Bloch Sphere Binary Trees: A method for the visualization of sets of
multi-qubit systems pure states
- URL: http://arxiv.org/abs/2302.02957v1
- Date: Mon, 6 Feb 2023 17:39:19 GMT
- Title: Bloch Sphere Binary Trees: A method for the visualization of sets of
multi-qubit systems pure states
- Authors: Alice Barthe, Michele Grossi, Jordi Tura, Vedran Dunjko
- Abstract summary: We present a mapping that can uniquely represent a set of arbitrary multi-qubit pure states on what we call a Binary Tree of Bloch Spheres.
The backbone of this technique is the combination of the Schmidt decomposition and the Bloch sphere representation.
We illustrate how this can be used in the context of understanding the time evolution of quantum states.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Understanding the evolution of a multi-qubit quantum system, or elucidating
what portion of the Hilbert space is occupied by a quantum dataset becomes
increasingly hard with the number of qubits. In this context, the visualisation
of 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 the
representation of a set of single qubits (not allowing multi-qubit systems) or
a just a single multi-qubit system (not suitable if we care about sets of
states), sometimes with additional restrictions, on symmetry or entanglement
for example. [1{3]. In this work we present a mapping that can uniquely
represent a set of arbitrary multi-qubit pure states on what we call a Binary
Tree of Bloch Spheres. The backbone of this technique is the combination of the
Schmidt decomposition and the Bloch sphere representation. We illustrate how
this can be used in the context of understanding the time evolution of quantum
states, e.g. providing immediate insights into the periodicity of the system
and even entanglement properties. We also provide a recursive algorithm which
translates from the computational basis state representation to the binary tree
of Bloch spheres representation. The algorithm was implemented together with a
visualization library in Python released as open source.
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