Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
1,321
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Fidelity concentration bound for random stabilizer states
Let $|\Phi\rangle$ be a normalized vector in $\mathbb{C}^d$ and let $|\psi\rangle$ be a random stabilizer state. I am trying to compute the quantity
$$\mathsf{Pr}\big[|\langle \Phi|\psi \rangle|^2 \...
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Can a polynomial-sized superposition of computational basis states be prepared with a polynomial-sized quantum circuit?
Suppose I am working with a class of states which consist of a superposition of $O(\text{poly}(N))$ computational basis states on $N$ qubits. Examples of this would be the subspace of states of fixed ...
CommunityBot
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Find min of a quantum state L2 norm
I have a problem minimizing this norm with respect to $\alpha$:
$\min_{\alpha}||e^{i\alpha}|\psi\rangle-|\phi\rangle ||^2$ (1)
The result is that this achieves min when $\alpha=-\measuredangle \langle\...
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Qubit reset using Grover iteration
Suppose I’m building a long circuit and I need to reuse a qubit from a previous step but I don’t want to use the reset operation (or I’m not using an IBM computer so I don’t even have the reset option)...
CommunityBot
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Is there another parameterization of a qutrit 3-level system, besides Gell-Mann?
Question:
Is there a parameterization of a a general qutrit 3-level system similar to:
$$\rho = \begin{bmatrix} p_1 & r_{12}e^{-i\phi_{12}} & r_{13}e^{-i\phi_{13}}\\ \cdot & p_2 & r_{...
glS♦
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1
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Adding phases of two qubits
Imaging a system of two qubits which at a given step of evolution is in the state
$|q_{1}(0)\rangle = |0\rangle + e^{-i\phi_{1}}|1\rangle$,
$|q_{2}(0)\rangle = |0\rangle + e^{-i\phi_{2}}|1\rangle$,
...
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2
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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 $...
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1
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Does applying an operator to a state have nothing to do with taking a measurement?
In class, it was mentioned that beginning students often mix up the application of an operator to a state with taking a measurement of that state, and that this is not the case. What's more, the TA ...
glS♦
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Recover local systems from composite systems
Define $A,B$ as two linear operator of two local systems. Define $C:= A \otimes B$ as the composite systems. How to recover $A$ and $B$ given $C$? For example, we set
\begin{align}
A=\left[\begin{...
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2
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Distributive property of Ket over addition
If:
$$|a> = \binom{-4i}{2} $$
$$|b> = \binom{1}{-1+i} $$
Then what will the value of $$|a + b> $$ be?
That is, is addition distributive over the ket notation?
6
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Understanding a quantum algorithm to estimate inner products
While reading the paper "Compiling basic linear algebra subroutines for quantum computers", here, in the Appendix, the author/s have included a section on quantum inner product estimation.
Consider ...
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2
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How to measure an unknown state produced by a source of qubits?
What kind of experiment can allow me to measure an unknown state produced by a source of qubits? For example: the state of photon polarization. But it can be another one.
I have no information about ...
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Why are Bell states the maximally entangled ones?
I just want to know why actually Bell states are examples of maximally entangled states and significance of that "maximal" term. Is there anything for proving that?
CommunityBot
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1
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Preparing a maximally entangled state among four qubits
I am trying to create the following states in Qiskit, but having trouble with the nested loops. Can someone help me create it?
$\left|\psi_o\right\rangle=\frac{1}{\sqrt{8}}\left(\sum_i \hat{\sigma}_{x,...
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1
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Upper bound on trace distance of subsystems based on full system
If we have the following upper bound on the sum of trace distances:
$$
\frac{1}{N} \sum_{a, b}||p_1(a | b) \rho_{ab} - p_2(a | b) \sigma_{ab}|| \le \epsilon,
$$
where $p_1$ and $p_2$ are two ...
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1
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Quantum algorithm to add zeroes between two halves of a vector
Is there a quantum gate or circuit that is capable of inputting any quantum state with $N$ qubits called $\left | \psi \right >$ and a state in $\left | 0 \right >$, and outputting a value that, ...
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Is it possible to use quantum state to store and read information without destorying it?
Like building a ROM device? Please consider the influence of the non-cloning theorem and better show some papers. Thanks!
PS: I heard that error-correction methods might help to achieve this goal. Is ...
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1
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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/...
CommunityBot
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Where am I going wrong in my understanding of qubit associativity?
I am studying the basics of quantum computing math and am confused about qubit associativity. As I understand it, in quantum math, multiple qubits are represented as the tensor product of the qubits ...
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1
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HHL Algorithm: How to compute the signs of the solution vector
Let us assume we have used the HHL algorithm to approximately prepare $|x\rangle$, where $|x\rangle$ is a normalized quantum state corresponding to $\vec{x}$, the solution of a system of linear ...
glS♦
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NEQR Technique in quantum computing for initialization
I am quite confused with the NEQR technique. It would be great if someone can explain me this technique with suitable mathematics and programs.
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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|...
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1
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Entanglement and superposition illustration
I found an example of how "the power" of superposition can be explained in simple words. Toss two coins. While they are still in the air, they can be thought of encoding 4 states. Wow! Cool! ...
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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}}{...
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1
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Quantum gate count minimization
In classical digital logic, we have K-map and Quine–McCluskey algorithm for minimizing boolean equation, thereby reducing the number of logic gates needed. Is there such a thing in quantum computing?.
...
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2
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Sorting two numbers using quantum computing
To better understand how quantum computing works, I am trying to sort two numbers using unitary matrix. Based on this definition, I understand a quantum Turing machine to have the automorphism (...
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How to calculate the evolution of ket states through a simple quantum circuit?
