Questions tagged [quantum-state]

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

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Is there an alternative algorithm to extract a probability of states of qubit after measuring?

Let a simple quantum circuit consist of one qubit and one classical bit. Initially, a qubit has the $|0\rangle$-state and then goes through some sequence of quantum gates, see the circuit below. The ...
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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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Quantum measurement on Bloch Sphere

I'm reading the paper "Data re-uploading for a universal quantum classifier". This paper proposes the classification process as follows $x_i $ with different rotation angle $\theta_i$ ...
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How to read data from multiple qubits and feed it to a MLP

Being new in the field of quantum computing, I tried with the implementation of "https://qiskit.org/textbook/ch-machine-learning/machine-learning-qiskit-pytorch.html" using a single qubit. ...
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Why are orthogonal quantum states represented as collinear in the Bloch sphere?

We know that the angle between two orthogonal qubit states is 90 degrees. Why then, when we use the Bloch sphere, the angle becomes 180 degrees?
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Construct the unitaries U by decomposition in TSP Qiskit? [duplicate]

I'm stuck in here and really don't understand this stuff. In order to construct the unitary matrices for Quantum Phase Estimation, Qiskit decomposes the diagonal unitary matrices U(j) by tensor ...
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Why is Dirac notation used for quantum states?

I am thinking that I am using Dirac notation to represent $|0\rangle$ and $|1\rangle$ and we are using column vector but why actually using column vector where first one is $(0 \,1)$ for $|1\rangle$ ...
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How simulation of noisy quantum circuits is done in Qiskit using the statevector method

While performing VQE calculations of medium-sized molecules like H2O, using Qiskit AerSimulator with noise, I noticed that even for a large number of shots, the speed of simulation using statevector ...
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Decomposing a projector in the computational basis in terms of Pauli matrices

I have a $x \in \mathbb{N}$, and I would like to decompose it in terms of the Pauli matrices $\sigma_x, \sigma_y, \sigma_z$ and the identity. My first steps are as follows: $$ \begin{align} |x \...
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How do I draw a multi control cz gate or do I have to make my own gate?

I want to build a diffuser and an oracle so that's why I wanted a multi control cz gate but I looked everywhere I didn't get any
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How to represent a statevector in Dirac notation form using Qiskit?

I am learning from qiskit textbook, and I was wondering how may I get a statevector of the following form: $$ \frac{\sqrt{2}}{2}|00\rangle + \frac{\sqrt{2}}{2}|10\rangle $$ If I run code for this in ...
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Preparing a superposition state modulo $k$

Consider being given the description of a function $f: \{0, 1\}^n \rightarrow \{0, 1\}^m$ and the binary representation of an integer $k$. Is the state \begin{equation} |\psi_{f, k}\rangle = \frac{1}{\...
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Truncating the bond dimension of an MPS -- how good is the approximation?

$\newcommand{\complex}{\mathbb{C}}\newcommand{\ket}[1]{|#1\rangle}$ Let $\ket{\psi}\in(\complex^d)^{\otimes n}$ be a pure quantum state. It is well-known that $\ket{\psi}$ is a matrix product state ...
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Formal measurement of the probability of an outcome of a Qubit in the hadamard base

I am fairly new to Quantum Computing and have a question which might be trivial for all of you, but I am really struggling with it. From Quantum Computation and Quantum Information I have learned, ...
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How to rewrite the quantum state to qubits?

I have a following state (indexing everything from 0 here) $$ | \psi \rangle = \frac{1}{\sqrt{2}} \left( | \uparrow_0 \downarrow_1 \rangle - | \downarrow_0 \uparrow_1 \rangle \right) $$ and I need to ...
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Is the post-measurement state always pure after a partial measurement?

Imagine I have two potentially entangled qudits and measure the first one using some Hermitian operator $M$ that has only one eigenstate per eigenvalue and get some outcome $m$. Can I know for sure ...
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Barren plateaus in multi-qubit system

I'm looking on pennylane's tutorial https://pennylane.ai/qml/demos/tutorial_barren_plateaus.html In this link, to illustrate barren plateaus, author used example circuit and barren plateau plots. ...
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Does a fidelity of $\mathcal{F}(U_1|0\rangle, U_2|0\rangle)=1$ imply that $U_1=U_2$?

