  We introduce an approach for performing quantum state reconstruction on
systems of $n$ qubits using a machine-learning-based reconstruction system
trained exclusively on $m$ qubits, where $m\geq n$. This approach removes the
necessity of exactly matching the dimensionality of a system under
consideration with the dimension of a model used for training. We demonstrate
our technique by performing quantum state reconstruction on randomly sampled
systems of one, two, and three qubits using machine-learning-based methods
trained exclusively on systems containing at least one additional qubit. The
reconstruction time required for machine-learning-based methods scales
significantly more favorably than the training time; hence this technique can
offer an overall savings of resources by leveraging a single neural network for
dimension-variable state reconstruction, obviating the need to train dedicated
machine-learning systems for each Hilbert space.
