Questions tagged [quantum-state]

Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant

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Magnitudes and phases of coefficients of a qubit

Quantum mechanics is based on the idea of waves, and waves have both a magnitude and a phase? $$|\psi\rangle = i\alpha|0\rangle + \beta|1\rangle.$$ Does $\alpha$ and $\beta$ represent magnitude and $...
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How to prepare mixed states on a quantum computer?

I am a little bit confused by density matrix notation in quantum algorithms. While I am pretty confident with working with pure states, I never had the need to work with algorithm using density ...
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How long can a qubit exist without decoherence?

In 2020, practically speaking, how long (time-wise) will a qubit function normally before decoherence kicks in?
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Can I generate 4 entangled states (each 5 qubits) on a 5 qubit quantum computer?

Suppose that I have a 5 qubit quantum computer and want to generate 4 entangled states (each of 5 qubits) Single 6 qubit entangled state. Are these 2 cases possible? I am a beginner please help!
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How to find measurement probabilities of a single qbit in a tensored state

Given a tensored state of qbits such as $$ \frac{1}{\sqrt{3}}|0\rangle_1|1\rangle_2 + \sqrt{\frac{2}{3}}|1\rangle_1|0\rangle_2 $$ or $$ \frac{1}{\sqrt{2}}(|0\rangle_1|+\rangle_2 + |+\rangle_1|-\...
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Affine Map of the Bloch sphere

I am referring to Equation (8.89) to (8.92) in Chapter 8 of "Quantum Computing and Information 10th Anniversary Edition" by Nielsen and Chuang. This section deals with the geometric picture of single ...
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How to set initial state on IBM Q?

For my undergraduate final project I am working on a Quantum Inspired Genetic Algorithm. For this I am using IBM Q real devices and I need to set a custom initial state on qubits. Using the ...
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Does quantum computing possess the level of abstraction already to be explicable even without knowledge of physics?

Currently, quantum computer science (in contrast to classical computer science) can mostly only be understood if one has a good inside knowledge of physics, or more precisely quantum physics. Only ...
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Can I compute the fidelity between two states without having to diagonalise them?

So I have been given the following quantum states: $$\rho = \frac{I}{2} + \frac{\bar{s}.\bar{\sigma}}{2}$$ $$\pi = \frac{I}{2} + \frac{\bar{r}.\bar{\sigma}}{2}$$ How do I calculate the fidelity ...
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Why do we need different basis vectors?

There is a basis consisting of $|0\rangle$ and $|1\rangle$ states, i.e. z-basis. Why do we need different basis (in quantum computation), like polar basis and others ($|+\rangle$ and $|-\rangle$)?
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The behaviour of ebits in Entanglement-assisted Quantum Error Correction Codes?

I am reading about Entanglement-assisted Quantum Error Correction Codes from Quantum Information Processing and Quantum Error Correction: An Engineering Approach (Chapter 9) . It is a scheme that ...
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What are $|+\rangle$ and $|-\rangle$?

On a view places, I've seen kets that look like this $\left|+\right>$ or this $\left|-\right>$ but I don't seem to find any explanation of this base online. Is it just a different notation for $...
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Quantum algorithm for binary assignment problem

Based on the properties of the qubit, how could I solve this problem: I have 3 person A B C and 2 taxis T1 and T2 A and B are friends B and C hate each other A and C hate each other How could I ...
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Quantum PCA State Preparation

In Quantum Algorithm Implementations for Beginners is an example of the Quantum PCA with an given 2 x 2 covariance matrix $\sum$. The steps for state preparation are given in the paper. The steps are: ...
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Implementation of tomography on IBM Q

I wanted to ask how do you implement a circuit that finds the non-diagonal values of the density matrix of a quantum state on IBM Q?
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What is the $\lambda$ parameter in the $U3$ gate used for?

The most general single qubit gate is $\mathrm{U3}$ given by matrix $$ \mathrm{U3}= \begin{pmatrix} \cos(\theta/2) & -\mathrm{e}^{i\lambda}\sin(\theta/2) \\ \mathrm{e}^{i\phi}\sin(\theta/2) & ...
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Unentangling a qubit from a system: can we convert $\alpha|000\rangle+\beta|111\rangle$ into $\alpha|00\rangle+\beta|11\rangle$?

