Les Houches lectures on random quantum circuits and monitored quantum dynamics

Romain Vasseur

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Les Houches lectures on random quantum circuits and monitored quantum dynamics

Romain Vasseur

Quantum Physics · Submitted 19 Feb 2026 · Published version

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to be generically intractable.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,338 input tokens.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

These lecture notes are based on lectures given by the author at the Les Houches 2025 summer school on "Exact Solvability and Quantum Information". The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to be generically intractable.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	These lecture notes are based on lectures given by the author at the Les Houches 2025 summer school on "Exact Solvability and Quantum Information".	background 0.98	0.52	0.02	asserted 0.99
s1	The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to be generically intractable.	contribution 0.89	0.19	0.17	asserted 0.55

What kind of paper the classifier reports this is: review 0.92 · evidence from argument 0.72.

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The paper

Original abstract

These lecture notes are based on lectures given by the author at the Les Houches 2025 summer school on "Exact Solvability and Quantum Information". The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to be generically intractable.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Surviving readout errors and incomplete postselection in monitored quantum circuits
quant-ph 2026-10 accept novelty 6.0 of 10

Charge sharpening in U(1)-symmetric monitored circuits persists under readout errors, with residual fluctuations forming a detectable minimum near the ideal transition point.
Entanglement manipulation and magic area-laws
quant-ph 2026-10 conditional novelty 6.0 of 10

Area-law quantum states split by their subsystem magic scaling: entanglement-dominated states host magic area-laws and efficient entanglement processing, while faster-than-area magic certifies magic domination and com...

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4 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Uses its method or tool 2 papers

Loop model and replica pairings.—Following the stat-mech framework for monitored circuits [ref] , we compute both diagnostics by contracting a replicated tensor network on the circuit spacetime, with $Q$ forward and $Q$ backward replicas.

Statistical Mechanics of Non-Abelian Learnability Transitions · Introduction · 0.96
By following [ref] , the replica logarithmic Rényi-$n$ purity for the circuit is given by [equation] where [equation] $ρ$ is a mixed state and $𝔼_u$ represents the average manipulation for the Haar random unitary gates [ref] .

Continuous Reset-Induced Phase Transition in Measurement-Free Random Quantum Circuits · EFFECTIVE SPIN MODEL · 0.95

Cites it as background 3 papers

(See Refs. [ref] for reviews.) When the dynamics preserves a global symmetry, the conserved charge becomes a natural target: how quickly the record reads out its value changes parametrically with system size across the charge-sharpening transition [ref] .

Statistical Mechanics of Non-Abelian Learnability Transitions · Introduction · 0.94
A paradigmatic setting for studying MIPTs is provided by random quantum circuits [ref] .

Universality of Measurement-Induced Criticality under Symmetry-Breaking Measurements · Introduction · 0.94
The study of monitored quantum systems has experienced a renaissance in recent years, driven by advances on both theoretical and experimental fronts [ref] .

Postselection-free ballistic-diffusive transition in monitored spin chains · Introduction · 0.96

What it cites · 2 sentences without a confident label

Cites as background 1 paper

Since the original papers, random quantum circuits have become part of the standard toolbox to study chaotic quantum dynamics, and provided crucial insights into, e.g thermalization and entanglement growth [ref] , many-body quantum chaos [ref] and operator spreading [ref] , or the emergence of irreversible hydrodynamics from unitary evolution [ref] .

Coarse-grained dynamics of operator and state entanglement · Discussion · 0.93

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