  In this work, we propose a generalization of the current most widely used
quantum computing hardware metric known as the quantum volume. The quantum
volume specifies a family of random test circuits defined such that the logical
circuit depth is equal to the total number of qubits used in the computation.
However, such square circuit shapes do not directly relate to many specific
applications for which one may wish to use a quantum computer. Based on
surveying available resource estimates for known quantum algorithms, we
generalize the quantum volume to a handful of representative circuit shapes,
which we call Quantum Volumetric Classes, based on the scaling behavior of the
logical circuit depth (time) with the problem size (qubit number).
