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DOI: 10.4230/LIPIcs.CCC.2025.12

New Lower-Bounds for Quantum Computation with Non-Collapsing Measurements

Authors: David Miloschewsky and Supartha Podder

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract

Aaronson, Bouland, Fitzsimons and Lee [Scott Aaronson et al., 2014] introduced the complexity class PDQP (which was original labeled naCQP), an alteration of BQP enhanced with the ability to obtain non-collapsing measurements, samples of quantum states without collapsing them. Although SZK ⊆ PDQP, it still requires Ω(N^(1/4)) queries to solve unstructured search. We formulate an alternative equivalent definition of PDQP, which we use to prove the positive weighted adversary lower-bounding method, establishing multiple tighter bounds and a trade-off between queries and non-collapsing measurements. We utilize the technique in order to analyze the query complexity of the well-studied majority and element distinctness problems. Additionally, we prove a tight Θ(N^(1/3)) bound on search. Furthermore, we use the lower-bound to explore PDQP under query restrictions, finding that when combined with non-adaptive queries, we limit the speed-up in several cases.

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David Miloschewsky and Supartha Podder. New Lower-Bounds for Quantum Computation with Non-Collapsing Measurements. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{miloschewsky_et_al:LIPIcs.CCC.2025.12,
  author =	{Miloschewsky, David and Podder, Supartha},
  title =	{{New Lower-Bounds for Quantum Computation with Non-Collapsing Measurements}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.12},
  URN =		{urn:nbn:de:0030-drops-237067},
  doi =		{10.4230/LIPIcs.CCC.2025.12},
  annote =	{Keywords: Non-collapsing measurements, Quantum lower-bounds, Quantum adversary method}
}

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New Lower-Bounds for Quantum Computation with Non-Collapsing Measurements

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