Diagonal operator decomposition on restricted topologies via enumeration of quantum state subsets
Jan Tułowiecki, Łukasz Czerwiński, Konrad Deka, Jan Gwinner, Witold Jarnicki, Adam Szady
Summary
We analyze the CX implementation cost of generic diagonal operators, based on the target device topology.
Details
Various quantum algorithms require usage of arbitrary diagonal operators as subroutines. For their execution on a physical hardware, those operators must be first decomposed into the target device's native gateset and its qubit connectivity for entangling gates. Here, we assume that the allowed gates are exactly the CX gate and the parameterized phase gate. We introduce a framework for the analysis of CX-only circuits and provide solution constructions for several different device topologies (fully-connected, linear, and circular). We also introduce two additional variants of the problem to enable further reduction in the CX cost of implementation. Finally, we discuss how to exploit the framework for the decomposition of particular diagonal operators.