  The Bloch Sphere visualization of the possible states of a single qubit has
proved a useful pedagogical and conceptual tool as a one-to-one map between
qubit states and points in a 3-D space. However, understanding many important
concepts of quantum mechanics, such as entanglement, requires developing
intuitions about states with a minimum of two qubits, which map one-to-one to
unvisualizable spaces of 6 dimensions and higher. In this paper we circumvent
this visualization issue by creating maps of subspaces of 1- and 2-qubit
systems that quantitatively and qualitatively encode properties of these states
in their geometries. For the 1-qubit case, the subspace approach allows one to
visualize how mixed states relate to different choices of measurement in a
basis-independent way and how to read off the entries in a density matrix
representation of these states from lengths in a simple diagram. For the
2-qubit case, a toroidal map of 2-qubit states illuminates the non-trivial
topology of the state space while allowing one to simultaneously read off, in
distances and angles, the level of entanglement in the 2-qubit state and the
mixed-state properties of its constituent qubits. By encoding states and their
evolutions through quantum logic gates with little to no need of mathematical
formalism, these maps may prove particularly useful for understanding
fundamental concepts of quantum mechanics and quantum information at the
introductory level. Interactive versions of the visualizations introduced in
this paper are available at https://quantum.bard.edu/.
