Sustained growth of quantum circuit complexity in many-body Hamiltonian dynamics

arXiv:2609.26885 · quant-ph, cond-mat.stat-mech, math-ph, math.MP · Submitted 2026-09-22 · Read on arXiv

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

Submitted: 2026-09-22

Updated: 2026-09-28

Comments: 9 pages, 3 figures; 36 pages (supplemental material). v2: corrected figures and typos

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

Terminology

• Trace — 27× in this paper · explained in 2 episodes
• Gibbs State — 23× in this paper · explained in 2 episodes
• Entanglement — 20× in this paper · explained in 5 episodes
• Spectral Gap — 18× in this paper · explained in 5 episodes
• Trace Distance — 15× in this paper · explained in 3 episodes
• Ancilla Qubits — 12× in this paper · explained in 2 episodes
• Clustering — 12× in this paper · explained in 2 episodes
• Fidelity — 10× in this paper · explained in 2 episodes
• Hilbert Space — 9× in this paper · explained in 2 episodes
• Quantum Circuits — 7× in this paper · explained in 2 episodes
• Deep Thermalization — 3× in this paper · explained in 2 episodes
• Effective Hamiltonian — 2× in this paper · explained in 2 episodes
• Foundations of Computer Science — 2× in this paper
• Generalization — 2× in this paper · explained in 14 episodes
• Krylov Complexity — 2× in this paper · explained in 3 episodes
• BQP — 1× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 4 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 4 episodes
• Eigenstate Thermalization Hypothesis (ETH) — 1× in this paper · explained in 6 episodes
• Entanglement Entropy — 1× in this paper · explained in 6 episodes
• No-Go Theorem — 1× in this paper · explained in 2 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes
• Stabilizer States — 1× in this paper · explained in 4 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes

Sources

• Unitary designs from statistical mechanics in random quantum circuits
• Random unitaries from Hamiltonian dynamics
• Random unitaries that conserve energy
• The Complexity of Quantum States and Transformations: From Quantum Money to Black Holes
• Quantum Complexity of Time Evolution with Chaotic Hamiltonians
• Incompressibility and spectral gaps of random circuits
• Black Holes and Complexity Classes
• Universal Hamiltonians for Exponentially Long Simulation
• Random product states at high temperature equilibrate exponentially well
• Growth and collapse of subsystem complexity under random unitary circuits
• Quantum Gibbs states are locally Markovian
• Instability of localization in translation-invariant systems
• Sharp Transitions for Subsystem Complexity
• The Scrooge ensemble in many-body quantum systems
• Extensive entropy from unitary evolution
• Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity
• Weak eigenstate thermalization with large deviation bound
• Online learning of quantum processes
• On the moments of random quantum circuits and robust quantum complexity

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