https://www.ekprojectjournal.com/ 2026-04-19T02:09:35+00:00 https://www.ekprojectjournal.com/ https://www.ekprojectjournal.com/lib/exe/fetch.php?media=wiki:dokuwiki.svg text/html 2025-05-01T19:23:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:categorical&rev=1746127381&do=diff Preamble Category theory has been a topic that has interested me in the periphery. Ever since picking up that C programming language book in the Uppsala University library and then exploring functional languages - Haskell, Clojure, others - and discovering the elusive monad, category theory has been a topic that has interested me in the periphery. I keep coming back to the topic on conversations with certain minded friends. Another language on top of the language? What else is in that box? text/html 2025-04-30T07:26:43+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:category-qc-foundation&rev=1745998003&do=diff Categorical Quantum Computing Series: Foundational Papers Introduction Below is a series of papers that have been setting the direction of category theory applied to quantum computing. The overview provides an easy reading that can give you (the reader) an idea of why you would want to read any of the chosen publications. The papers were selected in terms of general \(C\)\(C\)$Z$$X$$\delta$$\epsilon$ text/html 2025-04-16T13:41:11+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:category-qc&rev=1744810871&do=diff Categorical Quantum Computing Series: A Historical and Theoretical Overview Early Algebraic Approaches to Quantum Mechanics Quantum theory was originally formulated in algebraic terms using Hilbert spaces and linear operators. In the Dirac–von Neumann text/html 2024-12-06T15:05:52+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:distributed&rev=1733497552&do=diff Massive investments are being made in the European landscape of quantum computing. The question is what frameworks that enable orchestration of calculations to only deploy the most optimal problem formulation on the most suitable piece of hardware.\(\rho\)\(\mathcal{E}_{\text{dep}}\)$$ \mathcal{E}_{\text{dep}}(\rho) = (1 - p) \rho + p \frac{I}{2} $$\(p\)\(I\)\(\mathcal{E}_{\text{dep}}\)\(U\)\(\rho'\)$$ \rho' = \mathcal{E}_{\text{dep}}(U \rho U^\dagger) = (1 - p) U \rho U^\dagger + p \frac{I}{2} … text/html 2025-04-30T07:28:49+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:hawking-projector&rev=1745998129&do=diff Black Hole Mechanics in Quantum Image Compression Hawking Radiation and Information Theory The Hawking Projector uses black hole physics as inspiration for quantum data compression. The fundamental concept relates to how information behaves near a black hole's event horizon, particularly drawing from Hawking radiation theory.$$ \mathcal{H}(\rho) = -\text{Tr}(\rho \log \rho) $$$\mathcal{H}(\rho)$$\rho$$p_i$$i$$S(\rho) = -\text{Tr}(\rho\log\rho)$$$ |\psi\rangle = \sum_{i=0}^{2^n-1} \alpha_i |i\r… text/html 2025-09-23T09:46:55+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:hottblockp1&rev=1758620815&do=diff Post 1 — Qubits and the Bloch Sphere This first entry introduces the Bloch sphere representation of qubits and demonstrates how to obtain Bloch vectors with the accompanying Python code. ---------- 1. Qubit states and density matrices A pure qubit state is written as \[ |\psi\rangle = \alpha |0\rangle + \beta |1\rangle, \quad \alpha, \beta \in \mathbb{C}, \quad |\alpha|^2 + |\beta|^2 = 1. \]\[ \rho = |\psi\rangle \langle \psi |. \]\[ \sigma_x = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}, \… text/html 2025-09-23T10:20:21+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:hottblockp2&rev=1758622821&do=diff Post 2 — Unitary Evolutions as Paths on the Sphere This entry introduces how unitary operations generate continuous paths on the Bloch sphere with the accompanying Python code. ---------- 1. SU(2) rotations A unitary rotation about a unit axis $\mathbf{n}$ through an angle $\theta$ is given by\[ U(\theta) = \cos\left(\tfrac{\theta}{2}\right) I - i \sin\left(\tfrac{\theta}{2}\right)(\mathbf{n} \cdot \boldsymbol{\sigma}). \]$I$$\boldsymbol{\sigma} = (\sigma_x, \sigma_y, \sigma_z)$$\mathbf{n}$$… text/html 2025-09-23T10:22:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:hottblockp3&rev=1758622959&do=diff Post 3 — Closed Loops and Berry Phase This entry introduces closed loops on the Bloch sphere and the Berry phase, with examples using the accompanying Python code. ---------- 1. Closed loops on the sphere Certain unitary evolutions return a qubit state to its starting point. On the Bloch sphere these correspond to closed loops. $2\pi$$|0\rangle$$2\pi$$|+\rangle = (|0\rangle + |1\rangle)/\sqrt{2}$$\{\psi_k\}$\[ \phi \approx -\operatorname{Im} \log \prod_k \langle \psi_k | \psi_{k+1} \rangl… text/html 2025-09-23T10:24:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:hottblockp4&rev=1758623097&do=diff Post 4 — Homotopies Between Loops This entry introduces homotopies as continuous deformations between loops on the Bloch sphere, with examples using the accompanying Python code. ---------- 1. Homotopy concept A homotopy is a continuous deformation from one loop $\gamma_0$ to another loop $\gamma_1$\[ H : [0,1] \times [0,1] \to S^2, \]\[ H(0,t) = \gamma_0(t), \quad H(1,t) = \gamma_1(t). \]$\pi_1(S^2) = 0$$p,q \in S^2$$s$\[ \gamma_s = \frac{\sin((1-s)\theta)}{\sin \theta} \, p + \frac{\sin(s\… text/html 2025-09-23T10:26:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:hottblockp5&rev=1758623197&do=diff Post 5 — The Hopf Fibration and Global Phase This entry introduces the Hopf fibration, which lifts Bloch sphere paths into SU(2), and shows how to visualize the accumulated global phase with the accompanying Python code. ---------- 1. Global phase and projective space $e^{i\phi}$$\mathbb{C}P^1$$S^2$\[ S^3 \longrightarrow S^2, \]$S^1$$S^3$$\mathbb{C}^2$$S^2$$S^3$$\langle \psi_k | \psi_{k+1} \rangle$$2\pi$$S^2$$S^3 \to S^2$ text/html 2025-03-27T07:24:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:sierpinsky&rev=1743060269&do=diff Some time ago when seeing plots of 2D representations of Sierpinsky text/html 2025-02-17T13:09:58+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.ekprojectjournal.com/doku.php?id=projects:quantum:supergraph&rev=1739797798&do=diff A series of papers (superposition graph and the currently read quantum graph paper) have lead me to start exploring different quantum state representations in graphs. Specifically hypergraphs, and superpositions of them - i.e graphs of nodes and edges where each edge can connect any number of nodes, where a sum over different hypernode configurations for a superposition of graphs. The supergraph space is explored by reinforcement learning, where different metrics are used to guide the selection …