Quantum Circuit Optimization Techniques: A Literature Survey

We present a literature survey of the mathematical aspects of optimization and optimal synthesis of quantum circuits. The optimization techniques we consider perform the synthesis of quantum circuit by minimizing a given cost function. A total of 179 papers were filtered by inclusion/exclusion criteria and reviewed according to representation models adopted, the techniques used or developed, the kind of benchmarks adopted and the comparison against competitors performed. The survey shows that a very diverse literature has been accumulating in the recent years and although it resists a common formalization, some trends can be individuated. In particular, there is a lack of shared benchmarks with some exceptions. Moreover, many approaches change the representation of the problem to a formulation other than the simple sequence of gates. Final conclusions are drawn and possible lines of future research are suggested.