I'm now studying quantum ML and now studying about fidelity ($\mathcal{F}$). To my knowledge, fidelity means the distance between two quantum states, $\textit{i.e.,}$ if $\mathcal{F} ==1$, then the ...
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Method and Meaning of Quantum Encoding in Quantum Machine Learning

I'm now studying quantum machine learning. While studying papers about quantum machine learning, I have a question about quantum embedding. To my knowledge, some general embedding algorithms, such as ...
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What does the phase $\phi_1$ in a state $|\psi\rangle=a_1|0\rangle+a_2|1\rangle$ with $a_j=r_j e^{i\phi_j}$ say about state $|1\rangle$?

I'm a beginner in quantum computing and this question has been bugging me for quite some time. I have seen in various articles that a qubit is a device whose state can be represented by a unit vector ...
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How can you extract all the state probabilities in e.g. Grover's search?

In the Qiskit tutorial for e.g. Grover's algortihm, there is a 3-qubit implementation on a real quantum computer https://qiskit.org/textbook/ch-algorithms/grover.html#3.1.2-Experiment-with-Real-...
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Creating a uniform superposition of a subset of basis states

Assume we have an n qubit system and $K \subset \{1,...,2^n\}, K \neq \emptyset $ I want to describe a circuit that takes the input $|0\rangle....|0\rangle$ to the state $|\psi\rangle = \frac{1}{\sqrt{...
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Factoring some qubits with Kronecker product

I have this quantum state: $$|\phi \rangle =\frac{1}{4\sqrt{2}}|000\rangle +\frac{3-\sqrt{5}i}{8}|001\rangle +\frac{1}{4\sqrt{2}}|010\rangle +\frac{3-\sqrt{5}i}{8}|011\rangle \\+\frac{1}{4\sqrt{2}}|...
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CNOT entangling a third qubit and how measurement impacts entanglement

I'm trying to understand entanglement, superposition and the effects of measurement on entangled qubits a bit better. About entanglement: I know that the circuit below will entangle the two qubits: ...
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A path towards building quantum Computing graduation project for undergraduates

I need help. I'm a computer science student with a Data science major. I have a final graduation project this year. With that, I want to create a project in the Quantum computing field. I'm already ...
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How we can switch the digital multi-qubit gates to analog multi-qubit blocks?

What is the difference between the digital and Analog Quantum gate? and the multi-qubit gates involved in a VQE ansatz can be switched to analog multi-qubit blocks. so How we can switch the digital ...
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What is the rank of the pure state?

Consider pure or nearly pure quantum state, is it usually low-rank? Can you give a example of a concrete state and its rank?
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What actually StatePreparation perform in qiskit?

I used this method to initialize classical data in a circuit. I would like to know what's under the hood and the complexity of this procedure, but I can't find anything on the internet which suits my ...
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What is the value of a control qubit as a Controlled-X Gate or Tofolli Gate parameter?

For example in a Controlled-X or Tofolli gate, qubits can be assigned as control bits. But before the measurement ; what are the values of these qubits in the gate tensor since they can not be 1 or 0 ?...
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Quantum gate count minimization

In classical digital logic, we have K-map and Quine–McCluskey algorithm to minimize boolean equation, thereby reducing the number of logic gates needed. Is there such a thing in quantum computing?. ...
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Add a negative phase to selected states

I have $n$ qubits in superposition. I want to add a negative phase to all states with more than $m$ $1$s, e.g. for $n=3$ qubits and $m=1$ I want to get: $\frac{1}{\sqrt{N}}(|000\rangle + |001\rangle + ...
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Why after breaking the entanglement does the phase disk in the second qbit not match the result?

I am new in IBM composer quantum and I have a doubt. I have the next circuit After reinitializing q0 and reading it. (breaking entanglement) The phase disk for qubit q1 says that 100% is 0, but the ...
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What is size of the state space?

