Towards a SAT Encoding for Quantum Circuits: A Journey From Classical Circuits to Clifford Circuits and Beyond

Authors Lucas Berent , Lukas Burgholzer , Robert Wille

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Author Details

Lucas Berent
  • Technical University of Munich, Germany
Lukas Burgholzer
  • Johannes Kepler University Linz, Austria
Robert Wille
  • Technical University of Munich, Germany
  • Software Competence Center Hagenberg GmbH (SCCH), Austria

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Lucas Berent, Lukas Burgholzer, and Robert Wille. Towards a SAT Encoding for Quantum Circuits: A Journey From Classical Circuits to Clifford Circuits and Beyond. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Boolean Satisfiability (SAT) techniques are well-established in classical computing where they are used to solve a broad variety of problems, e.g., in the design of classical circuits and systems. Analogous to the classical realm, quantum algorithms are usually modelled as circuits and similar design tasks need to be tackled. Thus, it is natural to pose the question whether these design tasks in the quantum realm can also be approached using SAT techniques. To the best of our knowledge, no SAT formulation for arbitrary quantum circuits exists and it is unknown whether such an approach is feasible at all. In this work, we define a propositional SAT encoding that, in principle, can be applied to arbitrary quantum circuits. However, we show that, due to the inherent complexity of representing quantum states, constructing such an encoding is not feasible in general. Therefore, we establish general criteria for determining the feasibility of the proposed encoding and identify classes of quantum circuits fulfilling these criteria. We explicitly demonstrate how the proposed encoding can be applied to the class of Clifford circuits as a representative. Finally, we empirically demonstrate the applicability and efficiency of the proposed encoding for Clifford circuits. With these results, we lay the foundation for continuing the ongoing success of SAT in classical circuit and systems design for quantum circuits.

Subject Classification

ACM Subject Classification
  • Hardware → Electronic design automation
  • Hardware → Quantum computation
  • Satisfiability
  • Quantum Computing
  • Design Automation
  • Clifford Circuits


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