Unitary designs from perturbed time evolutions of a chaotic Hamiltonian

arXiv:2607.24851 · quant-ph · Submitted 2026-07-25 · Read on arXiv

quant-ph

Submitted: 2026-07-25

Updated: 2026-09-21

Comments: Updated with new resource bounds, additional numerical results, and improved presentation

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

Terminology

• Trace — 17× in this paper · explained in 2 episodes
• Benchmarking — 7× in this paper · explained in 3 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Quantum Circuits — 4× in this paper · explained in 2 episodes
• Chaotic Dynamics — 3× in this paper · explained in 2 episodes
• Deep Thermalization — 3× in this paper · explained in 2 episodes
• Entanglement — 3× in this paper · explained in 3 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Approximate Unitary t-design — 1× in this paper · explained in 1 episode
• Degeneracy — 1× in this paper · explained in 3 episodes
• S1 in Supplemental Material — 1× in this paper
• SYK Model — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes
• Universality Class — 1× in this paper · explained in 2 episodes

Sources

• Random unitaries from Hamiltonian dynamics
• Random unitaries that conserve energy
• Three Hamiltonians are Sufficient for Unitary $k$-Design in Temporal Ensemble
• Unitary Designs from Two Chaotic Hamiltonians and a Random Pauli Operation
• The Clifford group fails gracefully to be a unitary 4-design
• Nonstabilizerness Enhances Thrifty Shadow Estimation
• High-Precision Fidelity Estimation with Common Randomized Measurements
• Unitary $k$-designs without independent Hamiltonian quenches

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