Optimal Scaling of Unitary Design Formation in U(1) -Symmetric Random Circuits: A Bottleneck Slower than Charge Transport

arXiv:2609.39458 · quant-ph, cond-mat.stat-mech · Submitted 2026-09-30 · Read on arXiv

quant-ph, cond-mat.stat-mech

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Spectral Gap — 141× in this paper · explained in 5 episodes
• Quantum Circuits — 22× in this paper · explained in 2 episodes
• Conservation Laws — 11× in this paper · explained in 3 episodes
• Frustration — 9× in this paper · explained in 2 episodes
• Hypergraph — 9× in this paper · explained in 2 episodes
• Entanglement — 7× in this paper · explained in 3 episodes
• Entanglement Entropy — 4× in this paper · explained in 2 episodes
• Shadow Tomography — 4× in this paper · explained in 4 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Ancilla Qubits — 2× in this paper · explained in 1 episode
• Approximate Unitary t-design — 2× in this paper · explained in 1 episode
• Benchmarking — 2× in this paper · explained in 3 episodes
• Foundations of Computer Science — 2× in this paper
• RIKEN Center for Quantum Computing — 2× in this paper
• Robustness — 2× in this paper · explained in 5 episodes
• Symmetry Breaking — 2× in this paper · explained in 3 episodes
• Annual ACM-SIAM Symposium on Discrete Algorithms — 1× in this paper
• Embeddings — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hamming Distance — 1× in this paper · explained in 2 episodes
• Unitary Dynamics — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Unitary designs from statistical mechanics in random quantum circuits
• Local random quantum circuits form approximate designs on arbitrary architectures
• Random unitary circuits with constant spectral gap
• Unitary Designs from Random Symmetric Quantum Circuits
• Dynamics of Renyi entanglement entropy in local quantum circuits with charge conservation
• A framework for semi-universality: Semi-universality of 3-qudit SU(d)-invariant gates
• Efficient quantum pseudorandomness under conservation laws
• Arts & crafts: Strong random unitaries and geometric locality

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