# 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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### Question on State Transfers [closed]

I am beginner to quantum physics and I came across this problem that I cannot figure out[![enter image description here]]
1 vote
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### Can a many-qubit quantum state be represented on Bloch spheres? [duplicate]

Can a general multi-qubit quantum state be represented on Bloch spheres? If not, what is the maximal number? Are there any corresponding constraints? Thanks.
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### Rxx gate as a set of rotations

I'm trying to represent Rxx gate as a set of physical rotations of two qubits in 3D space (or as rotations of Bloch Spheres that is the same). In some simple cases it works well: If q0 is in the ...
83 views

### Find a set of vectors on the Bloch sphere such that $\langle \psi_i | \psi_j \rangle = \frac{1}{\sqrt{n}}$

How can I find a set of multiple vectors on the block sphere which satisfies $$\langle \psi_i | \psi_j \rangle = \frac{1}{\sqrt{n}}$$ where $n$ is any natural number greater than $2$? I think I have ...
1 vote
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### When using Qiskit's plot_bloch_vector function, how can I set colors for vectors?

I am able to visualize vectors on a bloch sphere using Qiskit as follows: ...
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### Are qubits just analog, continuous classical bits? [duplicate]

Topologically, classical bits (cbits) are essentially special cases of qubits restricted to the poles of the Bloch sphere. However, this restriction doesn't seem to be classical per se, but is simply ...
1 vote
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### How do I stepwise rotate a qubit on a Bloch sphere using $SO(3)$ and $SU(2)$ group?

Let us first introduce two fundamental functions for coordinate transformations: ...
189 views

### How to represent the Hadamard gate as a rotations on the Bloch sphere?

I am new to Quantum Computing, and I have decided to try and learn the quantum gates. I am trying to understand how to represent some basic gates as rotations on the Bloch Sphere. I was able to ...
369 views

### Why is the angle of Rz(π/4) Rx(π/4) an irrational multiple of π

It is stated in the Qiskit tutorial section 2.4 that if you apply a rotation around the z-axis of π/4 and subsequently a rotation around the x-axis of π/4, the end result is an angle around some axis ...
126 views

### Why can a ZY decomposition not decompose an arbitrary single qubit gate?

To decompose an arbitrary single qubit gate, we need to do a "$e^{i \alpha}$ZYZ" decomposition. Intuitively however I do not understand why a "$e^{i \alpha}$ZY" decomposition is ...
74 views

### Can the Bloch sphere representation be applied to many-qubit states with an iterative approach?

By ignoring the global phase, we can represent a single qubit state as \begin{equation} |\psi\rangle = \cos(\theta)|0\rangle + e^{i\phi}\sin(\theta)|1\rangle \end{equation} which very much looks like ...
1 vote
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### Calculate qubit state in terms of two states that are opposite points on Bloch sphere

I am new to quantum computing and reading the book "Introduction to Classical and Quantum Computing", by Wong (link). I do not understand how to calculate the qubit state for the below ...
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### How to prove that the coefficients of Pauli bases remain its length under unitary operation?

Formal problem statement. For a real vector $\vec r$ in bases of $\sigma_i\otimes \sigma_j$ with $i,j=0,1,2,3$, $i$ and $j$ not equal to $0$ at the same time, $\sigma_0=I$ and other indexes stands for ...
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### How do we define qubit measurements in a plane?

When does $\vec{a} \cdot \vec{\sigma}$ define a measurement in x-y, y-z, and x-z planes?
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### Why the Ry rotation matrix give counterclockwise rotation?

The y-axis centered rotation matrix is $R_{y}(\delta)=\left[\begin{matrix} \cos \frac{\delta}{2} & -\sin \frac{\delta}{2} \\ \sin \frac{\delta}{2} & \cos \frac{\delta}{2} \end{matrix} \right]$....
1 vote
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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 $|0>$ ...
158 views

### Can we rotate Bloch vectors for qudits like we do with qubits in the Bloch sphere?

I have been looking into the Bloch vectors for qudits and have been wondering if we can do rotations that are similar to the rotations in the qubit Bloch sphere. Like, once we create a Bloch vector ...
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### Show that the trace of squared density matrix gives ${\rm tr}(\rho^2)=\frac12(1+\|\mathbf n\|^2)$ [duplicate]

Equation 7.7 is given below: $$\hat\rho = \frac12(I +n_x(\hat X)+n_y(\hat Y)+n_z(\hat Z))$$ Where $I$ is the identity matrix and $\hat X,\hat Y,\hat Z$ are Pauli matrices. Now my attempt of this was ...