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Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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Number of measurements in quantum state tomography

I'm very curious to know more about bounds of number of measurements (or number of independent copies of state) required to reconstruct full density matrix $\rho$ such that it is $\epsilon$-close (...
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How to construct a quantum circuit that given $|\psi_0\rangle,|\psi_1\rangle$ outputs $\frac{1}{c}(|\psi_0\rangle+|\psi_1\rangle)$?

Suppose I have two arbitrary quantum states $\lvert \psi_1 \rangle $ and $\lvert \psi_2 \rangle$. Further suppose that we know $U_1$ such that $\lvert \psi_1 \rangle = U_1 \lvert 0 \rangle$, but we ...
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PhD topics in quantum computing [closed]

I am looking for PhD topics in quantum computing related to computer Engineering background (I don't have a background in physics). I tried searching for Machine learning, neural networks and Quantum ...
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Performance metrics in QSVM

I have implemented QSVM on breast cancer dataset using link: "https://qiskit.org/documentation/stable/0.24/tutorials/machine_learning/01_qsvm_classification.html" but unable to compute other ...
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Why should we purify a mixed state?

I'm new to quantum computing so I know this question may sound stupid. But I still want to know why purification is necessary sometimes. Please help me with it:)
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1 answer
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Are the pure quantum states that make up a mixed state orthogonal?

I came a cross a problem when leaning Quantum PCA. I know that a mixed state is an ensemble of several quantum states. But I wonder whether these states that make up for the mixed state are orthogonal....
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1 answer
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Converting data into a SHA256 hash using Qiskit quantum computer

I was wondering how can we convert data into a hash using Qiskit quantum computer? e.g, this code below will generate a SHA256 hash based on random data. ...
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2 answers
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How is the ket of a quantum state calculated in this code?

For the following code qc = QuantumCircuit(2) qc.h(1) qc.cx(1,0) ket = Statevector(qc) ket.draw() the output will be the following: ...
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How is this Variational Quantum Singular Value Decomposition paper efficient in any way?

Link to paper here. This algorithm seems neat but the unitary decomposition of the matrix M generally takes an exponential number of Pauli basis elements in the number of qubits $N$, therefore an ...
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What is the difference between $|+\rangle$ and $|-\rangle$?

What is the difference between $|+\rangle$ and $|-\rangle$. I was reading about quantum states and found that $|+\rangle$ and $|-\rangle$ represent state in superposition of other states. I was just ...
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1 answer
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ket statevector of a 2-quibit system

Given the following code: ...
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1 answer
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How to retrieve a quantum state after passing through a series of quantum gates?

Consider a qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\right> + (\beta_1 + i\beta_2 )\left|1\right>$$ Now if i pass this through a series of quantum gates or any typical ...
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Can I Convert a Qubit in complex form to polar form?

Let's say I have a qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\right> + (\beta_1 + i\beta_2 )\left|1\right>$$ Can I able convert this to polar form $$|\psi \rangle = \cos\...
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Grover search with index register entangled with ancilla

I have a question: when Grover's search is set up with ancilla qubits in an entangled state, does it still work or not? Consider an example with a 4-size search space. Firstly, we use 2 qubits ...
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Why does Qsample encoding require N Qubits for encoding size N probability distribution?

I'm reading Supervised Learning with Quantum Computers book https://link.springer.com/book/10.1007/978-3-319-96424-9. In the data encoding section, Qsample encoding is one of the techniques to encode ...
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Multi qubit states and the CNOT gate

I'm stuck on this passage from a book: Suppose we try to copy a qubit in the unknown state $|ψ\rangle = a|0\rangle + b|1\rangle$ in the same manner by using a $\text{CNOT}$ gate. The input state of ...
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How to sum equal terms in a superposition state?

