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

11.4K
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...
11.4K
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

26.5K
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:
26.5K
Chemical Formulas02:52

Chemical Formulas

60.8K
A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of elements and numbers. At times other symbols, such as dashes, parentheses, brackets, commas, plus, and minus signs, are also used. A chemical formula can be one of three types – molecular, empirical, and structural.
60.8K
Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations14:33

Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations

14.8K
Flue gas from power plants is a cheap CO2 source for algal growth. We have built prototype "flue gas to algal cultivation" systems and described how to scale up the algal cultivation process. We have demonstrated the use of a mass-transfer bio-reaction model to simulate and to design the optimal operation of flue gas for the growth of Chlorella sp. in algal...
14.8K
Ionic Compounds: Formulas and Nomenclature03:34

Ionic Compounds: Formulas and Nomenclature

86.1K
An element composed of atoms that readily lose electrons (a metal) can react with an element composed of atoms that readily gain electrons (a nonmetal) to produce ions through complete electron transfer. The compound formed by this transfer is stabilized by the electrostatic attractions (ionic bonds) between the oppositely charged ions.
86.1K
Molecular Compounds: Formulas and Nomenclature03:10

Molecular Compounds: Formulas and Nomenclature

55.2K
Molecular compounds or covalent compounds result when atoms share electrons to form covalent bonds. Since there is no electron transfer, molecular compounds do not contain ions; instead, they consist of discrete, neutral molecules. 
55.2K

You might also read

Related Articles

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

Sort by
Same author

Voriconazole therapeutic drug monitoring and safety in HIV-infected patients with invasive fungal disease.

Frontiers in pharmacology·2026
Same author

Advancing synthetic biology with engineered chemically inducible gene regulatory systems.

Biotechnology advances·2026
Same author

Listeria survival dynamics on pears under real-world storage: effects of variety, production practice, storage, and decay.

Food microbiology·2026
Same author

Validation of sanitizer efficacy in commercial apple dump tanks using a Listeria monocytogenes surrogate.

Food microbiology·2026
Same author

Multi-omics-based characterization and differentiation of fecal microbiota and metabolite profiles in high- and low-yielding laying hens.

Poultry science·2026
Same author

Regression-based model for predicting preterm birth using vaginal lactobacilli and routine clinical data.

BMC pregnancy and childbirth·2026

Related Experiment Video

Updated: Jan 20, 2026

Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations
14:33

Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations

Published on: October 1, 2013

14.8K

Nearly Optimal Lattice Simulation by Product Formulas.

Andrew M Childs1, Yuan Su1

  • 1Department of Computer Science, Institute for Advanced Computer Studies, and Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA.

Physical Review Letters
|September 7, 2019
PubMed
Summary
This summary is machine-generated.

We provide a rigorous proof for the gate complexity of simulating quantum Hamiltonians using product formulas. This method achieves nearly optimal gate complexity for lattice Hamiltonians, advancing quantum computation.

More Related Videos

Lattice Centering and Coordination Number
02:33

Lattice Centering and Coordination Number

11.4K
Trends in Lattice Energy: Ion Size and Charge
02:54

Trends in Lattice Energy: Ion Size and Charge

26.5K

Related Experiment Videos

Last Updated: Jan 20, 2026

Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations
14:33

Optimize Flue Gas Settings to Promote Microalgae Growth in Photobioreactors via Computer Simulations

Published on: October 1, 2013

14.8K
Lattice Centering and Coordination Number
02:33

Lattice Centering and Coordination Number

11.4K
Trends in Lattice Energy: Ion Size and Charge
02:54

Trends in Lattice Energy: Ion Size and Charge

26.5K

Area of Science:

  • Quantum Computing
  • Quantum Simulation
  • Computational Complexity

Background:

  • Simulating n-qubit Hamiltonians with nearest-neighbor interactions is crucial for quantum computing.
  • Product formulas offer a straightforward approach for quantum simulations, experimentally validated.
  • Rigorous proof for the gate complexity of product formulas was previously lacking.

Purpose of the Study:

  • To rigorously analyze and prove the gate complexity of simulating quantum Hamiltonians using product formulas.
  • To establish error bounds for canonical product formulas, including Lie-Trotter-Suzuki.
  • To develop a local error representation for time-dependent Hamiltonian simulation.

Main Methods:

  • Analysis of the local error structure of product formulas.
  • Proof of error bounds for canonical product formulas.
  • Development of a local error representation for time-dependent simulations.

Main Results:

  • Demonstrated a gate complexity of (nt)^{1+o(1)} for simulating n-qubit Hamiltonians with nearest-neighbor interactions.
  • Established rigorous error bounds for canonical product formulas.
  • Developed a local error representation applicable to time-dependent simulations.

Conclusions:

  • Product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.
  • The findings provide a rigorous justification for the efficiency of product formulas in quantum simulation.
  • The developed methods offer generalizations for various simulation scenarios.