  Quantum computers can exploit a Hilbert space whose dimension increases
exponentially with the number of qubits. In experiment, quantum supremacy has
recently been achieved by the Google team by using a noisy intermediate-scale
quantum (NISQ) device with over 50 qubits. However, the question of what can be
implemented on NISQ devices is still not fully explored, and discovering useful
tasks for such devices is a topic of considerable interest. Hybrid
quantum-classical algorithms are regarded as well-suited for execution on NISQ
devices by combining quantum computers with classical computers, and are
expected to be the first useful applications for quantum computing. Meanwhile,
mitigation of errors on quantum processors is also crucial to obtain reliable
results. In this article, we review the basic results for hybrid
quantum-classical algorithms and quantum error mitigation techniques. Since
quantum computing with NISQ devices is an actively developing field, we expect
this review to be a useful basis for future studies.
