Mapping Quantum Circuits to IBM QX Architectures Using the Minimal
  Number of SWAP and H Operations
The recent progress in the physical realization of quantum computers (the
first publicly available ones--IBM's QX architectures--have been launched in
2017) has motivated research on automatic methods that aid users in running
quantum circuits on them. Here, certain physical constraints given by the
architectures which restrict the allowed interactions of the involved qubits
have to be satisfied. Thus far, this has been addressed by inserting SWAP and H
operations. However, it remains unknown whether existing methods add a minimum
number of SWAP and H operations or, if not, how far they are away from that
minimum--an NP-complete problem. In this work, we address this by formulating
the mapping task as a symbolic optimization problem that is solved using
reasoning engines like Boolean satisfiability solvers. By this, we do not only
provide a method that maps quantum circuits to IBM's QX architectures with a
minimal number of SWAP and H operations, but also show by experimental
evaluation that the number of operations added by IBM's heuristic solution
exceeds the lower bound by more than 100% on average. An implementation of the
proposed methodology is publicly available at
http://iic.jku.at/eda/research/ibm_qx_mapping.
Robert Wille Lukas Burgholzer Alwin Zulehner