Diagonal operator decomposition on restricted topologies via enumeration of quantum state subsets

Abstract: 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 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 through its lens provide solution constructions for several different device topologies (fully-connected, linear and circular). We also introduce two additional variants of the problem. Those variants can be used in place of exact decomposition of the diagonal operator when the circuit following it satisfies a set of prerequisites, enabling further reduction in the CX cost of implementation. Finally, we discuss how to exploit the framework for the decomposition of a particular, rather than general, diagonal operator.