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En Route to a Standard QMA₁ vs. QCMA Oracle Separation

Authors David Miloschewsky , Supartha Podder , Dorian Rudolph

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ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum complexity theory
  • Quantum Merlin-Arthur (QMA)

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Abstract

We study the power of quantum witnesses under perfect completeness. We construct a classical oracle relative to which a language lies in QMA₁ but not in QCMA when the QCMA verifier is only allowed polynomially many adaptive rounds and exponentially many parallel queries per round. Additionally, we derandomize the permutation-oracle separation of Fefferman and Kimmel, obtaining an in-place oracle separation between QMA₁ and QCMA. Furthermore, we focus on QCMA and QMA with an exponentially small gap, where we show a separation assuming the gap is fixed, but not when it may be arbitrarily small. Finally, we derive consequences for approximate ground-state preparation from sparse Hamiltonian oracle access, including a bounded adaptivity frustration-free variant.

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David Miloschewsky, Supartha Podder, and Dorian Rudolph. En Route to a Standard QMA₁ vs. QCMA Oracle Separation. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 32:1-32:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.32

Author Details

David Miloschewsky
  • Department of Computer Science, Stony Brook University, NY, USA
Supartha Podder
  • Department of Computer Science, Stony Brook University, NY, USA
Dorian Rudolph
  • Department of Computer Science and Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Germany

Funding

  • Rudolph, Dorian: Funded by DFG Priority Programme 2514 (grant number 563388236).

Acknowledgements

We thank Srinivasan Arunachalam, Sevag Gharibian, Srijita Kundu, Sinan Oral, and Nengkun Yu for helpful discussions. This work was done in part while the authors were visiting the Simons Institute for the Theory of Computing.

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