# Questions tagged [quantum-state]

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

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### Density Matrices for states $|+\rangle$ and state represented by $\rho = \frac{|0\rangle \langle0| + |1\rangle \langle1|}{2}$

As per my understanding, the first one is a "pure state" and represents a system with one qubit having equal probability of being measured as $|0\rangle$ or $|1\rangle$ (standard basis ...
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### How does counting in classical 32-bit systems compare to quantum systems with 32 qubits in superposition?

I'm trying to understand how counting in a classical 32-bit system compares to a 32-qubit quantum system. In a classical 32-bit system, we can count from 0 to the maximum value (i.e., ) using a CPU ...
1 vote
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### Find a unitary to prepare state $|0\rangle$ to a specific vector

I am working with Variational Quantum Linear Solver (VQLS) algorithm, where it needs to prepare a control_b circuit. Given a vector $\bf b$ with $2^n$ elements in it I need to find a unitary $U$ ...
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### Why are orthogonal spins $(1,0)$ and $(0,1)$ represented as collinear vectors in the Bloch sphere?

I'm reading the book "Quantum Computing for Everyone" by Chris Bernhardt and I have a question about the following phrase on page 39 (Chapter 3) which says that As we mentioned in the ...
1 vote
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### Custom Quantum Gate equivalence to backend basis gate set

Hello I am using Qiskit and I have defined a custom gate which implements the array shown in the image: This array is unitary and the function R(theta) works by tuning a continious variable into 0 of ...
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### Bloch representation of a quantum channel acting on a 2-qubit density-matrix

A previous answer nicely show the relationship between the Pauli transfer matrix (PTM) and the Bloch representation of a quantum channel that acts on single-qubit density matrix. In short, given a ...
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### What are non-standard ways to describe the distance between states?

I understand that when comparing two arbitrary quantum states, one may use various measures to encapsulate the difference between states such as trace distance, fidelity or relative quantum entropy. I ...
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### Defining a discrete quantum walk on a 3D hypercube

I am trying to implement at a discrete-time quantum walk on a 3D hypercube using cirq. I have three qubits for the position register: the $|x\rangle$ qubit, $|y\rangle$ qubit and $|z\rangle$ qubit, ...
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### Does tensor product of mixed states produce a product, correlated, or entangled state? [closed]

I am trying to understand the difference between correlated and entangled states; from what I gather, a correlated state is to a product state what a mixed state is to a pure state — the former is a ...
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### How to prepare a cluster state $\frac12(|0000\rangle+|0110\rangle+|1001\rangle-|1111\rangle)$ in Qiskit?

Build the circuit in Qiskit, cluster state.
1 vote
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### Visualizing the Effect of a Parameterized Gate on a Qubit Using the Bloch Sphere in Qiskit 1.0

I am seeking assistance with visualizing the effect of a parameterized gate on a qubit using the Bloch Sphere representation. I have a preliminary code snippet as follows: ...
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### Can you store $2(2^n -1)$ classical bits of information in $n$ qubits?

I just had a lecture where my professor said that the relation in the title of the post was valid. He even told us that we could for example store 1TB of data, in just 35 qubits. But does this mean ...
1 vote
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### Can we find the quantum state using the Bloch vector in the Bloch sphere?

I had a question about qft. When we apply QFT in a circuit, we can display the qubits separately in the bloch sphere with the plot_bloch_multivector function. I realized that the bloch vectors do not ...
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### How to prepare a superposed state?

Given two arbitrary states, $|\psi\rangle\ \text{and}\ |\phi\rangle$ that are possibly unknown to the preparer, is there a way to prepare the superposition $|\psi\rangle+|\phi\rangle$ of them? (If it'...
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### In Qiskit, no state vector after measure and reset

The code below doesn't work. I am looking for a workaround. OK, I can save the state vector as numpy array, recreate the whole circuit and initialize it thanks to this array. It works, but any simpler ...
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### Clarification defining/finding the relative phase of a qubit

Let the vector $|V\rangle = r_0 e^{i\theta_0} |0\rangle + r_1 e^{i\theta_1} |1\rangle$ correspond to the state of a qubit where $r_0,r_1,\theta_0,\theta_1 \in \mathbb{R}$. According to p. 22 of ...
1 vote
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### Transformation between the canonical basis and the degraded Bell basis

I would like to know if the following results of mine made are correct. My goal is to express the canonical basis $\{ |00\rangle , |01\rangle , |10\rangle , |11\rangle \}$ using a degraded Bell ...
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### What's the intuition behind the definition of maximally entangled states?

I am trying to understand what it means for 2 qubits to be maximally entangled. When I look for information online or in books all I can find are rigorous mathematical definitions which I find a bit ...
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### What is the difference between "maximally entangled" and "entangled" states?

when we talk about bell state we say that these states are maximally entangled. so just wanted to understand is there any difference between just entangled and maximally entangled ?
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### Does an MCZ gate flip the phase of the target qubit if it is in the 0 state?

I am trying to flip the phase of the solution state in an oracle for Grover's algorithm. I am wondering if an MCZ gate will flip the target qubit of |0> if the control qubits are in their correct ...
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### Why does Schur's lemma imply that $\int \sigma^{\otimes n}_{HK} d(\sigma)$ must be a multiple of the identity on the symmetric subspace?

I am trying to understand Lemma 2 in this paper. Consider a state $\tau_{H^n}=\int \sigma^{\otimes n}_{H} \mu(\sigma)$ where $\mu(\sigma)$ is the measure on the space of density operators on a single ...
1 vote