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

Authors David Miloschewsky , Supartha Podder

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ACM Subject Classification
  • Theory of computation → Quantum query complexity
Keywords
  • Non-collapsing measurements
  • Quantum lower-bounds
  • Quantum adversary method

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.CCC.2025.12

Author Details

David Miloschewsky
  • Department of Computer Science, Stony Brook University, NY, USA
Supartha Podder
  • Department of Computer Science, Stony Brook University, NY, USA

Funding

Supported by US Department of Energy (grant no DE-SC0023179) and partially supported by US National Science Foundation (award no 1954311).

Acknowledgements

We want to thank Kunal Marwaha for helpful discussions. We thank the anonymous reviewers for their valuable comments and suggestions.

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