SAT-based {CNOT, T} Quantum Circuit Synthesis

  • Giulia Meuli
  • Mathias Soeken
  • Giovanni De Micheli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11106)


The prospective of practical quantum computers has lead researchers to investigate automatic tools to program them. A quantum program is modeled as a Clifford+T quantum circuit that needs to be optimized in order to comply with quantum technology constraints. Most of the optimization algorithms aim at reducing the number of T gates. Nevertheless, a secondary optimization objective should be to minimize the number of two-qubit operations (the CNOT gates) as they show lower fidelity and higher error rate when compared to single-qubit operations. We have developed an exact SAT-based algorithm for quantum circuit rewriting that aims at reducing CNOT gates without increasing the number of T gates. Our algorithm finds the minimum {CNOT, T} circuit for a given phase polynomial description of a unitary transformation. Experiments confirm a reduction of CNOT in T-optimized quantum circuits. We synthesize quantum circuits for all single-target gates whose control functions are one of the representatives of the 48 spectral equivalence classes of all 5-input Boolean functions. Our experiments show an average CNOT reduction of 26.84%.


Quantum computing Clifford+T circuits SAT-based rewriting algorithm 



This research was supported by H2020-ERC-2014-ADG 669354 CyberCare, the Swiss National Science Foundation (200021-169084 MAJesty), and the ICT COST Action IC1405.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Giulia Meuli
    • 1
  • Mathias Soeken
    • 1
  • Giovanni De Micheli
    • 1
  1. 1.École polytechnique fédérale de Lausanne (EPFL)LausanneSwitzerland

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