Papers › Random unitaries in extremely low depth
Random unitaries in extremely low depth
Thomas Schuster, Jonas Haferkamp, Hsin-Yuan Huang
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We prove that random quantum circuits on any geometry, including a 1D line, can form approximate unitary designs over n qubits in logn depth. In a similar manner, we construct pseudorandom unitaries (PRUs) in 1D circuits in poly(logn) depth, and in all-to-all-connected circuits in poly(loglogn) depth. In all three cases, the n dependence is optimal and improves exponentially over known results. These shallow quantum circuits have low complexity and create only short-range entanglement, yet are indistinguishable from unitaries with exponential complexity. Our construction glues local random unitaries on logn-sized or poly(logn)-sized patches of qubits to form a global random unitary on all n qubits. In the case of designs, the local unitaries are drawn from existing constructions of approximate unitary k-designs, and hence also inherit an optimal scaling in k. In the case of PRUs, the local unitaries are drawn from existing PRU constructions. Applications of our results include proving that classical shadows with 1D log-depth Clifford circuits are as powerful as those with deep circuits, demonstrating superpolynomial quantum advantage in learning low-complexity physical systems, and establishing quantum hardness for recognizing phases of matter with topological order.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections