Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
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Measuring one qubit in an entangled pair in another basis?
Qubits are usually measured in the computational basis, but we can change the basis by a unitary $U$ to measure in the basis formed by the columns of $U$.
For example, if $| \psi \rangle = | 0 \rangle$...
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Finding the "dual" basis of an overcomplete basis for Quantum State Tomography
This question is related to this stack exchange post: What does the POVM corresponding to single-qubit state tomography look like?
From what I understand, when we are interested in reconstructing a ...
glS♦
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Difference between Classical-Quantum states and States that are completely classical
States that are completly classical :
$$
\begin{aligned}
\tilde\rho_{A B} & =\sum_{x \in \mathcal{X}} \sum_{y \in \mathcal{Y}} p_{X, Y}(x, y)(|x\rangle \otimes|y\rangle)(\langle x| \otimes\langle ...
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Matrices size of n-qubit controlled gates and n+2 states qubit?
Operations on many qubits at the same time is the same as operation of qubits with many states.
For example the CNOT gate matrix with 1 control qubit will be the same of a "gate" acting on ...
glS♦
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Mutual information of shared state is larger than expectation values
Im trying to prove the following identity for a special case:
Alice and Bob share the Bell state
\begin{align*}
|\psi\rangle = \frac{1}{\sqrt{2}}(|00\rangle+|11\rangle).
\end{align*}
Consider the ...
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qiskit: convert from ising result to qubo result?
I have a very simple qubo problem:
...
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How many times the circuit need to run when i use get_stateVector in qiskit
In qiskit,i use get_statevector method to get the statevector from my circuit.
What i want to know is how many times the circuit need to run.
Does is it only one?
...
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How to show that the GHZ state is absolutely maximally entangled?
A multipartite state is called absolutely maximally entangled if for its any bipartition the reduced density matrix of smaller part is maximally mixed. Show that GHZ state has this property.
glS♦
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How does this measurement in the Hadamard basis look like?
I am reading this paper by Mahadev. In going from (19) to (20) the author does a Hadamard measurement on two registers. I don't understand what exactly the Hadamard measurement does.
The (simplified) ...
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Is possible to write a separable state as a finite or countable infinite sum of product states?
Let us consider the tensor product of two finite Hilbert spaces $\mathcal{H}_1\otimes \mathcal{H}_1$.
According to Watrous book, the set of separable states is the convex hull of the set of product ...
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Can you perform stochastic simulations on a quantum computer?
In the article "Biasing the quantum vacuum to control macroscopic probability distributions"[arXiv:2303.03455],
authors present what they call a "p-bit" i.e., a probabilistic bit. ...
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How to properly understand Born's rule as written in the Feynman Lectures?
$\newcommand{\complexes}{\mathbb{C}}$I'm trying to make sense of Born's rule involving a single qubit. Probably, I'm mixing apples and oranges here, but I can't tell where or why. In "The ...
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Which single-qubit mixed states work for magic state distillation?
I recently started learning about universal quantum computation using magic states, and I'm currently reading one of the early papers on the subject by Bravyi and Kitaev .
In the paper, they showed ...
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quantum generalisation of random variables
What is the quantum information equivalent of a classical probability random variable ? Is it a density matrix or an observable ? If so can someone show me how to write a random variable that follows ...
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Probability of measuring the first qubit in the state $\frac{1}{\sqrt 2}(|0⟩+|1⟩)$ in a two-qubit state
If I consider $a|00\rangle + b|01\rangle +c|10\rangle +d|11\rangle$ as a valid two-qubit system, what is the probability of measuring the first qubit in state $\frac{1}{\sqrt 2}(|0⟩+|1⟩)$?
I know ...
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How to combine measurement of each term in Hamiltonian $H = aH_1 + bH_2$ to get final results?
I have a Hamiltonian $$H = aH_1 + bH_2\,,\tag{1}$$ with $a$ and $b$ being coefficients, and I want to apply each term/evolution separately, then recombine the measurement results to get the result for ...
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Quantum Process Tomography for 2 qubits
I need clarification on a few aspects related to Box 8.5 and Exercise 8.34 from the book Quantum Computation and Quantum Information by Nielsen & Chuang .
While attempting Exercise 8.34, I ...
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Can transformations of qubits in quantum computing be carried out instead by transformations of the measurement instrument?
As far as I understand, transforming and maintaining states of qubit devices in quantum computers is associated with all sort of problems such as transformation errors and decoherence. At the same ...
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Is the full quantum circuit always in a pure state?
I'm aware, that if you measure just a subset of a circuit, which is entangled to another subset, it'll be in a mixed state. For example, if you measure q1 in the ...
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Phase shift on qiskit quantum teleportation simulation
I wonder in Qiskit why the phase shift occurred in my simulation and how I can turn it off.
I posted another question regarding the same simulation here, and while I tried to solve this on my own, I ...
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Is it true that for a quantum algorithm to be efficient it must feature a highly entangled state at some point?
I'm wrapping my head around how and why quantum computers can provide advantage over classical. A basic and naive argument is that the dimension of the Hilbert space of $n$ qubits grows as $2^n$. ...
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How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?
I'm working through the book "Introduction to the Theory of Quantum Information Processing" by Bergou and Hillary, and I've encountered a scenario that I'm not sure how to approach. In ...
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How to get $\theta$ and $\phi$ in a Bloch sphere for individual qubits in a quantum register?
I have a quantum register with some qubits (I'm just new to all of this). Is there a way to achieve $\theta$ and $\phi$ angle values in the Bloch sphere for each qubit separately? If I do a circuit ...
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SX operator and superposition
I am running some tests using the probabilities we get from statevector to assert values in qiskit. For instance, with two qubits and a hadamard gate on the first one we have:
...
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The expectation values for the values of both qubits [closed]
Let’s consider the two-qubit state
|Ψ⟩ =(1/2)|00⟩ + i(√3/4)|01⟩ +(3/4)|10⟩.
a) Find the expectation values for the values of both qubits separately.
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Quantum GAN implementation
Can anyone provide a good link to understand how to implement qgan using pytorch in qiskit. Trying to understand this ( https://qiskit.org/documentation/machine-learning/tutorials/...
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How to create a maximally entangled state of two 4-level quantum mechanical systems?
Let's say that I have a 4-level quantum state, which is described by a linear combination of the following four eigenbases:
$$|\text{red}⟩ = \begin{bmatrix}
1 \\
0 \\
0 \\
0
\end{bmatrix} , |\text{...
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Can we say what happens to phases after a reset?
Take a simple state-vector of a 2 qubit system:
$$
|\psi\rangle = \frac{1}{3\sqrt{2}}\pmatrix{1 \\ 2i\\ -3 i \\-2}
$$
Suppose we now reset the last (second) qubit. This forces the state space to ...
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For tetrapartite state, and another way of decomposition, is the Schmidt basis separable?
Consider two tetrapartite quantum states $|\phi\rangle^{AA^\prime BB^\prime}$ and $|\psi_1\rangle^{AA^\prime}|\psi_2\rangle^{BB^\prime}$ in a finite dimentional Hilbert space $\mathcal{H}^A\otimes\...
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Preparation of states that correspond to efficiently integrable probability distributions
I have been trying to implement methods from paper Creating superpositions that correspond to efficiently integrable probability distributions by Grover and Rudolph.
It is stated that there exists an ...
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Unitary Transformations for Schmidt Decomposition
$\newcommand{\ket}[1]{|#1\rangle}$
Suppose a pure state $\ket{\psi}$ has a Schmidt decomposition given by $\ket{\psi^{SD}}$, which can be obtained via the diagonalization of the reduced density matrix ...
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How to integrate a function with the Haar measure over multiple qubits
I am starting with a product state over multiple qubits. That looks like the expression below.
$$
|\psi\rangle = \left(\cos\left(\frac{\theta_1}{2}\right)|0\rangle+e^{i\phi_1}\sin\left(\frac{\theta_1}{...
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Why does the point $(0,0,-1)$ on the bloch sphere correspond to the state $|1\rangle$ and not $-|1\rangle$ or $e^{i \phi}|1\rangle$?
In this representation for points on the $Z$-axis, $\phi$ is not defined. If the point $(0, 0, 1)$ is taken since $\theta$ is $0$ and $\sin(\theta/2)$ is zero, it doesn't matter what $\phi$ is. The ...
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Considering a spin-$\frac{1}{2}$ qubit, which is the ground state, $|0\rangle$ or $|1\rangle$?
Considering a spin-$\frac{1}{2}$ qubit, which is the ground state, $|0\rangle$ or $|1\rangle$? I apologize for the simplicity of the question.
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Does the state obtained flipping $a,b$ in the state $(a,b)^T$ have a name?
