Constant depth pseudoentanglement - Shallow circuits, deep backstory
summary
Claim: pseudoentangled states are constructible by 2D-local constant-depth (QNC0) circuits that encode an entropy gap of order log N using linear maps turned into a randomized encoding evaluatable in constant depth. Construction relies on the dense-sparse LPN assumption, produces a 2D frustration-free Hamiltonian with constant gap whose ground state is the pseudostate, and yields 1D hardness via a Feynman–Kitaev history state with inverse-polynomial gap. The writeup and simplification use AI assistance.
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chapters (8)
- 0:00Pseudo-entanglement basics
- 7:52Pseudo vs pseudo-random states
- 13:57Constructing states classically
- 21:30Linear codes and LPN
- 31:16Randomized encodings in depth
- 44:52Research backstory
- 53:40Open questions
- 1:00:15Q&A
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