One-dimensional quantum Gibbs states in constant circuit depth

arXiv:2609.35973 · quant-ph, cond-mat.stat-mech, math-ph, math.MP · Submitted 2026-09-28 · Read on arXiv

quant-ph, cond-mat.stat-mech, math-ph, math.MP

Submitted: 2026-09-28

Updated: 2026-09-28

Terminology

• Entanglement — 74× in this paper · explained in 4 episodes
• Gibbs State — 58× in this paper · explained in 2 episodes
• Trace — 13× in this paper · explained in 2 episodes
• Multipartite Entanglement — 8× in this paper · explained in 2 episodes
• Mutual Information — 7× in this paper · explained in 2 episodes
• Clustering — 4× in this paper · explained in 2 episodes
• Topological Order — 4× in this paper · explained in 2 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Spectral Gap — 3× in this paper · explained in 5 episodes
• Entanglement Entropy — 2× in this paper · explained in 2 episodes
• Unitary Dynamics — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Cluster expansion — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Spin Squeezing — 1× in this paper · explained in 2 episodes

Sources

• Clustering theorem in 1D long-range interacting systems at arbitrary temperatures
• High-Temperature Gibbs States are Unentangled and Efficiently Preparable
• Entanglement in quantum spin chains is strictly finite at any temperature
• Spatial Entanglement Sudden Death in Spin Chains at All Temperatures
• When quantum thermal states look classical
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• The modified logarithmic Sobolev inequality for quantum spin systems: classical and commuting nearest neighbour interactions
• An efficient and exact noncommutative quantum Gibbs sampler
• Quantum Gibbs states are locally Markovian
• A Dobrushin condition for quantum Markov chains: Rapid mixing and conditional mutual information at high temperature
• Algorithmic Aspects of the Fermi--Hubbard Model
• Fast mixing of all-to-all quantum systems at high temperatures
• Characterizing the width of entanglement
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Localizable Entanglement
• Matrix Product State Representations
• Sequential generation of entangled multi-qubit states
• Entanglement of Assistance
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Fault-Tolerant One-Shot Entanglement Generation with Constant-Sized Quantum Devices in the Plane

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