Today’s quantum computers have too few qubits and too high error rates for fault-tolerant quantum computing. This constrains quantum circuits executable today to those requiring a short circuit depth. A way to constrain circuit depth is via the variational method. In this method a given computational task is formulated as an optimization problem such that the minimum of a cost function corresponds to the solution of the original task. Variational quantum algorithms compute the cost function using the measurement outcomes or expectation values of a short-depth parameterized quantum circuit. In typical implementations, the parameterized quantum circuits are evaluated on a quantum computer and parameters are optimized using classical optimization techniques. The feasibility of this approach for solving computational tasks at relevant scales is debated and subject to ongoing research.