  The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the effective number of degrees of freedom
in the computer must grow nearly linearly with the number of qubits in an
equivalent qubit-based quantum computer.
