  Applications such as simulating complicated quantum systems or solving
large-scale linear algebra problems are very challenging for classical
computers due to the extremely high computational cost. Quantum computers
promise a solution, although fault-tolerant quantum computers will likely not
be available in the near future. Current quantum devices have serious
constraints, including limited numbers of qubits and noise processes that limit
circuit depth. Variational Quantum Algorithms (VQAs), which use a classical
optimizer to train a parametrized quantum circuit, have emerged as a leading
strategy to address these constraints. VQAs have now been proposed for
essentially all applications that researchers have envisioned for quantum
computers, and they appear to the best hope for obtaining quantum advantage.
Nevertheless, challenges remain including the trainability, accuracy, and
efficiency of VQAs. Here we overview the field of VQAs, discuss strategies to
overcome their challenges, and highlight the exciting prospects for using them
to obtain quantum advantage.
