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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...

Block Diagram Reduction

Block Diagram Reduction

The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
The first step in this process is the identification and relocation of a branch point. A branch point, where a...

Network Function of a Circuit

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.

Norton Equivalent Circuits

Norton Equivalent Circuits

Norton's theorem is a fundamental concept in the field of electrical engineering that allows for the simplification of complex AC circuits. The theorem states that any two-terminal linear network can be replaced with an equivalent circuit that consists of an impedance, which is parallel with a constant current source. Figure 1 shows the AC circuit portioned into two parts: Circuit A and Circuit B, while Figure 2 depicts the circuit obtained by replacing Circuit A by its Norton equivalent...

RL Circuits

RL Circuits

An RL circuit consists of a resistor and an inductor and may have a source of emf connected to it. The inductor in the circuit helps to prevent rapid changes in current, which can be helpful if a steady current is required but the external source has a fluctuating emf. Consider an open RL circuit connected to a source of constant emf. As soon as the circuit is closed, the current begins to increase at a rate that depends only on the value of the inductance in the circuit. The greater the...

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Related Experiment Video

Updated: May 22, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Ultrafast quantum gates in circuit QED.

G Romero¹, D Ballester, Y M Wang

¹Departamento de Química Física, Universidad del País Vasco UPV/EHU, Apartado 644, 48080 Bilbao, Spain.

Physical Review Letters

|May 1, 2012

Summary

We developed ultrafast quantum gates for circuit quantum electrodynamics, achieving high fidelity in ultrastrong coupling regimes. This breakthrough enables subnanosecond quantum operations, advancing quantum computing speed and accuracy.

Related Experiment Videos

Last Updated: May 22, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum Computing
Quantum Information Science
Quantum Electrodynamics

Background:

Implementing high-fidelity quantum gates is crucial for scalable quantum computing.
Ultrastrong coupling regimes in circuit quantum electrodynamics present unique challenges for gate implementation.
Existing methods often struggle with speed and fidelity in these demanding regimes.

Purpose of the Study:

To propose and validate a novel method for ultrafast two-qubit gates.
To ensure the method's validity in ultrastrong and deep strong coupling regimes.
To achieve high-fidelity quantum gates at subnanosecond timescales.

Main Methods:

Utilizing state-of-the-art circuit quantum electrodynamics technology.
Designing a specific qubit architecture.
Implementing a four-step sequential displacement of the intracavity field.
Performing ab initio calculations to verify performance.

Main Results:

Demonstrated the feasibility of ultrafast two-qubit gates.
Confirmed validity in ultrastrong and deep strong coupling regimes.
Achieved gate operations at subnanosecond timescales.
Maintained a fidelity exceeding 99%.

Conclusions:

The proposed method enables efficient and high-fidelity quantum gate operations.
This approach is suitable for advanced circuit quantum electrodynamics systems.
The subnanosecond gate times represent a significant advancement for quantum computation speed.