REVIEW 2 cited by
Random Quantum Circuits are Approximate 2-designs
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Random Quantum Circuits are Approximate 2-designs
read the original abstract
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However, this requires exponential time. We show that random circuits of only polynomial length will approximate the first and second moments of the Haar distribution, thus forming approximate 1- and 2-designs. Previous constructions required longer circuits and worked only for specific gate sets. As a corollary of our main result, we also improve previous bounds on the convergence rate of random walks on the Clifford group.
Forward citations
Cited by 2 Pith papers
-
Quantum Simulation of Random Unitaries from Clebsch-Gordan Transforms
Clebsch-Gordan transforms give exact compressed oracles for Haar-random unitary group actions, with efficient circuits for U(d).
-
Entanglement and information scrambling in long-range measurement-only circuits
Long-range measurement-only Clifford circuits display several entanglement and scrambling phases, including a structured-circuit phase with volume-law entanglement, long-range correlations, rapid ancilla purification,...
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.