Mapping NCV Circuits to Optimized Clifford+T Circuits

  • D. Michael Miller
  • Mathias Soeken
  • Rolf Drechsler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8507)


The need to consider fault tolerance in quantum circuits has led to recent work on the optimization of circuits composed of Clifford+T gates. The primary optimization objectives are to minimize the T-count (number of T gates) and the T-depth (the number of groupings of parallel T gates). These objectives arise due to the high cost of the fault tolerant implementation of the T gate compared to Clifford gates. In this paper, we consider the mapping of a circuit composed of NOT, Controlled-NOT and square-root of NOT (NCV) gates to an equivalent circuit composed of Clifford+T gates. Our approach is heuristic and proceeds through three phases: (i) mapping a circuit of NCV gates to a Clifford+T circuit; (ii) optimization of the placement of the T gates in the Clifford+T circuit; and (iii) optimization of the subcircuits between T gate groupings. The approach takes advantage of earlier work on the optimization of NCV circuits. Examples are presented to show the approach presented here compares well with other approaches. Our approach does not add ancilla lines.


Quantum Computation Quantum Circuit Full Adder Control Gate Circuit Level 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • D. Michael Miller
    • 1
  • Mathias Soeken
    • 2
    • 3
  • Rolf Drechsler
    • 2
    • 3
  1. 1.Dept. of Computer ScienceUniversity of VictoriaVictoriaCanada
  2. 2.Institute of Computer ScienceUniversity of BremenBremenGermany
  3. 3.Cyber-Physical SystemsDFKI GmbHBremenGermany

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