**Quantum Control Optimization in Circuit Mode** - Dmitri Maslov

Most quantum circuits are time-dependent diagrams
describing the process of quantum computation. And, most often,
quantum algorithms must be mapped into a quantum circuit to be able
to run them on quantum hardware. Optimal synthesis of quantum
circuits is intractable and heuristic methods must be employed,
resulting in non-optimal circuit specifications. In this talk, I will
consider the problem of optimizing quantum circuits for better
performance. In particular, two methods, one designed for reducing
the weighted gate count and the other designed for optimizing the
time delay will be introduced. The methods will be discussed
generically, making it clear how they can be applied to the
simplification of quantum circuits constructed with different types
of quantum gates and in different technologies. For the purpose of
experimental testing, a gate library composed of NOT, CNOT, and
controlled-sqrt-of-NOT gates is chosen. Proposed underlying
technology is assumed to be liquid NMR. I will illustrate in detail
how the methods apply to simplify some small quantum circuits, such
as adders and small oracles. I will also present and discuss the
results of simplification of larger designs, e.g. multiple control
Toffoli gate (with positive and/or negative controls) implementations
and some arithmetic circuits (adders, comparators, and modular
exponentiation circuits) that were recently reported in the
literature.