The paper's claimed collapses of quantum-classical PCPs and the quantum polynomial hierarchy rest on invalid reductions, so the main theorems are unsupported.
A Collapsible Polynomial Hierarchy for Promise Problems
1 Pith paper cite this work. Polarity classification is still indexing.
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abstract
The polynomial hierarchy has been widely studied in classical complexity theory. In this paper, we will generalize some commonly known results about the polynomial hierarchy to a version of the hierarchy extended to promise problems. This paper proposes new definitions of existential and universal operators for classes of promise problems. Applying these to BQP, we recover the hierarchy proposed by Gharibian et al. (MFCS 2018). Moreover, using our definition, we give an easy proof of the collapse of this hierarchy under a Karp-Lipton-like scenario, which was an open question for the original definition of Gharibian et al.
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quant-ph 1years
2025 1verdicts
REJECT 1representative citing papers
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Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy
The paper's claimed collapses of quantum-classical PCPs and the quantum polynomial hierarchy rest on invalid reductions, so the main theorems are unsupported.