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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Qiskit: how can you use a different state for each shot in a quantum circuit? [duplicate]

I am trying to run a quantum circuit many times, each time using a different random state - a single qubit i.e. $|\psi\rangle= a|0\rangle + b|1\rangle$ with different $a$ and $b$. Once each qubit has ...
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Does $\frac{\Pi_A\otimes I_B}{\text{Tr}((\Pi_A\otimes I_B)\rho_{AB})}\rho_{AB}=\rho_{AB}$ hold for a state $\rho_{AB}$ and projector $\Pi_A$?

For some projector $\Pi_A$ and state $\rho_{AB}$, let $$\sigma_{AB} = \frac{\Pi_A\otimes I_B}{\text{Tr}((\Pi_A\otimes I_B)\rho_{AB})}\rho_{AB}$$ Is it the case that $\sigma_B = \rho_B$? It seems ...
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How do I represent my 3-qubit state in the computational basis?

I have taken the tensor product of $|0\rangle \otimes |-\rangle \otimes |+\rangle$ which resulted in the matrix $$\begin{bmatrix} 1/2\\ 1/2 \\ -1/2 \\ -1/2 \\ 0 \\ 0\\ 0\\ 0\\ \end{bmatrix}.$$ How ...
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unable to install qiskit-aqua[cvx]…While installing, i am getting the below error. If anyone can suggest

I am unable to install qiskit-aqua[cvx]...While installing, i am getting the below error. If anyone can suggest. I have pasted the error snapshot below
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Quantum supremacy: shallow depth Haar random circuits and unitary designs

I had a confusion about shallow depth Haar random quantum circuits. In this paper, in Section B (related works), it is mentioned that Haar random quantum circuits form approximate $2$-designs only ...
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Does $\mathrm{tr}(A \otimes B) = \mathrm{tr} (A) \otimes \mathrm{tr}(B)$ hold for partial trace?

I was reading this question from this site answered by DaftWullie. I would like to request you to read the question there. The answer says However, in this particular case, the calculation is much ...
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Condition that a tripartite/multipartite qubit state does/does not admit a Schmidt decomposition?

I saw answers such as this and this which provide examples of tripartite system that don't take a Schmidt decomposition, but I wonder if there's an explicit condition that can tell whether a state is ...
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What does “bipartite system” mean? [duplicate]

I have seen this term appearing multiple times when discussing density matrices. For example here is an excerpt from the lecture notes: We are now ready to introduce the idea of a reduced density ...
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How to calculate the average fidelity of an amplitude damping channel

An answer to this question shows how to calculate the average fidelity of a depolarizing channel. How would one go about calculating this for an amplitude dampening channel? I tried working out the ...
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How can I create an ADD gate for two quantum states?

I want create an ADD gate like this: in qiskit using elementary gates. Can it be done? How can I proceed?
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How do qubits in quantum computers work? [closed]

I was reading about quantum computers and qubits. While a classical bit can be either 0 or 1, a qubit can be 0 or 1 or both at the same time (can it be none too?). But how is this useful at all? If it ...
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In Grover's algorithm, how does the function know what element is to be searched for? [duplicate]

In grover's algorithm the oracle gives the output 1 if the element we want is there, my question is, how does the function know what element is to be searched for or how do you put in the element you ...
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What is the general form of a classical-quantum state?

In the literature, one comes across the following situation: Alice holds two registers $X$ and $A$ and it is given that $X$ is a classical register. What is the most general way to write down Alice's ...
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Parametric circuit to prepare the most general single-qubit state [closed]

I am highly confused with this statement and spent a lot of time understanding it.
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Do the Heisenberg uncertainty principle and quantum decoherence relate in some way?

Up until now I assumed (in simple words) that a qubit collapses because of the heisenberg uncertainty principle, meaning that we can not measure a qubit without changing it state. But now I've read ...
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How can one argue that the partial transpose $\rho^{T_B}$ of a general separable state is positive?

How can one argue that the partial transpose $\rho^{T_B}$ of a general separable state is positive?
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1answer
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EPR pair and individual operations [closed]

I have created an EPR pair. Let's suppose it's $(|00\rangle + |11\rangle)/\sqrt{2}$. We both of our halves and then we move into our places. If I ask you how does your half look like (mathematical ...
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How do I calculate the eigenvalues of the positive partial transpose of this two-qubit state?

