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Unconditional Pseudorandomness Against Shallow Quantum Circuits

Authors Soumik Ghosh , Sathyawageeswar Subramanian , Wei Zhan

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ACM Subject Classification
  • Theory of computation → Pseudorandomness and derandomization
  • Theory of computation → Quantum information theory
  • Theory of computation → Quantum complexity theory
  • Theory of computation → Quantum complexity theory
Keywords
  • quantum pseudorandomness
  • shallow quantum circuits
  • pseudorandomness
  • t-designs

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Abstract

Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects rely on complexity theoretic assumptions. 
In this work, we establish the first unconditionally secure efficient pseudorandom constructions against shallow-depth quantum circuit classes. We prove that:  
- Any quantum state 2-design yields unconditional pseudorandomness against both QNC⁰ circuits with arbitrarily many ancillae and AC⁰∘QNC⁰ circuits with nearly linear ancillae. 
- Random phased subspace states, where the phases are picked using a 4-wise independent function, are unconditionally pseudoentangled against the above circuit classes. 
- Any unitary 2-design yields unconditionally secure parallel-query pseudorandom unitaries against geometrically local QNC⁰ adversaries, even with limited AC⁰ postprocessing.  Our results stand in stark contrast to the standard guarantee of the 2-design property, which only ensures that they cannot be distinguished from Haar random ensembles using two copies or queries. Our work demonstrates that quantum computational pseudorandomness can be achieved unconditionally for natural classes of restricted adversaries, opening new directions in quantum complexity theory.

Cite As Get BibTex

Soumik Ghosh, Sathyawageeswar Subramanian, and Wei Zhan. Unconditional Pseudorandomness Against Shallow Quantum Circuits. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 70:1-70:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.70

Author Details

Soumik Ghosh
  • University of Chicago, IL, USA
Sathyawageeswar Subramanian
  • University of Oxford, UK
Wei Zhan
  • University of Chicago, IL, USA

Funding

  • Subramanian, Sathyawageeswar: funded by a Royal Society University Research Fellowship.

Acknowledgements

The authors would like to thank John Bostanci, Daniel Grier, Natalie Parham, Jack Morris, Francisca Vasconcelos, and Henry Yuen for stimulating discussions on related topics.

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