Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Circuits01:17

Linear Circuits

777
A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant 'k,' the voltage likewise...
777
Classification of Systems-I01:26

Classification of Systems-I

515
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
515
Linear time-invariant Systems01:23

Linear time-invariant Systems

821
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
821
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

56.3K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
56.3K
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

58.6K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
58.6K
Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

171
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
171

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

The physical Church-Turing thesis and non-deterministic computation over the real numbers.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2012
See all related articles

Related Experiment Video

Updated: Jan 3, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.6K

Two linearities for quantum computing in the lambda calculus.

Alejandro Díaz-Caro1, Gilles Dowek2, Juan Pablo Rinaldi3

  • 1CONICET-UBA, ICC, Pabellón 1, Ciudad Universitaria, Buenos Aires, Argentina; Universidad Nacional de Quilmes, R. Sáenz Peña 352, Bernal, BA, Argentina.

Bio Systems
|November 24, 2019
PubMed
Summary
This summary is machine-generated.

We unify logical and algebraic approaches to non-cloning in quantum lambda-calculi. Our quantum calculus allows superpositional types to be linear while permitting cloning of basis vectors.

Keywords:
Algebraic linearityLambda-calculusLinear logicMeasurementQuantum computing

More Related Videos

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

1.0K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.9K

Related Experiment Videos

Last Updated: Jan 3, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.6K
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

1.0K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.9K

Area of Science:

  • Quantum computing
  • Theoretical computer science
  • Linear algebra

Background:

  • Non-cloning is crucial in quantum computing.
  • Existing approaches include logical and algebraic linearities.
  • Unifying these approaches can lead to a more comprehensive understanding.

Purpose of the Study:

  • To propose a unified framework for non-cloning in quantum lambda-calculi.
  • To integrate logical and algebraic linearity concepts.
  • To develop a novel quantum lambda-calculus with specific type properties.

Main Methods:

  • Defining a quantum extension of the first-order simply-typed lambda-calculus.
  • Introducing linearity for superposed types.
  • Allowing cloning for basis vectors.
  • Providing an interpretation of types as vector spaces and bases.

Main Results:

  • A unified approach to non-cloning in quantum lambda-calculi is presented.
  • The proposed calculus features types that are linear on superposition but allow basis vector cloning.
  • A clear interpretation of superposed and non-superposed types is established.

Conclusions:

  • The unified framework enhances the understanding of non-cloning principles in quantum computation.
  • The developed calculus offers a novel perspective on type linearity and vector space interpretation.
  • This work provides a foundation for further research in quantum programming languages and theoretical quantum mechanics.