# 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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### Bloch representation of a quantum channel acting on a 2-qubit density-matrix

A previous answer nicely show the relationship between the Pauli transfer matrix (PTM) and the Bloch representation of a quantum channel that acts on single-qubit density matrix. In short, given a ...
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### Visualizing the Effect of a Parameterized Gate on a Qubit Using the Bloch Sphere in Qiskit 1.0

I am seeking assistance with visualizing the effect of a parameterized gate on a qubit using the Bloch Sphere representation. I have a preliminary code snippet as follows: ...
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### Can we find the quantum state using the Bloch vector in the Bloch sphere?

I had a question about qft. When we apply QFT in a circuit, we can display the qubits separately in the bloch sphere with the plot_bloch_multivector function. I realized that the bloch vectors do not ...
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### What do the angles in a Poincaré sphere represent?

I understand the principle of the Bloch sphere. You write your state in the following way: $$|\Psi\rangle = \cos(\theta/2)|0\rangle+e^{i\varphi}\sin(\theta/2)|1\rangle.$$ The angles $\varphi,\theta$ ...
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### Converting $H$ gate to $R_x$ and $R_z$

EDIT: My solution is supposed to work for $|1\rangle$ state too. See https://imgur.com/a/7F1cHu4 Right of the bat the answer is $$H=R_z(\pi/2)R_x(\pi/2)R_z(\pi/2)\,.$$ My question is, I cannot reach ...
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### Affine transformation of the Bloch sphere to Kraus representation of qubit channels

It is known that qubit channels can be written in the form: \begin{align} \Phi(\rho) = \frac{1}{2}\left(I+(T\vec{r}+\vec{t})\cdot\sigma\right)\ \end{align} where $\vec{r}$ is the Bloch vector ...
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### In the phase flip action on standard basis, why do we consider the $-1$ phase only for the $|1\rangle$?

Prof. Watrous in the first lecture of Qiskit summer school 2023, mentions: "....the significance of putting a minus sign in front of the $|1\rangle$ basis vector and not $|0\rangle$ will be more ...
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### Is a qubit passing through a gate a 3D rotation of the vector on the Bloch sphere?

When a qubit passes through a gate isnt it a 3D rotation of the vector on the Bloch sphere?
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### Closeness between two unitaries on the Bloch sphere

The fidelity between two (single-qubit) quantum states can be easily translated into the euclidean distance between the two states on the Bloch sphere (hilbert-schidmit distance). I'm curious if this ...
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### Sufficient conditions for a single-qubit unitary to be the identity

Say I have a unitary $U = e^{-iHt}$ where $H = \alpha X + Z$. First, suppose $U = I$. Then it rotates a set of initial states to themselves. Say I'm working on a computational basis, then on the Bloch ...
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### Representing networks with qubits as edges

I am looking to take a classical non-negative real valued network and generalize it to the quantum case for processing. A network is given by an adjacency matrix, essentially edge weights $e_{ij}$ for ...
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### How to represent an entangle state on Bloch Sphere [duplicate]

If states are not entangle, both bloch sphere represent the state of qubit but if they are entangle, why bloch sphere show nothing??
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### Plotting the Bell state on a Bloch sphere

How can you plot the bell state on a Bloch sphere? bell = QuantumCircuit(2) bell.h(0) bell.x(1) bell.cx(0,1) Is there any good reference for understanding how ...
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### Is the Bloch sphere the same as the electron spin?

A single qubit is represented with a bloch sphere and implemented on an electron with only two energy values from lots of them. So, I am confused about why an energy range is represented as a ...
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### Show that for pure states the description of the Bloch vector we have given coincides with that in section 1.2

$\newcommand\bra[1]{\left\langle#1\right|}\newcommand\ket[1]{\left|#1\right\rangle}$ I am having a little bit of difficulty with part (4) of Exercises 2.72 from Nielsen and Chuang's "Quantum ...
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### Why are probabilities represented with alpha^2 and beta^2?

To preserve the Complementary Rule of probability, the sum of the probabilities of the outcomes (measured |0> or measured |1>) must equal 1 or 100%. That's why alpha^2+beta^2=1. However, why the ...
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### Why is the conjugate being used when rewriting a qubit state in another basis?

I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with an example given on page 88 (point 4). The author gives the two following states, ...
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### Is there a criteria to ensure a one-qubit operator is exactly of the form $R_n(\theta)$ (i.e without a global phase $e^{i\alpha}$)?

Reading the Nielsen and Chuang, I saw that every unitary operator $U$ can be written as $e^{i\alpha} R_n(\theta)$ for some well chosen $n \in \mathbb{R}^3$ and $0 \leq \theta < 2\pi$. I would like ...
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### Is the function PU(2) and SO(3) induced by the Bloch sphere bijective?

I have difficulty understanding the fact that, as written in this reference, every single-qubit unitary corresponds to a unique rotation of R3 and vice versa. If I understand well, this means there ...
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### Finding the polar and azimuthal angles of the Bloch vector corresponding to $\frac1{\sqrt2}(1-i)|0\rangle-\frac i{\sqrt2}|1\rangle$ [duplicate]

I need to find the polar angles and azimuthal angles of the following bloch vector: $$\frac{1-i}{2}|0\rangle - \frac{i}{\sqrt{2}}|1\rangle$$ I just couldn't figure it out, and I could also not find ...
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### How many parameters do we need to characterize a pure state?

Suppose I have a pure qubit. I can think of starting with the state $\vert 0\rangle$ and apply some unitary to it. Such a unitary has three parameters according to this link. In $d$ dimensions, the ...
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### Geometric representation of rotation operator on Bloch sphere

I'm studying Nielsen&Chuang Book and need some clarification on mapping arbitrary rotation operator onto geometric tranformation of vector on Bloch sphere. I thought that $R_{\vec{n}}(\theta)$ ...
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### Where does 1/sqrt(2) come from in the state of i

I’m trying to learn about calculating coordinates for $\theta$ and $\varphi$ in a Bloch-sphere. I came accross this book about it, including example questions. At question 2.12b, they ask to give the ...
So far I learned that a qubit can be written as $| \psi \rangle = \alpha | 0 \rangle + \beta | 1\rangle$ with $|\alpha|^2 + |\beta|^2 = 1$ and reparametrized as $| \psi \rangle = cos( \theta / 2) + e^{... • 143 2 votes 2 answers 367 views ### What is the Bloch sphere representation of$\rho\to\mathcal{E}(\rho) = |+\rangle\langle+|ρ|+\rangle\langle+| + |−\rangle\langle−|ρ|−\rangle\langle−|$? Suppose a projective measurement is performed on a single qubit in the basis$|+\rangle, |−\rangle$, where$|±\rangle \equiv (|0\rangle\pm |1\rangle)/\sqrt{2}$. In the event that we are ignorant of ... • 831 2 votes 0 answers 39 views ### What do the values of θ, ɸ, and λ represent visually in the Bloch Sphere when defining a unitary gate? [duplicate] In IBM Quantum Docs, it is stated that a unitary matrix can be defined as$U = \begin{bmatrix} \cos(\theta/2) & -e^{j\lambda}\sin(\theta/2) \\ e^{j\phi}\sin(\theta/2) & e^{j\lambda+j\phi}\cos(\...
$$\begin{array}{l} |\psi\rangle=\frac{\sqrt{3 i}}{2}|0\rangle-\frac{1}{2}|1\rangle \\ |\psi\rangle=0.924|0\rangle-0.382 i |1\rangle \end{array}$$ Basically I’m trying to convert these to a standard ...