Suppose we have a qubit with a state vector of $\begin{pmatrix}
a \\
b
\end{pmatrix}
$.
If we flip $a$ with $b$ does the new qubit has a name in relation to the first qubit?
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How does application of a gate on one qubit/amplitude affects the rest of the multi-qubit system
Hadamard and Toffoli Gates form a universal set of gates, thus all quantum circuits can be created out of them. My question is assume any circuit with some $N$ inputs and $K$ gates.
For any such ...
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Qutip - Use of Create vs Fock state functions
I'd like to understand the physical difference between the states created using the following two means, i.e. state1 and state2:
...
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calculate the reduced density matrix of a 2 qubit state and compare the eigenvalues
So I have the exercise to apply a Cz gate to the following 2 Qubit state
$|a\rangle \otimes |b\rangle = (a_0 |0\rangle + a_1 |1\rangle) \otimes (b_0 |0\rangle + b_1 |1\rangle)\\\\$
Afterwards, I ...
glS♦
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Entangling attack on BB84 protocol
I am trying to solve the exercise 5.3 from the book "A Gentle Introduction to Quantum Computing". The exercise reads as follows:
Suppose Eve attacks the BB84 quantum key distribution of ...
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How can I get $|00\rangle |01\rangle |10\rangle |11\rangle$ entangled on IBMQ experience?
How can I get this situation entangled on IBMQ experience?
$$|00\rangle:\\
|01\rangle:\\
|10\rangle:\\
|11\rangle:
$$
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Measuring a state $\frac{1}{2}|0\rangle-\frac{\sqrt 3}{2}|1\rangle$ in the $X$ and $Z$-bases?
If a qubit is in the state $|\psi\rangle = \frac {1}{2}|0\rangle - \frac{\sqrt 3}{2} |1\rangle$, how do I measure it in the $Z$-basis, i.e. $\{|0\rangle,|1\rangle\}$, and the $X$ basis, i.e. $\{|+\...
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Why is a Bell state involved in quantum teleportation?
Notation: $|\text{qubit}_{1}, ..., \text{qubit}_{N}\rangle$.
The goal of quantum teleportation is to send quantum information using classical bits.
A source transmits a state $|\psi\rangle_{A_{0}} = \...
glS♦
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A question on a subset of projectors onto symmetric subspace
Use $\text{perm}_t$ to denote the set of all permutations among $t$ items. For any particular subset $S\subseteq\{0,1\}^n$ and any $\sigma\in \text{perm}_t$, we define
\begin{align}
P_S(\sigma) = \...
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Calculate qubit state in terms of two states that are opposite points on Bloch sphere
I am new to quantum computing and reading the book "Introduction to Classical and Quantum Computing", by Wong (link).
I do not understand how to calculate the qubit state for the below ...
glS♦
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What are the possible $\beta$ in a qubit state $\frac{e^{i\pi/8}}{\sqrt5}|0\rangle+\beta|1\rangle$?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with exercise 2.8 (page 86):
Exercise 2.8. A qubit is in the state
$$
\frac{e^{i\pi/8}}{...
glS♦
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What is $H\left| \psi \right>$ with $\left| \psi \right> = \alpha\left| 0 \right> + \beta\left| 1 \right>$?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with exercise 2.29 (page 107):
Exercise 2.29. Say $\left| \psi \right> = \alpha\left|...
glS♦
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What is $HTHTH\left| 0 \right>$?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with exercise 2.33 (page 108):
Exercise 2.33. Answer the following:
(a) Calculate $...
glS♦
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How to implement the state $|\psi\rangle = \frac{1}{\sqrt{2}}\left[|0\rangle \otimes |X_i\rangle + |1\rangle \otimes |X_j\rangle\right]$
I am trying to implement the quantum k-means algorithm proposed in https://arxiv.org/pdf/1909.04226.pdf.
In the equation (8) of the manuscript we need to implement a state $|\psi\rangle = \frac{1}{\...
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How does error accumulate when entangling two distant qubits with limited connectivity?
My goal is to minimize accumulated error when entangling two qubits that cannot be entangled via a single native two qubit gate operation.
I have a coupling map/graph for the qubits of an IBM quantum ...
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What is a Hadamard test?
What is a Hadamard test? I have seen this term at many places in video lectures and on various weblinks.
A detailed answer on this would be a great help. This is what Wikipedia says, but I really ...
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