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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…

Quantum Physics · Physics 2024-05-31 Li-Heng Henry Chang , Shea Roccaforte , Ziyu Xu , Paul Cadden-Zimansky

Quantum computing is rapidly gaining popularity, necessitating intuitive visualization tools for complex quantum states. While the Bloch Sphere effectively visualizes single-qubit states, it fundamentally lacks scalability for multi-qubit…

Quantum Physics · Physics 2025-08-27 Fritz Schinkel

In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…

This paper presents an introduction to geometric representations of quantum states in which each distinct quantum state, pure and mixed, corresponds to a unique point in a Euclidean space. Beginning with a review of some underappreciated…

Quantum Physics · Physics 2026-02-17 Athanasios Kostikas , Yaroslav Valchyshen , Paul Cadden-Zimansky

Understanding the structure of multi-qubit quantum states is essential for both quantum information research and education, yet intuitive visualization beyond the single-qubit Bloch sphere remains challenging. In this work, we propose a…

Quantum Physics · Physics 2026-03-11 Satoru Shoji

We extend Bloch Sphere formalism to pure two qubit systems. Combining insights from Geometric Algebra and analysis of entanglement in different conjugate bases we identify Two Bloch Sphere geometry that is suitable for representing…

Quantum Physics · Physics 2024-03-19 Stanislav Filatov , Marcis Auzinsh

Visualizations in interactive computer simulations are a powerful tool to help students develop productive mental models, particularly in the case of quantum phenomena that have no classical analogue. The QuVis Quantum Mechanics…

Physics Education · Physics 2014-10-06 Antje Kohnle , Charles Baily , Scott Ruby

The extended Bloch representation of quantum mechanics was recently derived to offer a (hidden-measurement) solution to the measurement problem. In this article we use it to investigate the geometry of superposition and entangled states,…

Quantum Physics · Physics 2017-01-02 Diederik Aerts , Massimiliano Sassoli de Bianchi

The focus of this Visualization Viewpoints article is to provide some background on Quantum Computing (QC), to explore ideas related to how visualization helps in understanding QC, and examine how QC might be useful for visualization with…

As the quantity and resolution of spectral-cubes from optical/infrared and radio surveys increase, desktop-based visualization and analysis solutions must adapt and evolve. Novel immersive 3D environments such as the CAVE2 at Monash…

Instrumentation and Methods for Astrophysics · Physics 2016-10-05 Dany Vohl , Christopher J. Fluke , Amr H. Hassan , David G. Barnes

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…

Quantum Physics · Physics 2023-02-07 Alice Barthe , Michele Grossi , Jordi Tura , Vedran Dunjko

We propose a novel method for image representation in quantum computers, which uses the two-dimensional (2-D) quantum states to locate each pixel in an image through row-location and column-location vectors for identifying each pixel…

Multimedia · Computer Science 2015-07-20 Madhur Srivastava , Subhayan R. Moulick , Prasanta K. Panigrahi

The geometry of the Quantum State Space, described by Bloch vectors, is a very intricate one. A deeper understanding of this geometry could lead to the solution of some difficult problems in Quantum Foundations and Quantum Information such…

Quantum Physics · Physics 2013-09-30 Jose Ignacio Rosado

Quantum state tomography is a fundamental task in quantum computing, involving the reconstruction of an unknown quantum state from measurement outcomes. Although essential, it is typically introduced at the graduate level due to its…

Quantum Physics · Physics 2025-07-14 Mohammad Aamir Sohail , Ranga Sudharshan , S. Sandeep Pradhan , Arvind Rao

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…

Quantum Physics · Physics 2013-03-21 Pawel Kurzynski

As the variety of commercially available quantum computers continues to increase so does the need for tools that can characterize, verify and validate these computers. This work explores using quantum state tomography for characterizing the…

Quantum Physics · Physics 2022-05-06 Adrien Suau , Marc Vuffray , Andrey Y. Lokhov , Lukasz Cincio , Carleton Coffrin

Quantum computing is a rapidly evolving field that enables exponential speed-up over classical algorithms. At the heart of this revolutionary technology are quantum circuits, which serve as vital tools for implementing, analyzing, and…

Quantum Physics · Physics 2023-10-30 Zhen Wen , Yihan Liu , Siwei Tan , Jieyi Chen , Minfeng Zhu , Dongming Han , Jianwei Yin , Mingliang Xu , Wei Chen

Data visualization is important in understanding the characteristics of data that are difficult to see directly. It is used to visualize loss landscapes and optimization trajectories to analyze optimization performance. Popular optimization…

Quantum Physics · Physics 2023-12-04 Yoshiaki Kawase , Kosuke Mitarai , Keisuke Fujii

We introduce a visual representation of qubits to assist in explaining quantum computing to a broad audience. The representation follows from physical devices that we developed to explain superposition, entanglement, measurement, phases,…

Quantum Physics · Physics 2022-11-30 Sophie Laplante , Loris Perez , Sylvie Tissot , Lou Vettier

We introduce a generalized phase-space representation of qubit systems called the BEADS representation which makes it possible to visualize arbitrary quantum states in an intuitive and an easy to grasp way. Our representation is exact,…

Quantum Physics · Physics 2025-03-06 Dennis Huber , Steffen J. Glaser
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