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Absence of censoring inequalities in random quantum circuits
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abstract
Ref. 1 asked whether deleting gates from a random quantum circuit architecture can ever make the architecture a better approximate $t$-design. We show that it can. In particular, we construct a family of architectures such that the approximate $2$-design depth decreases when certain gates are deleted. We also give some intuition for this construction and discuss the relevance of this result to the approximate $t$-design depth of the 1D brickwork. Deleting gates always decreases scrambledness in the short run, but can sometimes cause it to increase in the long run. Finally, we give analogous results for spectral gaps and when deleting edges of interaction graphs.
Forward citations
Cited by 2 Pith papers
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Apparent Universal Behavior in Second Moments of Random Quantum Circuits
Most random circuit geometries form approximate 2-designs in O(log n) depth with explicit constants; bridge/lollipop graphs need Ω(n²) gates, and 10-20 layers suffice for 50-qubit near-random circuits.
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Anti-concentration is (almost) all you need
For LU-invariant local random quantum circuits, anti-concentration implies a relative-error state 2-design with error ≈ 4× the anti-concentration error, making the two properties equivalent.
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