I'm taking my first Quantum Computing MOOC and the image below is from one of the very first slides: My question is, what is the state space? I've a guess that it is the set of all possible results ...
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Qutip: Mesolve gives different and weird results with different fock state numbers

I have been trying to simulate the average number of particles at 3 sites of coupled harmonic oscillators. I have used the code from the below tutorial: https://notebook.community/ajgpitch/qutip-...
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In a state $\alpha \vert HL \rangle + \beta \vert VR \rangle$ can a particle be measured in the $\{|L\rangle,|R\rangle\}$ basis?

Given a pair of entangled particles: $\alpha \vert HL \rangle + \beta \vert VR \rangle$ where: $\alpha^2 + \beta^2=1$ $H$ and $V$ are orthonormal vectors. $L$ and $R$ are orthogonal vectors (but not ...
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What is the solution to Nielsen and Chuang Exercise 2.65?

Nielsen&Chuang Exercise2.65: Express the states (|0 + |1)/ √ 2 and (|0−|1)/ √ 2 in a basis in which they are not the same up to a relative phase shift. Consider an orthnormal basis :$\begin{cases}...
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It is possible to obtain amplitudes from superposition with certain probability?

In many papers and books on quantum theory it is written that it is not possible to obtain amplitudes exactly when we have a qubit in superposition. In a course we said that actually it is possible, ...
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Is there any way to always output |1> if the measurement has a probability to output 1?

Let's say I have an oracle that outputs 1 on a specific input (there can be multiple inputs x so that f(x)=1), else it outputs 0. If there is no such input so that f(x)=1, the quantum state of the ...
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Set relative phase of qubit to zero without measurement?

Is there a quantum way to set the unknown relative phase of a qubit (assumed in a pure state) to zero, without measurement? The relative phase is not known, otherwise I would subtract it using a phase ...
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A doubt regarding Mach-Zehnder Interferometer functioning

I am tying to understand the working of Mach-Zehnder Interferometer in the physical sense (how it behaves and why it does so etc.). The source I am referring to is this: (https://www.cs.princeton.edu/...
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A doubt regarding probabilities of a entangled states?

Given an state of entangled particle pair in Horizontal-Vertical basis ($H,V$): $ \psi_{hybrid}= (1/\sqrt2) (HH+VV)$ Let us define a new Right-Left basis ($R,L$) as follows: $L=(1/\sqrt2)(H-iV)$ $R=(...
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Why are qubits represent as unit vectors in an Hilbert space?

Mathematically, our qubits (pure quantum states) can be represented as a normalized vector (of length 1) in a complex Hilbert space. is it because of the sum of squares of vertical and horizontal ...
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How to calculate the average fidelity of Pauli error channel

This question is related to this and this. I am working on Qiskit to design QEC schemes. My model works with Pauli errors. I would like to give to my Pauli error channel probabilities $p_x,p_y,p_z$ ...
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Grover Diffuser for states with amplitude value 0?

Is ist possible to do the grover amplification while excluding states with amplitude values of zero? I was testing this with the classic grover and two diffrent superpositions. In the first I used the ...
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Append a controlled Initialize in Qiskit

I would like to create a controlled initialize, I have the following code: ...
3 votes
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Implementing quantum swap operation such that $|x\rangle|f(x)\rangle$ changes to $|x\rangle|f(x+1)\rangle$

Suppose that a quantum state $|\psi\rangle$ in question is $|\psi\rangle \propto \sum_x |x\rangle|f(x)\rangle$. I want to implement a quantum swap operation such that computational basis $|x\rangle|f(...
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Why can two atoms can be entangled?

As a qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in ...
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Is effective quantum cloning possible, given that any classical function can be implemented as a quantum circuit?

As in Compiling a classical function to a quantum circuit in practice, as far as my understanding goes, it is known that any classical function can be implemented as a quantum circuit. So given $f(x)=...
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Can EPR pairs be established with only classical communication?

EPR pairs are used in superdense coding and quantum teleportation, but these protocols assume that Alice & Bob "share" half of an entangled quantum state. How does this "sharing&...
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A question on random quantum states and the uniform distribution

Consider an $n$ qubit Haar random quantum state $|\psi\rangle$. Consider a distribution $\mathcal{D}_1$ over $n$ bit strings defined as $$ p_x = |\langle x| \psi \rangle|^{2}, $$ for $x \in \{0, 1\}^{...

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