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Nonuniform QCPH Collapse Implies QCPH Collapse

  • Jeremy Ahrens Huang
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Abstract

Despite the importance of the non-uniform Polynomial-Time Hierarchy (PH/poly) in classical complexity understanding the collapse conditions of the Polynomial-Time Hierarchy (PH), a quantum equivalent of PH/poly has yet to be studied in the literature. We introduce the non-uniform computational Quantum Polynomial-Time Hierarchy (QCPH/mpoly), the quantum equivalent of PH/poly, and show that it collapses if and only if QCPH, the quantum equivalent of PH introduced by Gharibian et al. (comput. complex. 2022), also collapses. We also show that QCPH collapses if coQCMA is contained in QCMA/mpoly. These results are analogous to those of Yap (TCS 1983) commonly used to invoke the collapse of PH in classical complexity. QCPH/mpoly is analogous to QCPH with non-uniform quantum verifier circuits.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026nonuniform,
  title = {{Nonuniform QCPH Collapse Implies QCPH Collapse}},
  author = {Jeremy Ahrens Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04423},
  eprint = {2610.04423},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04423},
}
RIS
TY  - UNPB
TI  - Nonuniform QCPH Collapse Implies QCPH Collapse
AU  - Jeremy Ahrens Huang
PY  - 2026
DA  - 2026/10/03
PB  - arXiv
DO  - 10.48550/arxiv.2610.04423
UR  - https://arxiv.org/abs/2610.04423
AB  - Despite the importance of the non-uniform Polynomial-Time Hierarchy (PH/poly) in classical complexity understanding the collapse conditions of the Polynomial-Time Hierarchy (PH), a quantum equivalent of PH/poly has yet to be studied in the literature. We introduce the non-uniform computational Quantum Polynomial-Time Hierarchy (QCPH/mpoly), the quantum equivalent of PH/poly, and show that it collapses if and only if QCPH, the quantum equivalent of PH introduced by Gharibian et al. (comput. complex. 2022), also collapses. We also show that QCPH collapses if coQCMA is contained in QCMA/mpoly. These results are analogous to those of Yap (TCS 1983) commonly used to invoke the collapse of PH in classical complexity. QCPH/mpoly is analogous to QCPH with non-uniform quantum verifier circuits.
ER  -