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kelly0303

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kelly0303

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Physics news on Phys.org

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gentzen

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It is different for photons (polarization), and for particles with a magnetic moment (spin). I recently fell into that trap:kelly0303 said:Hello! I am curious about how different rotations on the Bloch sphere are done in practice.

I am not sure how to exactly do it for particles with a magnetic moment. My guess is:gentzen said:Well, I was thinking mostly in terms of optics and polarization. A more correct translation of that situation to an electron is that the spin states perpendicular to the direction of propagation are much easier to measure directly (by Stern-Gerlach type experiments) than the ones parallel to the direction of propagation.

[...]

My optics analogies were wrong, but the distinctions they suggested still remain somewhat true for electrons: Even so it seems easy to change the direction of propagation of a "particle" from y-direction to x-direction, it is only "theoretically easy" to do so without changing the spin in case the "particle" is not electrically neutral. But in that case, the Stern-Gerlach type experiment itself becomes difficult.

Let me be clear that my optical analogies had been more wrong than I was aware of. And because they were wrong, my post that you corrected was certainly confusing, both for experts and novices.

gentzen said:But maybe one could use Lamor precession to rotate the spin of the "particle" instead of the direction of propagation. At least it seems possible "theoretically".

The Bloch Sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit). It is important because it provides an intuitive visualization of qubit states and their transformations, making it easier to understand quantum operations and algorithms.

Single-qubit rotations on the Bloch Sphere are represented mathematically by unitary matrices, specifically by the Pauli matrices and the identity matrix. These rotations can be described using rotation operators, such as \(R_x(\theta)\), \(R_y(\theta)\), and \(R_z(\theta)\), which rotate the qubit state by an angle \(\theta\) around the respective axes (x, y, z) of the Bloch Sphere.

Rotations on the Bloch Sphere are implemented using various physical systems such as superconducting qubits, trapped ions, quantum dots, and nitrogen-vacancy centers in diamond. Each system employs different techniques to manipulate qubit states, such as microwave pulses, optical lasers, or magnetic fields.

In superconducting qubits, microwave pulses are used to achieve rotations by resonantly driving transitions between the qubit's energy levels. The frequency, phase, and duration of these pulses are carefully controlled to perform precise rotations around desired axes on the Bloch Sphere, allowing for the implementation of quantum gates.

Challenges in implementing precise rotations include maintaining coherence and minimizing decoherence, accurately calibrating pulse parameters, and dealing with noise and imperfections in the physical system. Additionally, achieving high-fidelity operations requires precise control over experimental conditions and advanced error-correction techniques.

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