How can I calculate the eigenvalues of $\rho^{T_{B}}$ (PPT) of the following state $$ \rho =\frac{1}{2}|0\rangle\langle0|\otimes|+\rangle\langle+|+\frac{1}{2}|+\rangle\langle+|\otimes|1\rangle\langle1|...
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Multiply-Controlled X Gate/MCT Gate Implementation

I am currently trying to implement a multi-controlled Toffoli/multi-controlled X gate in Braket, but I am confused as to the general concept of cascaded X gates and other implementations. I've read ...
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Why is the transpose of a density matrix positive and trace preserving?

With density matrix $\rho=\sum_{a,b=0}^1\rho_{a,b}|a\rangle\langle b|$ and it's transpose $\rho^T=\sum_{a,b=0}^1\rho_{a,b}|b\rangle\langle a|$. How to confirm that $\rho^T$ is positive and trace ...
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What are tentpole topics in quantum computing?

Lots of beginners are starting to learn quantum computing. But there are also experienced people that have been working in this field for many years. What are some topics that might be considered ...
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What is the difference between $|0\rangle+|1\rangle$ and a balanced mixture of $|0\rangle$ and $|1\rangle$? [duplicate]

Suppose I have a quantum state $\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle$. Also I have a mixture of two quantum states $S_{1} = |0\rangle$ and $S_{2} = |1\rangle$. In this mixture $50\%$...
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1answer
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Probability of measuring one qubit from the state of two qubits

I am new to quantum information and I am trying to work on some problems but I have confused myself over a qubit problem. I have the state of two qubits $|\psi\rangle_{AB}=a_{00}|00\rangle+a_{01}|01\...
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1answer
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Formula for a single unit gate acting on a lexicographically represented state

I've been trying to find in textbooks a discussion on the action of arbitrary single qubit gates on a lexicographic state. That is, given an operator $G_{l}= 1\otimes 1...\otimes G \otimes ... \...
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proof that the gate U is equivalent to the given circuit mathematically

I have solved this question by this, but can't able to get my mistake in it.
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How do I arrange these two-qubit states based on their entanglement?

How can I arrange the following states in decreasing order based on their entanglement? i) $\rho_1 = \frac{1}{2}|0\rangle \langle0|\otimes |+\rangle \langle+| +\frac{1}{2}|+\rangle \langle+|\otimes |...
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Preparing Bell state $(1/\sqrt{2}) (|01\rangle + |10\rangle)$ in Qiskit

I'm working through the Qiskit textbook right now, and wanted to complete part 1 of exercise 3.4, which asks me to use qiskit to produce the Bell state: $$\frac{|01\rangle + |10\rangle}{\sqrt{2}}$$ ...
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Shouldn't the input state of Deutsh-Jozsa's algorithm look like $|0\rangle^{\otimes n}\otimes |1\rangle$ rather than $|0\rangle^{\otimes n}|1\rangle$?

According to this wikipedia page the initial state in Deutsch–Jozsa algorithm is written as follows: $$|0\rangle^{\otimes n} |1\rangle$$ shouldn't it look like this?: $$|0\rangle^{\otimes n} \otimes |...
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How are inputs during the quantum communication between Alice and Bob placed in the Galois Field?

I have to write a report on "Classical Interaction Cannot Replace a Quantum Message" by Gavinsky (arxiv link). The author gave a lecture, and at 14:55 explains that a communication problem ...
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What do the off-diagonal elements of a density matrix physically represent?

For simplicity, let's take a density matrix for a single qubit, written in the $\{|0\rangle,|1\rangle\}$ basis: $$ \rho = \begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10}^* & 1-\rho_{00} \...
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HHL algorithm, How can I get result from register $|b\rangle$?

From the paper A survey on HHL algorithm: From theory to application in quantum machine learning , I use qasm code from here. I try to follow the example in page 7. with Ax = b and the answer x ...
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1answer
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$\rho_{SE}(0)=\rho_S(0)\otimes\rho_E(0)$: No coupling or no entanglement?

We know that the entangled states cannot be expressed like product state, e.g. $|\omega\rangle = |\psi\rangle\otimes|\phi\rangle$. In the density matrix describing the correlations between system $S$ ...
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Confusion about the output distribution of Haar random quantum states

Consider a Haar random quantum state $|\psi \rangle$. I was confused between two facts about $|\psi \rangle$, which appear related: Consider the output distribution of a particular $n$-qubit $|\psi \...
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1answer
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How to construct a controlled-Hadamard gate using single qubit gates and controlled phase-shift?

