Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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.

First-Order Circuits

First-Order Circuits

First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...

Second-Order Circuits

Second-Order Circuits

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...

Ampere-Maxwell's Law: Problem-Solving

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...

Design Example: Capacitance Multiplier Circuit

Design Example: Capacitance Multiplier Circuit

In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.

Hybridization of Atomic Orbitals II

Hybridization of Atomic Orbitals II

sp3d and sp3d 2 Hybridization

You might also read

Related Articles

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

Sort by

Same author

Generalised quantum computational spectroscopy on a quantum chip.

Nature communications·2026

Same author

Alterations in Metabolites Associated With Umbilical Cord Blood in Monozygotic Twins Discordant for Congenital Heart Disease.

Pediatric discovery·2026

Same author

What are the primary roles of peroxidases in enzymatic browning of fresh-cut fruits and vegetables, browning promoters or ROS scavengers?

Frontiers in nutrition·2026

Same author

No cloning of quantum ensembles.

Nature communications·2026

Same author

Atrophy of specific amygdala subregion precedes the conversion from mild cognitive impairment with neuropsychiatric symptoms to dementia.

International psychogeriatrics·2026

Same author

Finite element analysis of impacted canine disimpaction: effects of anchorage systems and T-loop gable bend angles.

Frontiers in bioengineering and biotechnology·2026

Search research articles

Related Experiment Video

Updated: Aug 16, 2025

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

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

Published on: May 30, 2014

Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications.

Xiao-Ming Zhang¹, Tongyang Li¹, Xiao Yuan¹

¹Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China and School of Computer Science, Peking University, Beijing 100871, China.

Physical Review Letters

|December 23, 2022

Summary

We developed a faster quantum state preparation algorithm for sparse quantum states, significantly reducing circuit depth. This advance offers exponential speedups for key quantum computing tasks like solving linear systems.

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Related Experiment Videos

Last Updated: Aug 16, 2025

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

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

Published on: May 30, 2014

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Area of Science:

Quantum Computing
Quantum Information Science

Background:

Quantum state preparation is crucial for quantum algorithms.
Current methods can be resource-intensive in terms of circuit depth or qubit count.

Purpose of the Study:

To develop efficient quantum state preparation algorithms.
To reduce circuit depth and resource requirements for sparse quantum states.

Main Methods:

Designing a novel quantum circuit for state preparation.
Analyzing circuit depth and ancillary qubit requirements.
Investigating applications in Hamiltonian simulation, linear systems, and quantum RAM.

Main Results:

Any n-qubit state preparation requires Θ(n)-depth circuits.
Sparse states (d nonzero entries) can be prepared with Θ(log(nd)) depth using O(ndlogd) ancillary qubits.
Achieved exponential speedups for Hamiltonian simulation, linear systems, and quantum RAM.

Conclusions:

The new algorithm offers significant improvements for sparse state preparation.
Demonstrated exponential circuit depth reductions for critical quantum computing applications.
Identified new quantum algorithms for linear systems with exponential speedups.