Jin-Yi Cai

We show that the class ${\rm S}_2^p$ is a subclass of

${{\rm ZPP}^{\rm NP}}$. The proof uses universal hashing, approximate counting

and witness sampling. As a consequence, a collapse first noticed by

Samik Sengupta that the assumption NP has small circuits collapses

PH to ${\rm S}_2^p$

becomes the strongest version ...
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Venkatesan Chakaravarthy, Sambuddha Roy

We study some problems solvable in deterministic polynomial time given oracle access to the (promise version of) the Arthur-Merlin class.

Our main results are the following: (i) $BPP^{NP}_{||} \subseteq P^{prAM}_{||}$; (ii) $S_2^p \subseteq P^{prAM}$. In addition to providing new upperbounds for the classes $S_2^p$ and $BPP^{NP}_{||}$, these results are interesting ...
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Scott Aaronson, Andrew Drucker

We prove the following surprising result: given any quantum state rho on n qubits, there exists a local Hamiltonian H on poly(n) qubits (e.g., a sum of two-qubit interactions), such that any ground state of H can be used to simulate rho on all quantum circuits of fixed polynomial size. ... more >>>

Lijie Chen, Dylan McKay, Cody Murray, Ryan Williams

Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

A frontier open problem in circuit complexity is to prove P^NP is not in SIZE[n^k] for all k; this is a necessary intermediate step towards NP is not in P/poly. Previously, for several classes containing P^NP, including NP^NP, ZPP^NP, and ... more >>>