Let's say I start with the following arbitrary qubits: $$ \color{red}{\vert Q_1 \rangle = \alpha_1 \vert 0 \rangle + \beta_1 \vert 1 \rangle}\\ \color{green}{\vert Q_2 \rangle = \alpha_2 \vert 0 \...
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Quantum Circuit teleportation

Sender and receiver use teleportation protocol,where sender teleport a quantum state $\left| \varphi \right>=\alpha\left| 0 \right> + \beta \left|1\right>$ to receiver . I want to implement ...
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Partial trace condition in Choi state

Consider Hilbert spaces $\mathcal{X}, \mathcal{Y}$. For any quantum channel $\mathcal{E}_{\mathcal{X}\rightarrow \mathcal{Y}}$, the bipartite Choi state $J(\mathcal{E}) \in L(\mathcal{Y}\otimes\...
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Can two intrinsic angular momentum directions (spin) be used for future entanglement after collapse? [closed]

Persuant to all contributors, here I will use a coin toss analogy since the vector direction is either up or down (heads or tails). Two coins will be used for each of two tosses. It's assumed that the ...
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How can I build up an arbitrary quantum circuit given a certain unitary matrix operation?

Suppose I want to put a qubit whose initial state is $|0\rangle$ to the final state $\frac{1}{\sqrt{3}}|0\rangle + \sqrt{\frac{2}{3}}|1\rangle$. Well, in that case, the unitary matrix that performs ...
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Is there anything practical that can be done with a single qubit?

Is there anything practical that can be done with a single qubit? And by "practical," I mean a problem that can be solved or information that can be stored. I realize that one practical thing that ...
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Are there different orderings of the fifteen SU(4) generators in common use?

I've recently performed certain analyses (Archipelagos of Total Bound and Free Entanglement) pertaining to eq. (50) in Separable Decompositions of Bipartite Mixed States , that is \begin{equation} ...
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How many real-valued coefficients does it take to specify an $n$-qubit state?

Let a quantum register of size $n$ be in the following state, expressed in the computational basis for $n$-qubit states: $$\left| \psi \right> = \sum_{i=0}^{2^n-1} \alpha_i \left| i \right>, \...
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How to find eigenvalues and eigenvector for a quantum gate? [closed]

I need to know how can I find eigenvalues and eigenvectors for a quantum gate, for example $X$ gate.
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What is the |+⟩ and |-⟩ state?

In the Gates Glossary of IBM Quantum Experience it states H gate The H or Hadamard gate rotates the states |0⟩ and |1⟩ to |+⟩ and |−⟩, respectively. It is useful for making superpositions. ...
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How can I check if the following are possible states of a qubit?

I would like to check if state $$ |\psi\rangle = \cos{\theta}|0\rangle + i \sin{\theta}|1\rangle $$ is properly defined. But when I calculated $\langle \psi | \psi \rangle$ is get $$ \cos^2{\theta}...
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Can a qubit be in the inside of the Bloch Sphere?

Can qubit be inside Bloch Sphere, i.e. its length is less than 1? If yes, how we represent that state since we have only parameter for angles and not the length (norm) of the vector?
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How to compute the probability of finding a given state in the $|+\rangle$ state?

Consider the state $$ \left| \varphi \right>=\frac{i}{\sqrt{3}} \left| 0 \right> + \sqrt{\frac{2}{3}} \left| 1\right>. $$ What is the probability of qubit system when measured in the state $\...
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How to know if any two arbitrary qubits are entangled? [duplicate]

Suppose there are two quits called q1 and q2. They are in two different superposition states. If we represent their states on ...
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1answer
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Is it possible to get the $\alpha$ and $\beta$ (amplitudes) of a qubit in Qiskit?

Is it possible to get the $\alpha$ and $\beta$ (amplitudes) of a qubit in Qiskit, i.e. not only probabilities after measurement but complete quantum state?
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What value of K parameter of the following two vectors? [closed]

I have two vectors: $$ a=\begin{pmatrix} {1} & {1} & {1} \ \end{pmatrix} \\ b=\begin{pmatrix} {1} & {2} & {k} \ \end{pmatrix} $$ These vectors should be orthogonal. What is value of $k$...
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What is a better ansatz for VQE?

