Non-Equilibrium Quantum Many-Body Physics with Quantum Circuits
arXiv:2601.22375 · doi:10.21468/SciPostPhysLectNotes.124
Abstract
These are the notes for the 4.5-hour course with the same title that I delivered in August 2025 at the Les Houches summer school ``Exact Solvability and Quantum Information''. In these notes I pedagogically introduce the setting of brickwork quantum circuits and show that it provides a useful framework to study non-equilibrium quantum many-body dynamics in the presence of local interactions. I first show that brickwork quantum circuits evolve quantum correlations in a way that is fundamentally similar to local Hamiltonians, and then present examples of brickwork quantum circuits where, surprisingly, one can compute exactly several relevant dynamical and spectral properties in the presence of non-trivial interactions.
49 pages, 6 figures; v2 minor changes
References in corpus (45)
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Time-dependence of correlation functions following a quantum quench
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Quantum Entanglement Growth Under Random Unitary Dynamics
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Ballistic spreading of entanglement in a diffusive nonintegrable system
- Entanglement and thermodynamics after a quantum quench in integrable systems
- Random Quantum Circuits
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Entanglement Tsunami: Universal Scaling in Holographic Thermalization
- Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
- Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
- Quasilocal charges in integrable lattice systems
- Random Quantum Circuits are Approximate 2-designs
- Semiclassical Foundation of Universality in Quantum Chaos
- Solution of a minimal model for many-body quantum chaos
- Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
- Emergent statistical mechanics of entanglement in random unitary circuits
- Spectral statistics in spatially extended chaotic quantum many-body systems
- Exact dynamics in dual-unitary quantum circuits
- Operator space entanglement entropy in transverse Ising chain
- Entanglement spreading in a minimal model of maximal many-body quantum chaos
- Unitary circuits of finite depth and infinite width from quantum channels
- The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
- Sub-ballistic growth of Rényi entropies due to diffusion
- Is efficiency of classical simulations of quantum dynamics related to integrability?
- The entanglement membrane in chaotic many-body systems
- Quantum algorithm for simulating real time evolution of lattice Hamiltonians
- Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
- Exact convergence times for generation of random bipartite entanglement
- Entanglement dynamics in hybrid quantum circuits
- Entanglement spreading in non-equilibrium integrable systems
- Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
- Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
- The Weingarten Calculus
- Maximal entanglement velocity implies dual unitarity
- Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
- Many-Body Quantum Chaos and Space-time Translational Invariance
- Translation symmetry restoration under random unitary dynamics
- Growth of entanglement of generic states under dual-unitary dynamics
- Non-equilibrium dynamics of charged dual-unitary circuits
- Exactly solvable many-body dynamics from space-time duality
- Entanglement of Disjoint Intervals in Dual-Unitary Circuits: Exact Results
- Growth of Rényi Entropies in Interacting Integrable Models and the Breakdown of the Quasiparticle Picture
- Les Houches lectures on random quantum circuits and monitored quantum dynamics