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

Laws of Logarithms I01:30

Laws of Logarithms I

353
Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log⁡(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions...
353
Laws of Logarithms II01:28

Laws of Logarithms II

309
Logarithmic laws provide essential tools for simplifying and evaluating exponential expressions, particularly in mathematical and applied settings where powers and repeated multiplication play a central role. Two important rules are the power law and the change-of-base formula, both allowing for transforming expressions into more manageable forms.The power law of logarithms states that the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the base...
309
Logarithmic Differentiation01:28

Logarithmic Differentiation

83
When a car’s weight and driving forces act on a tire, they impose an external load on the rubber material. This load is resisted internally by forces distributed throughout the tire structure, which are defined as stress. The resulting deformation of the rubber due to this stress is quantified as strain. The relationship between stress and strain governs how the tire deforms under load and is central to understanding its mechanical response during operation.Rubber exhibits a nonlinear...
83
Derivatives of Logarithmic Functions01:22

Derivatives of Logarithmic Functions

113
Logarithmic and Exponential RelationshipA logarithmic function is the inverse of an exponential function. If y = logb x then, it can be rewritten as by = x. This relationship allows for implicit differentiation, making logarithmic functions useful in calculus. Logarithmic scales are widely used to represent data that span multiple orders of magnitude, such as earthquake magnitudes (Richter scale) and sound intensity (decibels).Differentiation of Logarithmic FunctionsTo differentiate y = logb x,...
113
Molecular Orbital Theory I02:35

Molecular Orbital Theory I

47.9K
Overview of Molecular Orbital Theory
47.9K
Applications of Logarithms01:28

Applications of Logarithms

304
Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...
304

You might also read

Related Articles

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

Sort by
Same author

Adaptive hybrid optimal quantum control for imprecisely characterized systems.

Physical review letters·2014
Same author

Observation of measurement-induced entanglement and quantum trajectories of remote superconducting qubits.

Physical review letters·2014
Same author

Multimode circuit quantum electrodynamics with hybrid metamaterial transmission lines.

Physical review letters·2013
Same author

Microwave photon counter based on Josephson junctions.

Physical review letters·2011
Same author

Efficient creation of multipartite entanglement in flux qubits.

Nanotechnology·2010
Same author

Simple pulses for elimination of leakage in weakly nonlinear qubits.

Physical review letters·2009
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: Feb 19, 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

9.8K

Linear and Logarithmic Time Compositions of Quantum Many-Body Operators.

F Motzoi1, M P Kaicher2, F K Wilhelm2

  • 1Department of Physics and Astronomy, Aarhus University, 8000 Aarhus, Denmark.

Physical Review Letters
|November 4, 2017
PubMed
Summary
This summary is machine-generated.

Researchers developed a new framework for constructing complex quantum many-body interactions efficiently. These methods significantly reduce time and space requirements for quantum computations, improving scalability.

More Related Videos

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

15.1K
Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

13.3K

Related Experiment Videos

Last Updated: Feb 19, 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

9.8K
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

15.1K
Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

13.3K

Area of Science:

  • Quantum Computing
  • Quantum Information Science
  • Computational Physics

Background:

  • Constructing complex quantum many-body interactions is crucial for advancing quantum simulation and computation.
  • Current methods for implementing these interactions can be resource-intensive in terms of time and qubit overhead.
  • Developing efficient and scalable protocols is essential for realizing the potential of quantum technologies.

Purpose of the Study:

  • To introduce a generalized framework for constructing many-body-interaction operations.
  • To provide protocols that operate in linear or logarithmic time with linear ancilla qubits.
  • To offer exact gate decompositions for various complex quantum operations.

Main Methods:

  • A linear time protocol utilizing superposition of operator strings and dynamical decoupling.
  • A logarithmic time protocol employing ancilla registers and parallel chaining operations.
  • Development of exact gate decompositions for Pauli strings, Toffoli gates, and other many-body operators.

Main Results:

  • Demonstrated linear and logarithmic time protocols for constructing many-body interactions.
  • Achieved substantial reductions in time and space complexity compared to existing strategies.
  • Showcased applicability to diverse physical interaction mechanisms (e.g., CNOT, XX, XX+YY).

Conclusions:

  • The developed framework offers significant improvements in efficiency and scalability for quantum computations.
  • The protocols are versatile and applicable to a broad range of many-body operators and physical systems.
  • This work paves the way for more complex and resource-efficient quantum simulations and algorithms.