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Questions tagged [fidelity]

In quantum information theory, fidelity is a measure of the "closeness" of two quantum states. It expresses the probability that one state will pass a test to identify as the other. The fidelity is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space. (Wikipedia)

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17
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1answer
549 views

Purpose of using Fidelity in Randomised Benchmarking

Often, when comparing two density matrices, $\rho$ and $\sigma$ (such as when $\rho$ is an experimental implementation of an ideal $\sigma$), the closeness of these two states is given by the quantum ...
11
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2answers
696 views

What is the longest time a qubit has survived with 0.9999 fidelity?

I am pretty intrigued by the record time that a qubit has survived.
8
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2answers
980 views

How can I calculate the inner product of two quantum registers of different sizes?

I found an algorithm that can compute the distance of two quantum states. It is based on a subroutine known as swap test (a fidelity estimator or inner product of two state, btw I don't understand ...
5
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3answers
442 views

What does fidelity mean?

I am learning qiskit software and this term keeps popping up and I am unable to get a grasp on the technical definition given by wikipedia. For example, the functions state fidelity and process ...
5
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3answers
329 views

Intuitive role of the polar decomposition in proof of Uhlmann's theorem for fidelity

I have read the Wikipedia article which relates the polar decomposition to a complex number being split into its modulus and phase but this analogy isn't very intuitive to me. In Nielsen and Chuang, ...
5
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2answers
94 views

Are there disadvantages in using the inner product between states instead of the fidelity?

Would there be any disadvantages of using inner product, that is, $\mathrm{Tr}(A^{\dagger}B)$ (say making it, $\mathrm{Tr}(\sqrt A \sqrt B)$ to normalise) to quantify how far two quantum states are ...
5
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1answer
226 views

How to calculate the fidelity of a certain gate of a IBMQ device in Qiskit using randomized benchmarking/tomography?

For example, I want to calculate the fidelity of a 1-qubit and 2-qubit gates (similar to the result shown in figure 2 in this paper). Is there any way to do that in Qiskit? I've gone through the ...
4
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1answer
59 views

Do avoided crossings / CTs /ZEFOZs optimize quantum fidelity in practice?

CTs / ZEFOZs: Energy level structures that include avoided crossings at accessible energies tend to be resilient to noise and therefore present high coherence times, at least in the case of spin ...
3
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1answer
84 views

What would be an ideal fidelity measure to determine the closeness between two non unitary matrices?

The Hibert Schmidt norm $tr(A^{\dagger}B)$ works well for unitaries. It has a value of one when the matrices are equal and less than one otherwise. But this norm is absolutely unsuitable for non-...
3
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0answers
43 views

On the distribution of the fidelity of a random product state with an arbitrary many-qubit state

Consider an arbitrary $n$-qubit state $\lvert \psi \rangle$. How much do we understand about the probability distribution of the fidelity of $\lvert \psi \rangle$ with a tensor product $\lvert \alpha \...
3
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0answers
71 views

How to implement the mixed quantum state fidelity in a quantum circuit?

Suppose we use Uhlmann-Josza fidelity $F(\rho, \sigma):=(\mathrm{tr}\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})^2$, can we construct a quantum circuit that help us to calculate the fidelity of two mixed ...
2
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1answer
61 views

Proving the inequality $|\mathrm{tr}(AU)|\le \mathrm{tr}|A|$ in Uhlmann's theorem

In Nielsen and Chuang, in the Fidelity section, (Lemma 9.5, page 410 in the 2002 edition), they prove the following. $$ \mathrm{tr}(AU) = |\mathrm{tr}(|A|VU)| = |\mathrm{tr}(|A|^{1/2}|A|^{1/2}VU)| $$ ...
0
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1answer
49 views

Is phase factor negligible in fidelity of quantum states?

One well-known fidelity is defined as $(Tr\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})^2$. And for pure states, fidelity is always in the form $|\langle\psi|\phi\rangle|^2$. As we know, in the context of two-...