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

First Order Systems01:21

First Order Systems

167
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
167
Second Order systems II01:18

Second Order systems II

177
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
177
Second Order systems I01:20

Second Order systems I

245
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
245
Second-order Op Amp Circuits01:19

Second-order Op Amp Circuits

434
Implementing second-order low-pass filters in audio systems is crucial in refining audio signals by eliminating undesirable high-frequency noise. These filters typically involve second-order op-amp circuits configured as voltage followers, encompassing two nodes with distinct storage elements.
The analysis of such circuits follows a systematic approach, similar to the second-order RLC circuits. In practical scenarios, bulky inductors are rarely employed due to their size and weight. This means...
434
Second-Order Circuits01:17

Second-Order Circuits

1.7K
Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
1.7K
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

430
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
430

You might also read

Related Articles

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

Sort by
Same author

Quantum-enhanced Markov chain Monte Carlo.

Nature·2023
Same author

Bias in Error-Corrected Quantum Sensing.

Physical review letters·2022
Same author

Efficient Quantum Error Correction of Dephasing Induced by a Common Fluctuator.

Physical review letters·2020
Same author

Ancilla-Free Quantum Error Correction Codes for Quantum Metrology.

Physical review letters·2019
Same author

Experimental validation of optimum input polarization states for Mueller matrix determination with a dual photoelastic modulator polarimeter.

Optics letters·2013
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: Sep 20, 2025

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

5.1K

First-Order Trotter Error from a Second-Order Perspective.

David Layden1

  • 1IBM Quantum, Almaden Research Center, San Jose, California 95120, USA.

Physical Review Letters
|June 10, 2022
PubMed
Summary
This summary is machine-generated.

We simplify understanding of quantum dynamics simulation errors using the Trotter formula. Our method provides a more accurate error bound, reducing circuit depth for quantum simulations.

More Related Videos

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior
06:38

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior

Published on: June 9, 2020

5.0K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.7K

Related Experiment Videos

Last Updated: Sep 20, 2025

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

5.1K
Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior
06:38

Using a Virtual Reality Walking Simulator to Investigate Pedestrian Behavior

Published on: June 9, 2020

5.0K
Experimental Methods to Study Human Postural Control
08:12

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

9.7K

Area of Science:

  • Quantum computing
  • Computational physics
  • Quantum information science

Background:

  • Quantum computers promise to simulate complex quantum dynamics intractable for classical systems.
  • Trotter-based algorithms are key near-term quantum simulation methods, but their approximation errors are not fully understood.
  • Anomalously low errors and unexpected scaling have been reported for Hamiltonians of the form H=H₁+H₂.

Purpose of the Study:

  • To provide a simplified explanation for observed low approximation errors in Trotter-based quantum simulations.
  • To develop a generalized and more robust method for bounding simulation errors.
  • To elucidate the origins of errors within the quantum circuit for H=H₁+H₂ systems.

Main Methods:

  • Relating the standard Trotter formula to its second-order variant for Hamiltonians H=H₁+H₂.
  • Developing a generalized error bound that overcomes limitations of previous studies.
  • Numerical comparison of the derived error bound against the true simulation error.

Main Results:

  • A simpler theoretical picture of error behavior in Trotter-Suzuki methods for H=H₁+H₂ systems.
  • Generalized error bounds that closely match numerical results over a wide range of simulation parameters.
  • Demonstration of how specific components of the quantum circuit contribute to the total simulation error.

Conclusions:

  • The developed method offers a more accurate and broadly applicable way to bound quantum simulation errors.
  • Findings reduce the necessary quantum circuit depth for certain quantum simulation tasks.
  • This work provides insights into error mechanisms and a framework for analyzing simulation fidelity.