Benedetti, M., Lloyd, E., Sack, S., & Fiorentini, M. (2019). Parameterized quantum circuits as machine learning models. Quantum Science and Technology, 4(4), 043001.
Parameterized quantum circuits (PQCs) offer a concrete way to implement algorithms and demonstrate quantum supremacy in the NISQ era. PQCs are typically composed of fixed gates, e.g. controlled NOTs, and adjustable gates, e.g. qubit rotations. Even at low circuit depth, some classes of PQCs are capable of generating highly non-trivial outputs.
The hybrid algorithmic approach turned out to be successful in attacking scaled-down problems in chemistry, combinatorial optimization and machine learning.
For example, the variational quantum eigensolver (VQE, 变分量子本征求解器) [5] has been used for searching the ground state of the electronic Hamiltonian of molecules (分子电子哈密顿量的基态) [6, 7].
Similarly, the quantum approximate optimization algorithm (量子近似优化算法) [8] has been used to find approximate solutions of classical Ising models [9] and clustering problems formulated as MaxCut [10].