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Free quantum computing.

Jacques Carette1, Chris Heunen2, Robin Kaarsgaard3

  • 1Department of Computing and Software, McMaster University, Hamilton, ON L8S 4K1, Canada.

Proceedings of the National Academy of Sciences of the United States of America
|February 17, 2026
PubMed
Summary
This summary is machine-generated.

Researchers developed a new discrete axiomatization and category-theoretical model for quantum computing, clarifying its relationship with classical computing and enabling optimization through combinatorial methods.

Keywords:
axiomatizationcategory theoryfree modelreversible computing

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Area of Science:

  • Quantum Computing
  • Theoretical Computer Science
  • Category Theory

Background:

  • The precise relationship between quantum and classical computing remains unclear.
  • Classical algorithms are improved by quantum computing for specific problems.
  • Free models can clarify this relationship by adding minimal physical principles.

Purpose of the Study:

  • To develop a discrete axiomatization of quantum computing.
  • To introduce a category-theoretical free model for quantum computing.
  • To understand the source of quantum advantage.

Main Methods:

  • Replaced standard continuous postulates with discrete equations.
  • Developed a category-theoretical model instead of a linear-algebraic one.
  • Based the framework on reversible classical computing principles.

Main Results:

  • Isolated quantum advantage in the ability to compute specific square roots.
  • Linked the new model to various quantum computing hardware.
  • Enabled optimization of quantum computations via combinatorial methods.
  • The free model offers the same expressivity and universality as the standard model.

Conclusions:

  • The discrete axiomatization and free model provide a new perspective on quantum computing.
  • This approach facilitates automated verification and reasoning for quantum programs.
  • It potentially allows for optimization of quantum computations using classical techniques.