Suppose after some computation we get a superposition like $\frac{1}{\sqrt{4}}(\left|00\right>+\left|00\right>+\left|10\right>+\left|11\right>)$. How do we merge the same term in this ...
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Why do [1 0 0 1] and [-1 0 0 -1] represent the same physical state? [duplicate]

Below screen shot is from qiskit textbook Because the differences between each of the amplitudes is the same. You could say these two vectors are different mathematically, but the same physically. ...
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Describe |00> and |10> in terms of |0> and |1>

I came across following lines: $|00\rangle$ : both quibts are in state of $|0\rangle$ since $|00\rangle = [1 0 0 0]$ in column vector and $|0\rangle = [1 0]$ in column vector, so if each single qubit ...
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what does the multiplication of Quantum state represent? [duplicate]

According to my understanding of QC/QM: A matrix is a function/operation which when applied on vectors, changes/rotates them. Ket and bra notation is used to denote quantum state. Question 1: ...
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What is dual space, and why is it required?

I recently started QC/QM and came across something called dual space? How do we explain concept of dual space to a layman. why do we need dual space? I tried to read and watch some resources on dual ...
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1 vote
1 answer
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ket zero $|0\rangle = [1,\, 0]$, why a qubit which is initialized with zero is 1 in first basis state?

ket zero $|0\rangle = [1,\, 0]$ The $[1,\, 0]$ is telling us that the probability amplitude for being in the first basis state is $1$, and the probability amplitude for being in the second basis state ...
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what is difference between the following two results

If this question sounds trivial please bear with me as I am beginner in QC. Code 1 ...
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1 vote
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The enery levals crossover problem in Quantum Annealing

How to avoid energy levals crossover in quantum annealing by Kibble-Zurek mechanism? Any detailed references?
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Create a 2-qubit quantum circuit with given state probabilities

Let's say we are given two probability values $p_1 > 0$ and $p_2 > 0$, with $p_1+p_2 \leq 1$ but not necessarily equals to $1$. We are asked to create a 2-qubit quantum circuit with state $|01\...
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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 ...
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1 vote
3 answers
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Is there a way to know if a probability amplitude is negative or positive?

I have a quantum system that outputs a state similar to: $|\psi\rangle = \frac{1}{2}(|00\rangle + |01\rangle + |10\rangle \pm |11\rangle)$. So my question is: is there a way (by measurement or by ...
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4 votes
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How to implement a gate that generate a uniform superposition of all permutation of element

I'm looking for a quantum circuit that permits generating a uniform superposition of all possible permutations for example if we have as input $|0123\rangle$ the output will be the uniform ...
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1 answer
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Generating a random 32-byte hex integer using Qiskit

Hello I posted here yesterday about generating random 16 digits using Qiskit, and a gentle guy helped me but how about a string? How can I generate random 256 bit key in hex format in a superposition ...
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3 votes
2 answers
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Can any rank-$n$ POVM be realized as a rank-one POVM?

Let, $\mathcal{M}$ is a POVM measurement whose elements are $M_i=\sum_{k=1}^np_{ki}|\phi_{ki}\rangle\langle\phi_{ki}|$ with $p_{ki}\geq 0$ and $\sum_{i=1}^sM_i=I$ where $|\phi_{ki}\rangle$ is a ...
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2 votes
1 answer
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Question about mock backends!

I recently learned about the mock backends or the fake backends provided by Qiskit and I was wondering, do they behave the same way IBMQ systems backends like (ibmq_brooklyn)? also, can I depend on ...
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Generating a random 16-digits in a superposition state using Qiskit

Im trying to create a script using Qiskit for a days but somehow i couldn't seem to get it done!! Im new to QuantumComputing, so pardon me if i don't explain something properly. I need to create a ...
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2 votes
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How to find the Choi state of a bipartite quantum channel?

The Choi state of a quantum channel $\mathcal{N}_A$ acting on a system $\rho_A \in \mathcal{H}^A$ is given by: $Choi(\mathcal{N}_A) =( \mathcal{I}_{A'} \otimes \mathcal{N}_A)|\Phi^+\rangle \langle\...
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2 votes
1 answer
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How does a quantum computer find the correct password faster than classical computers using brute-force?