I am having difficulties with the calculations of qubits.
I think I can do them, but it feels so massivly inefficient!
In this tutorial grover's algorithm for example, there's a simple oracle given ...
- 4,233
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What is a simple example to showcase quantum computing to a broad audience?
I would like to write a code to demonstrate an advantage of QC over classic computations. However, I'm really struggling to find the simplest example for a broad audience. Can someone suggest an ...
glS♦
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How to derive the state of a qubit after a partial measurement?
I am trying to solve a problem from the course "Quantum Information Science I" of MIT Open Learning Library, but I get stuck.
Here is the problem. Consider the below circuit where the meter ...
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1
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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 ...
CommunityBot
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Why is the conjugate being used when rewriting a qubit state in another basis?
I'm currently going through Introduction to Classical and Quantum Computing, by Thomas Wong, and I'm struggling with an example given on page 88 (point 4).
The author gives the two following states, ...
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2
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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 ...
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0
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How do I find Quantum Fisher Information from an array of fidelity values for various parameter values?
I have an array of Fidelity values corresponding to parameter values.
For example,
eps=[0,0.1,0.2....,1]
where eps is the parameter
Fid=[1.0, 0.9, 0.96, 0.91, 0.85, 0.78, 0.71, 0.65, 0.59, 0.54]
I ...
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How to prepare all the computational basis states by running the same quantum ansatz with distinct $\theta$ values?
Given a 2-qubits system, the 4 computational basis states are $|00\rangle$, $|01\rangle$, $|10\rangle$, $|11\rangle$.
Is it possible to prepare these states by a one-parameter quantum circuit "...
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Quantum hardness of XQUATH conjecture
Consider the XQUATH conjectures, as defined here (https://arxiv.org/abs/1910.12085, Definition 1).
(XQUATH, or Linear Cross-Entropy Quantum Threshold Assumption). There
is no polynomial-time ...
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Quantum Ising model correlation function query
In this paper on quantum Ising model dynamics, they consider the Hamiltonian
$$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$
and the correlation function
$$\mathcal{G}...
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Parametrization of a two-qubit state
A single-qubit state can be parametrized with real $\theta$ and $\phi$ as follows:
$$|\psi(\theta, \phi)\rangle = \cos\frac{\theta}{2}|0\rangle + e^{i \phi} \sin\frac{\theta}{2}|1\rangle.$$
I would ...
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1
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Minimum number of 2-qubit gates required to implement a Toffoli gate
I'm trying to design a quantum circuit that has an output that is closest to a CCNOT gate with no more than four 2-qubit gates (but I can use additional single qubit gates).
A lot of resources/papers ...
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How to check the jmat operators on Qutip?
I'm trying to reproduce this Qobject form Qutip
https://qutip.org/docs/latest/guide/guide-tensor.html#a-two-level-system-coupled-to-a-cavity-the-jaynes-cummings-model
but, I'm using the Jmat ...
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Find the desire state with a set of gates?
I encoded a state |000> applied by a U3 gate, resulting in state: a|000>+b|100>. I need to create a circuit to achieve the desired state (a'|**0>+b'|**1>) with * as any 0 or 1 state. ...
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What is the difference between a qubit and a quantum state?
In general, a qubit is mathematically represented as a quantum state of the form $\lvert \psi\rangle = \alpha \lvert 0\rangle + \beta \lvert 1\rangle$, using the basis $\{ \lvert 0\rangle, \lvert 1\...
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Deriving the choi matrix definition of the quantum depolarizing channel
I was reading up on the quantum depolarizing channel (Preskill's Notes) (stack exchaange explanation), and I'm failing to see how the form
\begin{align}
\sigma &= (\mathcal E \otimes \mathbb I)(|\...
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What is the mathematical essence of Qiskit simulators?
As a newcomer to quantum computing, I have a question about the simulation of a quantum computer using Qiskit on a classical computer. Does Qiskit actually perform matrix manipulations in its ...
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What's the matrix representation of the CSWAP?
I don't know how to represent the matrix format of the CSWAP gate in the circuit:
Despite reviewing some material about CSWAP from Qiskit CSWAP, I am still unable to understand the concept. I am ...
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Locally commuting operators and positivity on tensor product spaces
I am reading this paper https://arxiv.org/abs/quant-ph/0501020 and two questions have been arisen for me: 1. In page 3 (left column) has been written: "Hence it follows that if $\tilde{S}_{k}^{(...
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Operating Hamiltonian on discrete variable state [closed]
I have a hamiltonian consisting of combinations of a and a(dragger). i need to act this on discrete variable state like |0,0,0,1> and so on. Is there any library to do these kinds of operations?
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Is it possible to separate a quantum circuit into several small sub circuits and measure individually?
For example, if I have a BV3 circuit and I execute and measure them together, the results are 100% 111.
If I separate it into three subcircuits and measure only one qubit each time, the measurement ...
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Is tomography of the Choi state sufficient for channel tomography?
Given that there is an isomorphism between quantum states and quantum channels (the Choi-Jamiolkowski isomorphism) and given that state tomography is well-researched, why is quantum process or quantum ...
glS♦
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Does changing the state of an entangled qubit affect its entangled partner?
I have a question about the single qubit gate effect after entanglement. Suppose we have a circuit as I draw. Qubit 0 and qubit 1 are entangled. B gate is applied to qubit 0, and C gate is applied to ...
glS♦
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What exactly does it mean to embed classical data into a quantum state?
As the title states.
I am a Machine Learning Engineer with a background in physics & engineering (post-secondary degrees). I am reading the Tensorflow Quantum paper. They say the following within ...
