Related Experiment Video
Updated: Nov 11, 2025
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
10.0K
Ergodic and Nonergodic Dual-Unitary Quantum Circuits with Arbitrary Local Hilbert Space Dimension
Pieter W Claeys1, Austen Lamacraft1
1TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
Physical Review Letters
|March 30, 2021
Summary
Researchers developed dual-unitary quantum circuits to model 1+1 dimensional systems. These circuits allow explicit calculation of dynamical correlations and tunable ergodicity, leading to insights into thermalization and prethermalization phenomena.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Condensed matter physics
Background:
- Dual-unitary quantum circuits offer a powerful framework for studying 1+1 dimensional lattice models.
- Explicit calculation of dynamical correlations in such models is crucial for understanding their behavior.
Purpose of the Study:
- To analytically construct dual-unitary circuits with controllable ergodicity.
- To investigate thermalization dynamics in both ergodic and non-ergodic regimes.
- To explore the effects of perturbations on non-ergodic circuits.
Main Methods:
- Analytical construction of dual-unitary circuits.
- Characterization of ergodicity levels for arbitrary local Hilbert space dimensions.
- Derivation of analytical results for thermalization to infinite-temperature Gibbs states and generalized Gibbs ensembles.
Main Results:
- Demonstrated the ability to create dual-unitary circuits with any desired ergodicity.
- Presented analytical results for thermalization in both ergodic (infinite-temperature Gibbs state) and non-ergodic (generalized Gibbs ensemble) systems.
- Showcased how a tunable perturbation can induce prethermalization plateaux in non-ergodic circuits without breaking dual unitarity.
Conclusions:
- Dual-unitary circuits provide a versatile tool for studying quantum dynamics and thermalization.
- The framework allows for fine-tuning of ergodicity and the emergence of complex phenomena like prethermalization.
- This work opens avenues for exploring quantum chaos and statistical mechanics in exactly solvable models.
Related Concept Videos
01:17Second-Order Circuits
2.4K
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...
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...
2.4K
01:15First-Order Circuits
2.9K
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...
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...
2.9K
01:25Network Function of a Circuit
457
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.
457
01:30Fundamental Theorem of Algebra
47
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as: with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the Complete...
47
01:34Woodward–Hoffmann Selection Rules and Microscopic Reversibility
3.5K
Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
3.5K
01:27State Space Representation
354
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Consider an RLC circuit, a...
354