Probabilistic generation of quantum contextual sets

2014 37th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO)

2014

Finding even the simplest Kochen-Specker sets for contextual experiments-a hot subject in the field of quantum information theory, theoretically and experimentally-by brute force would take all the clusters on Earth more than the Age of Universe. Human ingenuity found about a dozen such sets in the last 40 years. I will present how our group reduced this finding of contextual needles in a haystack to a manageable task, by first visualising them via hypergraphs, human-derived from the space symmetries, and then running jobs that generate the sets-billions of them-in parallel.

“…Details of the programs mmpstrip, states01, vectorfind, and shortd and the algorithms behind them are given in [6]- [9].…”

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 98%

Obtaining massive data sets for contextual experiments in quantum information

2014 37th International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO)

2014

“…A number of examples are given below. We generate, process, and handle MMP hypergraphs by means of algorithms in the programs SHORTD, MMP-STRIP, MMPSUBGRAPH, VECFIND, STATES01, and others [21,34,37,45,47,49]. We have also defined extensions to the notation (prefixes and suffixes) that allow us to attach additional information such as a vector assignment to the vertices [48].…”

Section: Contextual Hypergraph Language-algorithms and Programsmentioning

confidence: 99%

“…Most of the results in the paper are generated within our hypergraph language and its algorithms and programs written in C we developed in [21,34,36,37,[45][46][47][48] and extended here, as well as the parity-proof algorithms and programs developed in [23,35,38,42].…”

Section: Introductionmentioning

confidence: 99%

Vector generation of contextual sets

Megill

2019

EPJ Web Conf.

Self Cite

As quantum contextuality proves to be a necessary resource for universal quantum computation, we present a general method for vector generation of Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method supersedes all three previous methods: (i) fortuitous discoveries of smallest KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random downward generation of sets from fortuitously obtained big master sets. In contrast to previous works, we can generate master sets which contain all possible KS sets starting with nothing but a few simple vector components. From them we can readily generate all KS sets obtained in the last half a century and any specified new KS sets. Herewith we can generate sufficiently large sets as well as sets with definite required features and structures to enable varieties of different implementations in quantum computation and communication.

“…To date, all papers on KS sets in the literature have been focused on (i) discovering or implementing smallest sets (e.g., [28]), or on (ii) an exhaustive upward hypergraph-generation of sets, e.g., [29], or on (iii) a top-down, random downward generation of sets from fortuitously obtained master sets (e.g., [23,[30][31][32][33][34][35][36][37][38][39]), or on (iv) generating sets in higher dimensions from the ones in smaller dimensions (e.g., [40][41][42]), or on (v) generating big master sets from simple vector components in order to compare them with master sets obtained via (i-iii) methods ( [43]).…”

Section: Introductionmentioning

confidence: 99%

Automated generation of Kochen-Specker sets

Waegell

Megill

et al. 2019

Sci Rep

Self Cite

Quantum contextuality turns out to be a necessary resource for universal quantum computation and also has applications in quantum communication. Thus it becomes important to generate contextual sets of arbitrary structure and complexity to enable a variety of implementations. In recent years, such generation has been done for contextual sets known as Kochen-Specker sets. Up to now, two approaches have been used for massive generation of non-isomorphic Kochen-Specker sets: exhaustive generation up to a given size and downward generation from master sets and their associated coordinatizations. Master sets were obtained earlier from serendipitous or intuitive connections with polytopes or Pauli operators, and more recently from arbitrary vector components using an algorithm that generates orthogonal vector groupings from them. However, both upward and downward generation face an inherent exponential complexity barrier. In contrast, in this paper we present methods and algorithms that we apply to downward generation that can overcome the exponential barrier in many cases of interest. These involve tailoring and manipulating Kochen-Specker master sets obtained from a small number of simple vector components, filtered by the features of the sets we aim to obtain. Some of the classes of Kochen-Specker sets we generate contain all previously known ones, and others are completely novel. We provide examples of both kinds in 4- and 6-dim Hilbert spaces. We also give a brief introduction for a wider audience and a novice reader.