How can I construct a controlled-Hadamard gate using single qubit gates and controlled phase-shift? I am stuck in this and any help would be appreciated.
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Prove that $a|00\rangle+b|01\rangle+c|10\rangle+d|11\rangle$ is separable iff $ad-bc=0$

I am having trouble rigorously proving that a two qubit state $|\psi\rangle=a|00\rangle+b|01\rangle+c|10\rangle+d|11\rangle$ is unentangled/separable if $ad-bc=0$ I currently have fairly little ...
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Derivation of the identity $\sum_j p_j \langle \psi_j|M|\psi_j \rangle = \sum_j p_j \operatorname{tr}\left(|\psi_j \rangle \langle \psi_j|M\right)$

For measurement, we know $$\langle M \rangle = \sum_j p_j \langle \psi_j|M|\psi_j \rangle = \sum_j p_j \operatorname{tr}\left(|\psi_j \rangle \langle \psi_j|M\right).$$ My question is, how can we go ...
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1answer
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Cirq: n-qubit GHZ state

I am trying to write $n$ party GHZ state but at the end of the day, it seems like bi partite state. I am missing a detail. Here is my code ...
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1answer
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How is a two qubit mixed state represented in the form of Bloch vector?

How is a two qubit mixed state represented in the form of Bloch vector?
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Aren't qubits just ternary?

Qubits have 3 states: 1, 0, and 1 and 0 at the same time. If a qubit can have 3 states, then how come they are seen as different from ternary computing, which also has 3 states? Is it that the 3 ...
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No. of bits in 160 qubits computer [duplicate]

I read in a book that (https://hub.packtpub.com/quantum-expert-robert-sutor-explains-the-basics-of-quantum-computing/) 160 qubits (quantum bits) could hold $2^{160} \approx1.46\times 10^{48}$ bits ...
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Does applying the transformation $\sum\alpha_{jk}|j,f(k)\rangle\mapsto\sum\omega_N^{-jk}\alpha_{jk}|j,f(k)\rangle$ require computing $f^{-1}$?

Suppose that I have a bijective function $f: \mathbb{Z}_N → Y$ where $Y$ is a finite set. Suppose that $f$, but not its inverse, can be computed efficiently classically. I would like to apply the ...
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Where does the term $|\psi\rangle\langle\psi|$ come from while calculating the expectation value?

Suppose there're two systems $A$ and $B$, if we're in a pure state $|\psi\rangle\in\mathbb{H}_a\otimes\mathbb{H}_b$. Let $\hat A$ be an operator acting on $\mathbb{H}_a$ and $|\psi\rangle=\sum_{i,j}\...
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Is the column vector of a uniformly sampled random unitary matrix a uniformly sampled random state vector?

I am wondering if a random unitary matrix taken from a Haar measure (as in, it is uniformly sampled at random) can yield a uniformly sampled random state vector. In section 3 of this paper it says &...
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What's the difference between $p(i|m)$ and $p(m|i)$ in measurement?

Suppose we perform a measurement described by measurement operators $M_m$. If the initial state is $|{\psi_i}\rangle$, then the probability of getting result $m$ is $$ \begin{align} p(m|i)=\| M_m|\...
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Distinguishing collapsed and uncertain qubit in a quantum circuit

I have been through the Young's double slit experiment. It's a direct proof or instance of showing that a wave is collapsed via observation or measurement, and shows no interference patterns. I want ...
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What does $M_m |\psi_i\rangle$ mean in the equation $p(m|i)=\langle\psi_i|M_m^\dagger M_m|\psi_i\rangle$?

I have trouble understanding two equations in the Nielsen & Chuang textbook. Suppose we perform a measurement described by the operator $M_m$. If the initial state is $|\psi_i\rangle$, then the ...
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How to describe the state of a qubit passing through two Hadamard gates? [duplicate]

Describe the state of the qubit at points A, B and C. How does this demonstrate that we need the “ket” (or the vector) representation of qubits, rather than just describing them in terms of ...
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Measurement of any qubit state in Y-basis [duplicate]

how can I measure any qubit state in Y-basis in qiskit. there is this solution here How to measure in another basis but it gives the qubit's position on bloch sphere in z-axis where as I think it ...
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1answer
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Probability on measuring bell state in x-basis with pauli operator sigma x [duplicate]

I am confused about how to calculate the probabilities of getting a certain result when measuring a Pauli observable on a Bell state. When you measure an observable the state is projected onto an ...

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