Quantum State Designs from Minimally Random Quantum Circuits

arXiv:2503.05698 · quant-ph, cond-mat.stat-mech, hep-th, math-ph, math.MP · Submitted 2025-03-07 · Read on arXiv

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

Submitted: 2025-03-07

Updated: 2026-09-16

Comments: 17 pages, 11 figures; v2 as appears in the journal

Journal ref: PRX Quantum 7, 033047 (2026)

DOI: 10.1103/kfzr-2k5r

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Quantum Circuits — 28× in this paper · explained in 2 episodes
• Entanglement — 10× in this paper · explained in 3 episodes
• Unitary Dynamics — 5× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Benchmarking — 3× in this paper · explained in 3 episodes
• Deep Thermalization — 3× in this paper · explained in 2 episodes
• Anticoncentration — 2× in this paper · explained in 1 episode
• Chaotic Dynamics — 2× in this paper · explained in 2 episodes
• Domain Walls — 2× in this paper · explained in 2 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Approximate Unitary t-design — 1× in this paper · explained in 1 episode
• BQP — 1× in this paper · explained in 2 episodes
• BQP-complete — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Non-Hermitian Skin Effect — 1× in this paper · explained in 2 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes

Sources

• Approximation by Quantum Circuits
• Unitary designs from statistical mechanics in random quantum circuits
• Unitary k-designs from random number-conserving quantum circuits
• Random unitaries in extremely low depth
• Incompressibility and spectral gaps of random circuits
• Approximate Unitary $k$-Designs from Shallow, Low-Communication Circuits
• Unitary Designs from Random Symmetric Quantum Circuits
• Universal distributions of overlaps from generic dynamics in quantum many-body systems
• Universality in the Anticoncentration of Chaotic Quantum Circuits
• Absence of censoring inequalities in random quantum circuits
• Deep thermalization under charge-conserving quantum dynamics
• More global randomness from less random local gates
• Two-stage relaxation of operators through domain wall and magnon dynamics
• Exactly solvable many-body dynamics from space-time duality
• Absolutely Maximally Entangled Qudit Graph States
• Weingarten Calculus
• Coarse-grained dynamics of operator and state entanglement

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