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

Bergfeld, Jort M.; Sack, Joshua

doi:10.1007/s00500-015-1802-6

Cited by 10 publications

(7 citation statements)

References 30 publications

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“…In complexity theory, Hilbert quantum logic provides an example of an N P R -complete (Blum-Shub-Smale complete) problem; see [55]. While the classical quantum logics express relationships among static testable properties of a quantum system, the Logic of Quantum Programs (LQP) provides a more dynamic approach capable of describing non-probabilistic properties of quantum programs (see [56] and [57]). Putting logic into a different context, one could introduce Logical Bell Inequalities (see [58], especially sections IA and IB).…”

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

Self Cite

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“…In particular, they make use of the probabilistic logic of quantum programs to provide a formal specification of the quantum voting protocol for anonymous surveying with its correctness. Applications to quantum key distribution protocol and to quantum leader election protocol, that aims to randomly select a leader in a group of agents, are shown in [17].…”

Section: Inputmentioning

confidence: 99%

Quantum Uncertainties and Holism Seem to Render Irrelevant Qudit-Semantics

Leporini

2021

Entropy

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We consider a semantics based on the peculiar holistic features of the quantum formalism. Any formula of the language gives rise to a quantum circuit that transforms the density operator associated to the formula into the density operator associated to the atomic subformulas in a reversible way. The procedure goes from the whole to the parts against the compositionality-principle and gives rise to a semantic characterization for a new form of quantum logic that has been called “Łukasiewicz quantum computational logic”. It is interesting to compare the logic based on qubit-semantics with that on qudit-semantics. Having in mind the relationships between classical logic and Łukasiewicz-many valued logics, one could expect that the former is stronger than the fragment of the latter. However, this is not the case. From an intuitive point of view, this can be explained by recalling that the former is a very weak form of logic. Many important logical arguments, which are valid either in Birkhoff and von Neumann’s quantum logic or in classical logic, are generally violated.

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“…Axioms of epistemic logic are valid because

is an equivalence relation. The validity of axioms of probability can be found in [ 21 ]. The rules MP and US are valid in all logical systems.…”

Section: Categorical Logic For Quantum Programsmentioning

confidence: 99%

“…The logic for quantum programs (LQP) [ 17 , 18 , 19 , 20 , 21 ] is an extension of traditional quantum logic and quantum Hoare logic. It has been used to verify quantum search algorithms [ 20 ], quantum leader election [ 20 ], quantum key distribution [ 21 ] and quantum voting [ 22 ]. The expressive power of LQP is largely determined by the constant symbols it incorporates.…”

Section: Introductionmentioning

confidence: 99%

A First Step to the Categorical Logic of Quantum Programs

Sun

2020

Entropy

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The long-term goal of our research is to develop a powerful quantum logic which is useful in the formal verification of quantum programs and protocols. In this paper we introduce the basic idea of our categorical logic of quantum programs (CLQP): It combines the logic of quantum programming (LQP) and categorical quantum mechanics (CQM) such that the advantages of both LQP and CQM are preserved while their disadvantages are overcome. We present the syntax, semantics and proof system of CLQP. As a proof-of-concept, we apply CLQP to verify the correctness of Deutsch’s algorithm and the concealing property of quantum bit commitment.

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

Cited by 10 publications

References 30 publications

Quantum Undergraduate Education and Scientific Training

Quantum Undergraduate Education and Scientific Training

Quantum Uncertainties and Holism Seem to Render Irrelevant Qudit-Semantics

A First Step to the Categorical Logic of Quantum Programs

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