Random Gaussian Augmented Matrix Product States

arXiv:2609.25458 · quant-ph, cond-mat.str-el · Submitted 2026-09-21 · Read on arXiv

quant-ph, cond-mat.str-el

Submitted: 2026-09-21

Updated: 2026-09-21

Terminology

• Entanglement — 49× in this paper · explained in 3 episodes
• Trace — 18× in this paper · explained in 2 episodes
• Anticoncentration — 10× in this paper · explained in 1 episode
• Non-Gaussianity — 10× in this paper · explained in 2 episodes
• Entanglement Entropy — 9× in this paper · explained in 2 episodes
• Trace Distance — 8× in this paper · explained in 3 episodes
• Hilbert Space — 6× in this paper · explained in 2 episodes
• Quantum Circuits — 6× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Benchmarking — 2× in this paper · explained in 3 episodes
• Munich Center for Quantum Science and Technology — 2× in this paper
• Area Law — 1× in this paper · explained in 1 episode
• Inverse Participation Ratio (IPR) — 1× in this paper · explained in 2 episodes
• Stabilizer States — 1× in this paper · explained in 2 episodes

Sources

• Algorithms for entanglement renormalization
• Clifford circuits Augmented Matrix Product States for fermion systems
• Fermionic Linear Optics and Matchgates
• Matchgate circuit representation of fermionic Gaussian states: optimal preparation, approximation, and classical simulation
• Augmenting Density Matrix Renormalization Group with Matchgates and Clifford circuits
• Theory of the Matchgate Commutant
• The commutant of fermionic Gaussian unitaries
• Geometry of Free Fermion Commutants
• Practical Tests and Witnesses of Fermionic non-Gaussianity
• Weingarten Calculus
• Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms
• Computable fermionic non-Gaussianity from the covariance matrix
• Fermionic entropy: an efficiently measurable strong monotone for non-Gaussianity
• Williamson majorization theory of fermionic non-Gaussianity
• Typical Entanglement of Superpositions
• Unitary Designs from Doped Matchgate Circuits

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