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

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

11.2K
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
11.2K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

26.3K
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
26.3K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.4K
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
1.4K
Quantum Numbers02:43

Quantum Numbers

48.6K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
48.6K
Atomic Orbitals02:44

Atomic Orbitals

42.3K
An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.
42.3K
VSEPR Theory02:37

VSEPR Theory

13.5K
Valence shell electron-pair repulsion theory (VSEPR theory) enables us to predict the molecular structure around a central atom from an examination of the number of bonds and lone electron pairs in its Lewis structure. The VSEPR model assumes that electron pairs in the valence shell of a central atom will adopt an arrangement that minimizes repulsions between these electron pairs by maximizing the distance between them. The electrons in the valence shell of a central atom form either bonding...
13.5K

You might also read

Related Articles

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

Sort by
Same author

Factoring semi-primes with (quantum) SAT-solvers.

Scientific reports·2022
Same author

On speeding up factoring with quantum SAT solvers.

Scientific reports·2020
Same author

Novel Technique for Robust Optimal Algorithmic Cooling.

Physical review letters·2019
Same author

Differences in work injury risk between immigrants and natives: changes since the economic recession in Italy.

BMC public health·2019
Same author

Asymptotic bound for heat-bath algorithmic cooling.

Physical review letters·2015
Same author

Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits.

Physical review letters·2013

Related Experiment Video

Updated: Dec 25, 2025

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

7.0K

Finding shortest lattice vectors faster using quantum search.

Thijs Laarhoven1, Michele Mosca2,3,4, Joop van de Pol5

  • 11Eindhoven University of Technology, Eindhoven, The Netherlands.

Designs, Codes, and Cryptography
|April 1, 2020
PubMed
Summary

Quantum algorithms improve lattice shortest vector problem solutions. This research offers faster provable and heuristic methods, guiding post-quantum cryptography parameter selection.

Keywords:
LatticesQuantum searchShortest vector problemSieving

More Related Videos

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots
15:47

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

Published on: November 1, 2013

16.9K
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

Related Experiment Videos

Last Updated: Dec 25, 2025

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

7.0K
Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots
15:47

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

Published on: November 1, 2013

16.9K
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

Area of Science:

  • Quantum computing
  • Computational complexity theory
  • Cryptography

Background:

  • The shortest vector problem (SVP) on lattices is a foundational problem in computational geometry and cryptography.
  • Current classical algorithms for SVP have significant time complexities, posing challenges for cryptographic applications.
  • Post-quantum cryptography relies on the presumed hardness of problems like SVP.

Purpose of the Study:

  • To enhance asymptotic quantum results for solving the shortest vector problem (SVP) on lattices.
  • To provide improved quantum time complexities for both provable and heuristic SVP algorithms.
  • To guide the selection of parameters for post-quantum cryptosystems.

Main Methods:

  • Application of a quantum search algorithm to existing heuristic and provable sieve algorithms.
  • Analysis of resulting asymptotic quantum time complexities for SVP.

Main Results:

  • Provable quantum algorithms achieve a time complexity of , outperforming classical complexities and .
  • Heuristic quantum algorithms are expected to achieve a time complexity of , improving upon the classical complexity .
  • The derived quantum complexities offer a benchmark for SVP solution times.

Conclusions:

  • Quantum algorithms provide significant speedups for solving the shortest vector problem on lattices.
  • These findings are crucial for assessing the security and parameter choices in post-quantum cryptography.
  • The study highlights the potential impact of quantum computation on cryptographic hardness assumptions.