Evaluating ESOP Optimization Methods in Quantum Compilation Flows

  • Giulia MeuliEmail author
  • Bruno Schmitt
  • Rüdiger Ehlers
  • Heinz Riener
  • Giovanni De Micheli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11497)


Exclusive-or sum-of-products (ESOP) expressions are used as intermediate representations in quantum circuit synthesis flows, and their complexity impacts the number of gates of the resulting circuits. Many state-of-the-art techniques focus on minimizing the number of product terms in a ESOP expression, either exactly or in a heuristic fashion.

In this paper, we investigate into ESOP optimization considering two recent quantum compilation flows with opposite requirements. The first flow generates Boolean functions with a small number of Boolean variables, which enables the usage of methods from exact synthesis; the second flow generates Boolean functions with many Boolean variables, such that heuristics are more effective. We focus on the reduction of the number of T gates, which are expensive in fault-tolerant quantum computing and integrate ESOP optimization methods into both flows. We show an average reductions of 36.32% in T-count for the first flow, while in the second flow an average reduction of 28.23% is achieved.


Reversible Logic Synthesis Logic optimization ESOP Quantum circuit 



This research was supported by the European COST Action IC 1405 ‘Reversible Computation’, by the EPFL Open Science Fund and the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Giulia Meuli
    • 1
    Email author
  • Bruno Schmitt
    • 1
  • Rüdiger Ehlers
    • 2
  • Heinz Riener
    • 1
  • Giovanni De Micheli
    • 1
  1. 1.École Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.University of BremenBremenGermany

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