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.