with one preparation and several measurements. We identify novel quantum dimension witnesses, including a family that can certify arbitrarily high quantum dimensions with few events.
  arXiv  Detail & Related papers  (2020-07-21T12:18:52Z)
• Spectra of Perfect State Transfer Hamiltonians on Fractal-Like Graphs [62.997667081978825]
  We study the spectral features, on fractal-like graphs, of Hamiltonians which exhibit the special property of perfect quantum state transfer. The essential goal is to develop the theoretical framework for understanding the interplay between perfect quantum state transfer, spectral properties, and the geometry of the underlying graph.
  arXiv  Detail & Related papers  (2020-03-25T02:46:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.