In quantum mechanics and computing, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit), named after the physicist Felix Bloch. [1] Mathematically each quantum mechanical system is associated with a separable complex Hilbert space .

Jan 3, 2023 · The Bloch sphere is a geometrical representation of a qubit’s state, a unit of quantum information. It is named after physicist Felix Bloch, who introduced the concept in a 1946 paper.

We call this sphere the Bloch sphere, and the unit vector \vec{s} defined by \theta and \varphi the Bloch vector. This is a very useful way to visualise quantum states of a single qubit and unitary operations that we perform on it.

Feb 7, 2021 · The Bloch sphere is such a tool- a mathematical representation of a given quantum state of a qubit, with which researchers can pinpoint and manipulate various such states...

Simulate the evolution of a qubit or spin on the Bloch sphere. This tool is ideal to understand quantum operations and to generate plots for presentations or publications.

Sep 4, 2015 · One common way to represent a state in the Bloch sphere is to give just the two $\theta$ and $\phi$ angles as shown below: Source. Since a sphere is non-Euclidean, a good way to visualize it is to walk through some easy to understand paths around it. On the following image we do two paths: start at 0, pass through +, 1, -, and return back to 0

Oct 21, 2024 · The Bloch Sphere is a projection of the state space onto the more familiar two dimensional sphere in three dimensional space $S^2 \subset \mathbb{R}^3$. Importantly, under this projection unitary transformations of the state space correspond to …

The Bloch sphere is typically used in the quantum information context. So rather than talk about spin vectors, we’ll often be talking about the states of quantum bits.

The Bloch Sphere, shown in Figure 2, is named for the physicist Felix Bloch [1] and gives us a beautiful way to think about and visualize the state of a qubit in 3-dimensional space. In the Bloch Sphere the pure state of a qubit j i is represented as a point on the surface of the sphere.

May 5, 2024 · The Bloch sphere provides a geometric representation of the state of a single qubit, mapping all possible states onto the surface of a unit sphere. The Bloch sphere is a concept introduced by Felix Bloch in 1946 and later developed by Werner Heisenberg.