Duality for the Logic of Quantum Actions

Bergfeld, Jort M.; Kishida, Kohei; Sack, Joshua; Zhong, Shengyang

doi:10.1007/s11225-014-9592-x

Cited by 6 publications

(3 citation statements)

References 14 publications

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“…An alternative approach is to consider graphs whose vertex set consists of atoms in an ortholattice, and whose edges are given by Sasaki projections (see [59,Section 5.1]) and ortholattice automorphisms. See [60] and [61] for more details. Graph theory courses often include algorithms (such as traveling salesman) and some complexity theory.…”

Section: Qist In Mathematics Coursesmentioning

confidence: 99%

Quantum Undergraduate Education and Scientific Training

Perron,

DeLeone,

Sharif

et al. 2021

Preprint

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The best way to prepare undergraduates for careers in this field is still an open question. In 2016 the United States' federal government identified quantum workforce development as a priority, citing that "academic and industry representatives identify discipline-specific education as insufficient for continued progress in quantum information science." [1] More recently, the National Quantum Initiative Act was passed [2], which included the goal of creating a stronger workforce pipeline; more specifically, the goal is to "expand the number of researchers, educators, and students with training in quantum information science and technology to develop a workforce pipeline." [3] Government investments like this, as well as recent significant investments from industry in quantum information science, highlight the need for a workforce with the skills and agility to thrive in this growing field.Currently, education and workforce training in quantum information science and technology (QIST) exists primarily at the graduate and postdoctoral levels, [4] with few undergraduate efforts beginning to grow out of these. In order to meet the anticipated quantum workforce needs and to ensure that the workforce is demographically representative and inclusive to all communities, the United States must expand these efforts at the undergraduate level beyond what is occurring at larger PhD granting institutions and incorporate quantum information science into the curriculum at the nation's predominantly undergraduate institutions (PUIs). On June 3rd and 4th, 2021 the Quantum Undergraduate Education and Scientific Training (QUEST) workshop was held virtually with the goal of bringing together faculty from PUIs to learn the state of undergraduate QIST education, identify challenges associated with implementing QIST curriculum at PUIs, and to develop strategies and solutions to deal with these challenges. The first day of the workshop included three panels: 1. Establishing industry's anticipated needs This panel included Heather J. Lewandowski from the University of Colorado-Boulder and JILA, staff research scientist Daniel Sank from Google, and lead quantum technologist Isabella Bello Martinez from Booz Allen Hamilton. The goal of the panel was to inform workshop participants of what knowledge and skills are valued in the quantum industry.

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Section: Qist In Mathematics Coursesmentioning

confidence: 99%

Quantum Undergraduate Education and Scientific Training

Perron,

DeLeone,

Sharif

et al. 2021

Preprint

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“…Therefore, v is non-orthogonal to p , so there exists a unique w ∈ p such that (v, w) ∈ R p . Now w (as the projection of v onto p ) can be characterized by being the element of p where v Ru iff w Ru for all u ∈ p (see, for example, Bergfeld et al 2015, Proposition 2.15). So we have w Rx iff v Rx for all x ∈ p ⊃ p ∧ q , and therefore we have w ∈ p ∩ ∼ p ∧ q .…”

Section: Theorem 41 the Rules Inmentioning

confidence: 99%

Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs

Bergfeld

Sack

2015

Soft Comput

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This paper presents a sound axiomatization for a probabilistic modal dynamic logic of quantum programs. The logic can express whether a state is separable or entangled, information that is local to a subsystem of the whole quantum system, and the probability of positive answers to quantum tests of certain properties. The power of this axiomatization is demonstrated with proofs of properties concerning bases of a finite-dimensional Hilbert space, composite systems, entangled and separable states, and with proofs of the correctness of two probabilistic quantum protocols (the quantum leader election protocol and the BB84 quantum key distribution protocol).

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“…Categorical equivalences with quantum significance include those between quantum geometries and quantum lattices (between Hilbert geometries and propositional systems, as well as projective geometries and projective lattices), as given in [7], and significant categorical dualities include those between quantum lattices and quantum graph-like structures (between Piron lattices and quantum dynamic algebras), as given in [3]. Our equivalence connects quantales to these structures by connecting them to a class of lattices that includes propositional systems and Piron lattices.…”

Section: Introductionmentioning

confidence: 99%

Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices

et al. 2017

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This paper provides a categorical equivalence between two types of quantum structures. One is a complete orthomodular lattice, which is used for reasoning about testable properties of a quantum system. The other is an orthomodular dynamic algebra, which is a quantale used for reasoning about quantum actions. The result extends to more restrictive lattices than orthomodular lattices, and includes Hilbert lattices of closed subspaces of a Hilbert space. These other lattice structures have connections to a wide range of different quantum structures; hence our equivalence establishes a categorical connection between quantales and a great variety of quantum structures.

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Duality for the Logic of Quantum Actions

Cited by 6 publications

References 14 publications

Quantum Undergraduate Education and Scientific Training

Quantum Undergraduate Education and Scientific Training

Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs

Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices

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