Quantum Circuit Simpli£cation and Level Compaction

Quantum circuits are time dependent diagrams describing the process of quantum computation. Every (quantum) algorithm must be mapped into a quantum circuit to be able to run it on a quantum hardware. Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed, resulting in non-optimal circuit speci£cations. In this paper, we consider the use of local optimization technique called the templates to simplify and compact levels in a quantum circuit initially found by other means. We present and analyze templates in the general case, and then provide particular details for the circuits composed of NOT, CNOT and controlledsqrt-of-NOT gates. We introduce templates for this set of gates and apply them to simplify and compact levels in quantum simulations of multiple control Toffoli gates and quantum Boolean circuits found by other authors. While the number of templates and runtime of our software are quite small, the reduction in number of quantum gates and number of levels is often signi£cant.