I am using Qiskit. I made two quantum circuits to generate $\cos\theta|00\rangle + \sin\theta|00\rangle$ for VQE calculations as follows. Apparently, the first one which has fewer CNOT gates is ...
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Find coordinates $\theta$ and $\phi$ on the Bloch sphere of a given qubit state [duplicate]

In last time there is a lot of questions how to find $\theta$ and $\phi$ for particular state on Bloch sphere. I think that it would be useful to solve one example to stop stream of very similar ...
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What unitary gate produces these quantum states from the computational basis?

Suppose that we have one-qubit unitary $U$ that maps $$ \left| 0 \right> \longmapsto \frac{1}{\sqrt{2}} \left| 0 \right> + {\frac{1+i}{2}} \left| 1\right> $$ and $$ \left| 1 \right> \...
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Simplify the system to find the $\theta$, $\phi$ on bloch sphere [duplicate]

I have problem to simplify the quantum system states on bloch sphere to get $\theta$, $\phi$ values, My question is not duplicated! $$ \left| \varphi \right>=\frac{1+i}{\sqrt{3}} \left| 0 \right>...
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What is the probability of a single qubit state lying over the surface of Bloch sphere?

I want to compute the POVM $E_{(\theta, \phi)}$ of the measure which gives the probability of a qubit state lying over the surface of Bloch sphere, with angles $\theta, \phi$. How can I handle this? ...
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Qubit measurement of the state $\frac{1}{\sqrt2}|00\rangle+\frac{i}{2}|01\rangle-\frac{1}{2}|11\rangle$

If we measure the first qubit and obtain $|0\rangle$, what does the second qubit collapses to? $$ \left| \varphi \right>=\frac{1}{\sqrt{2}} \left| 00 \right> + {\frac{i}{2}} \left| 01\right> ...
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what are the angles 𝜃, and ϕ values of the following quantum state? [duplicate]

I need to find the coordinate 𝜃 and ϕ values of the quantum state on the bloch sphere $$ \left| \varphi \right>=\frac{1+i}{\sqrt{3}} \left| 0 \right> + {\sqrt{\frac{1}{3}}} \left| 1\right> $$...
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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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1answer
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Why is a Hadamard gate unitary?

The Hadamard gate is a unitary gate, but how does the matrix times its own conjugate transpose actually result in the $I$ matrix? I am currently looking at it as a scalar, 0.707..., multiplied by the ...
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Is a qubit always in superposition?

I am introduced to ancilla qubits which are usually initialized to $\vert 0 \rangle$. It seems that an ancilla qubit is equivalent to the $0$ bit in classical computing as it will evaluate to $\vert 0 ...
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deliver a quantum register to/from a function in qiskit

Can I create a function in qiskit which receive a quantum register as an argument, and/or returns a quantum register? In the example below, I created a quantum register, and a quantum circuit which ...
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1answer
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Finding the optimal projective measurement to distinguish between two pure states

I would like some help on what should be a simple computation that I'm failing to see through to the end. Suppose I have a qubit which can be in the state $|v\rangle$ with probability $p$, or $|w\...
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What is the corresponding code for finding the state of a qubit on the Bloch sphere?

To find the state of a qubit on the Bloch sphere we use the following formula: \begin{equation} |\psi\rangle=\mathrm{cos}\frac{\theta}{2}|0\rangle+\mathrm{e}^{i\phi}\mathrm{sin}\frac{\theta}{2}|1\...
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1answer
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Is it possible to write a Q# teleportation code which returns a qubit?

In the teleportation codes I have found so far from Microsoft, the codes are written based on returning the bool values but I wonder if in teleportation process, ...
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Print data() with statevector and qasm simulator - Qiskit

I am new to Qiskit and I am trying to implement some very simple 1-qubit gates. I want to initialize the state of the qubit (to 0 and then to 1) and then apply the gate and print the new state of the ...
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Can a classical limit of qubit emerge on a classical computer? [closed]

Hello, I am uncertain; however, today at a toy museum, I might have captured a qubit on a classical computing structure, “ a broken 90-marble abacus,” as shown in the attached photos above. I did ...
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What is the difference between “intraphoton” and “interphoton” entanglement?

I am trying to better understand the following: What is the difference between Intraphoton Entanglement and Interphoton Entanglement? I am new in this field and i want to proceed some work on ...
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Find the qutrit analogue of certain qubit and ququart formulas of Li and Qiao for testing separability

In eqs. (33), (43)-(46), (56) of their paper, "Separable Decompositions of Bipartite Mixed States" https://arxiv.org/abs/1708.05336, Li and Qiao present a number of formulas pertinent to testing the ...

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