I didn't get this part right! For example, we have an online box with a 16-digit password, and we don't know what the password is! How can a quantum computer find the correct password faster than ...
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1 vote
1 answer
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Grover's Search Number of iterations for M > 1

In Grover's Search algorithm, how to determine the number of iterations for any $M$ such that $1 < M < N/2$? The calculations given in the Nielsen and Chuang book say that $R \leq \frac{\pi}{4} ...
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2 votes
1 answer
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Calculating entanglement with CRZ Gates on non-neighbor qubits

I'm trying to prove that my quantum circuit is behaving the way I want it to, which means I want to calculate its state vector. Until entanglement, I can show it works using the bloch-sphere - after ...
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2 votes
1 answer
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Show that $\|M|ψ⟩\|^2 =⟨ψ|M^† M|ψ⟩$

I'm a newcomer to Quantum Computing and I'm currently working through a tutorial shown here. At one point (second last section in Part II), there is an exercise that I'm really struggling with. I'm ...
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4 votes
2 answers
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Is there a way to convert a superposition $\sum_i a_i |x_i\rangle$ into $\sum_i |a_i,x_i\rangle$?

I am wondering if there is a way to convert a superposition $$\left|\phi\right>=\sum_{i}a_i\left|x_i\right>$$ into $$\left|\phi'\right>=\frac{1}{|{\rm norm}|}\sum_{i}\left|a_i,x_i\right>,$$...
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1 vote
1 answer
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How does superposition in a quantum register work?

When I put each single qubit within a quantum register using Hadamard gates in superposition, how does it work that the whole register quantum-state is in superposition? On the math-level the register-...
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1 vote
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Best way to measure similarity of two quantum circuits?

Suppose you have some unknown circuit X. You don't know the structure of circuit X, but you do have a set of inputs and corresponding outputs, i.e. you know what the circuit does. Then suppose you ...
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1 vote
1 answer
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Why can you check for entanglement using the quantum Fourier transform?

I'm reading this paper on quantum random oracles, and I have some fundamental questions about certain statements that seem to be intuitive (but I can't seem to figure it out). My goal is to have a ...
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0 votes
1 answer
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How does quantum computer store data in QPU and how to calculate? [duplicate]

I couldn't understand any popular science books and articles about quantum mechanisms. And that's why I post here to find an answer to my years-long confusion. Popular science articles tell us that a ...
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5 votes
1 answer
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What is a bipartite quantum state?

I'm very confused for the definition bipartite quantum states. If it's just quantum states defined in $H_1 \otimes H_2$, then if $H_1$ and $H_2$ both are just 1 qubit system, then the bipartite ...
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1 vote
1 answer
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How to prove that there are only 2 classes in 3 qubits entangled state?

Given 2 non-biseparable classes of 3 qubits (more generally tripartite) entangled states : $|GHZ\rangle = \frac{1}{\sqrt{2}} \left(|000\rangle + |111\rangle\right) $ $|W\rangle = \frac{1}{\sqrt{3}} \...
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1 vote
1 answer
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What is $𝑈|1⟩_𝐴|0⟩_𝐵=|0⟩_𝐴|1⟩_𝐵$ called? Is it possible in quantum computing?

I have read about the no-cloning theorem and read that if the states are known then it is a different situation, I was wondering about this transportation of qubits, can the $U$ be for example an $X$-...
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Are there separable states $\rho$ with separable pure decompositions requiring $\operatorname{rank}(\rho)^2$ components?

This question is tightly related to What separable $\rho$ only admit separable pure decompositions with more than $\mathrm{rank}(\rho)$ terms?. In there, examples were given of separable states $\rho$ ...
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1 vote
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How to mathematically determine the final state of a system after some Gaussian microwave pulse?

I'm trying to figure out the final state of a system after some arbitrary microwave pulse (let's say some physical Gaussian pulse with a duration $d$, amp $a$ and width $\sigma$). (I’m looking for how ...
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1 answer
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Calculating counts from statevector in Qiskit

In Qiskit, how are counts calculated from statevectors ? For example ; ...
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3 votes
2 answers
85 views

Existence of a perturbed channel that achieves a perturbed output state

Consider a $d$-dimensional maximally entangled state $\vert\phi\rangle = \frac{1}{d}\sum_{i=1}^d\vert i\rangle_A\vert i\rangle_B$. Let $N_{A\rightarrow A'}$ be a quantum channel and consider $\rho_{A'...
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How to extract solution from HHL statevector on qskit?

I want to extract the HHL solution from the StateVector. I am doing this on a $4\times4$ matrix. For a $2$ by $2$ the solution is available in the StateVector $8$, $9$. However for a $4$ by $4$ matrix ...
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