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Understanding the evolution of a multi-qubit quantum system, or elucidatingwhat portion of the Hilbert space is occupied by a quantum dataset becomesincreasingly hard with the number of qubits. In this context, the visualisationof sets of multi-qubit pure quantum states on a single image can be helpful.However, the current approaches to visualization of this type only allow therepresentation of a set of single qubits (not allowing multi-qubit systems) ora just a single multi-qubit system (not suitable if we care about sets ofstates), sometimes with additional restrictions, on symmetry or entanglementfor example. [1{3]. In this work we present a mapping that can uniquelyrepresent a set of arbitrary multi-qubit pure states on what we call a BinaryTree of Bloch Spheres. The backbone of this technique is the combination of theSchmidt decomposition and the Bloch sphere representation. We illustrate howthis can be used in the context of understanding the time evolution of quantumstates, e.g. providing immediate insights into the periodicity of the systemand even entanglement properties. We also provide a recursive algorithm whichtranslates from the computational basis state representation to the binary treeof Bloch spheres representation. The algorithm was implemented together with avisualization library in Python released as open source.

Bloch Sphere Binary Trees: A method for the visualization of sets of multi-qubit systems pure states