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Bloch Sphere – Geometric Representation of Quantum State

 

 

It is very difficult to visualize quantum states before our eyes. The Bloch sphere represents quantum state functions quite well.

The Bloch sphere is named after physicist Felix Bloch. As you can see in the Bloch sphere figure below, it geometrically shows the pure states of two-level quantum mechanical systems.

The poles of the Bloch sphere consist of bits |0⟩ and |1⟩. Classically, the point on the sphere indicates either 0 or 1. However, from a quantum mechanics point of view, quantum bits contain possibilities to be found on the entire surface of the sphere.

Traditionally, the z-axis represents the |0⟩ qubit, and the z-axis the |1⟩ qubit. When the wave function in superposition is measured, the state function collapses to one of the two poles no matter where it is on the sphere. The probability of collapsing into either pole depends on which pole the vector representing the qubit is closest to. The angle θ that the vector makes with the z-axis determines this probability. The probability of the vector collapsing to the other poles of the x-axis or y-axis is 50%.

If you want to visualize your quantum calculations, you can take a look at the simulators whose links I have left below.

 

 

 

Reference

https://en.wikipedia.org/wiki/Bloch_sphere

https://stem.mitre.org/quantum/quantum-concepts/bloch-sphere.html

Links for the Bloch simulators:

1) https://bits-and-electrons.github.io/bloch-sphere-simulator/#{%22blochSphereStateProperties%22:{%22theta%22:%220.0000%22,%22phi%22:%2290.0000%22},%22customGatesProperties%22:{},%22lambdaGatesProperties%22:{%22polarAngle%22:%220%22,%22azimuthAngle%22:%220%22}}

 2) https://www.st-andrews.ac.uk/physics/quvis/simulations_html5/sims/blochsphere/blochsphere.html

3) https://attilakun.net/bloch/

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