# Questions tagged [bloch-sphere]

For questions related to the Bloch sphere. In quantum mechanics, 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. (Wikipedia)

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### How to read a Q sphere representation?

I'm trying to understand the Q-sphere representation of a 3-qubit system. I get that the 3-qubits are in a superposition of 2 different states. The first qubit (rightmost) is in a superposition of <...
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### Which states can reached using single-qubit Clifford gates?

Starting with the qubit state $|0\rangle$, which single-qubit states can be obtained by applying single-qubit Clifford gates, i.e. Pauli + Hadamard + $S$ gates?
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### Does composition of two single qubit rotations yield a single rotation around a unit vector?

$\newcommand{\coefcos}[0]{c_1 c_2 - s_1 s_2 \hat{n}_1 \cdot \hat{n}_2} \newcommand{\coefsin}[0]{s_1 c_2 \hat{n}_1 + c_1 s_2 \hat{n}_2 - s_1 s_2 \hat{n}_2 \times \hat{n}_1}$This question relates to ...
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### What is the rotation matrix corresponding to a point on the Bloch sphere?

A qubit is given in the following form: $\left|\psi\right\rangle = \cos\left(\dfrac{\theta}{2}\right)\left|0\right\rangle + e^{i\phi}\sin\left(\dfrac{\theta}{2}\right)\left|1\right\rangle$. Let's ...
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### Reduced Density Matrix Equation of Motion to describe an Ellipse

Given a pure two qubit state $|\psi_{AB}\rangle$. If we trace out system $B$, the remaining density matrix $\rho_A = Tr_B|\psi_{AB}\rangle\langle\psi_{AB}|$, can be represented as a point lying ...
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### Deriving Bloch vector $dr$ from master equation

I am trying to derive the Bloch vector $dr$ for a measurement of a observable in any arbitrary direction $\theta$. For context this is the setup and derivation I have for continuous measurement along ...
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### How to add states on the Bloch sphere from a master equation?

Can you please help me to find an answer to this question: I am using qutip for the study of quantum systems. suppose I have calculated the solution of the master equation using the ...
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### Spin precession using a laser

According to Christopher Monroe: "Modular Ion Trap Quantum Networks: Going Big", the hyperfine states of the valence electron in the Yb+ is used as a qubit. I know that we can change the spin ...
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### Is every single-qubit unitary just a rotation around some unit vector on the Bloch sphere?

I remember reading this somewhere... Is there an elegant proof for this?
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### Why can any density operator be written this way? (quantum tomography)

From page 24 of the thesis "Random Quantum States and Operators", where $(A,B)$ is the Hilbert-Schmidt inner product: \begin{aligned} \rho &=\left(\frac{1}{\sqrt{2}} I, \rho\right) \frac{...
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### How can I find the $\theta$ and $\phi$ values of a qubit on the Bloch sphere?

If I have the following state: $$\left| \varphi \right>=\frac{1}{\sqrt{2}}\left(\left(\frac{1+i}{\sqrt{2}} \right)\left| 0 \right> + \left| 1\right>\right)$$ How can I find the $\theta$ ...
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### Do quantum gates rotate a qubit around the Bloch sphere, or do quantum gates rotate the Bloch sphere around a qubit?

Do quantum gates rotate a qubit around the Bloch sphere? Or do quantum gates rotate the Bloch sphere around a qubit? "The simplest quantum gates are the Paulis: X, Y, and Z. Their action is to ...
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### What does the notation $|+\rangle,|−\rangle,|±i \rangle$ mean in Bloch sphere?

The axis in a a 2D diagram like the following, usually represent 2 quantities. Eg in pic below, $x$ represents time and $y$ represents velocity What gets measured along each axis of a Bloch sphere? ...
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### Can I plot a bigger Bloch sphere using kaleidoscope?

I'm plotting a vector on the Bloch sphere using kaleidoscope: from kaleidoscope import bloch_sphere Is there a way I can make the plot bigger? (Instead of zooming ...
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### Does normalizing a mixed state give a pure state?

According to bloch sphere interpretation, any point on the surface of the sphere corresponds to a pure state and any point inside the sphere corresponds to a mixed state. Suppose you have a point ...
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### Why the Ry rotation matrix give counterclockwise rotation?

The y-axis centered rotation matrix is $R_{y}(\delta)=\left[\begin{matrix} \cos \frac{\delta}{2} & -\sin \frac{\delta}{2} \\ \sin \frac{\delta}{2} & \cos \frac{\delta}{2} \end{matrix} \right]$....
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### How to derive the rotations caused by the H gate?

In Nielsen and Chuang, there's the following paragraph: The Hadamard operation is just a rotation of the sphere about the ˆy axis by 90◦, followed by a rotation about the ˆx axis by 180◦. I am ...
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### $N(\frac{1}{2},2)=3$ for vectors in a Hilbert Space

Came across This question regarding the maximum number of almost orthogonal vectors one can embed in a Hilbert space. They state that $N(\frac{1}{2},2)=3$, and that explicit construction of the ...
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### Bloch sphere, where are magnitude and phase of a qbit?

Where are magnitude and phase of a qbit on Bloch sphere? Phase is angle φ. What do you mean by magnitude? Amplitudes? They are given by angle θ - amplitude of |0⟩ is cos(θ/2) and amplitude of |1⟩ ...
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### What is the "phase" of a state in terms of the Bloch sphere?

I am pretty new to Quantum Computing and am not exactly sure what the phase is. Could you please explain in terms of the Bloch sphere and point out how to mathematically calculate and represent the ...
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### Where is $i|0\rangle$ located on the bloch sphere?

I understand linear transformations on the plane but cannot understand the Bloch sphere. How can a three dimensional sphere be generated by two linearly dependent vecotrs (the basis states 0 and 1)?
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### What kind of transformation does the Y-gate do on the bloch sphere?

I'm going through "Quantum Computation & Quantum Information" by Michael A. Nielsen and Isaac L. Chuang, and as a high school student with no previous knowledge, I cannot understand some things ...
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### How to change the probability of observation by some set amount when initial probability is unknown?

If I have some state $|\psi> = \alpha |0> + \beta|1>$, I know that the probability of observing $|0>$ is $p_1 = |\alpha|^2$. Is it possible to change the probability of observing $|0>$ ...
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### Vector math of applying an X-gate on an $|i\rangle$ basis state

It is well known that the X-gate will apply a rotation about the x-axis on the bloch sphere. Knowing this, the $|i\rangle$ state should be converted to the $|-i\rangle$ state on the application of ...
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### How to get Bloch sphere Cartesian coordinates from density matrix

I am vexed by a particular derivation. Given a state $\psi$ and corresponding density matrix $\rho = |\psi\rangle \langle \psi|$, or $\rho = \begin{bmatrix} a & c \\ b & d \end{bmatrix}$, I ...
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