Questions tagged [eigenvalue]

Eigenvalues are numbers associated with a linear operator from a vector space 𝑉 to itself: 𝜆 is an eigenvalue of 𝑇:𝑉→𝑉 if the map 𝑥↦𝜆𝑥−𝑇𝑥 is not injective.

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Finding Eigen Values from Quantum Phase Estimation - Using qiskit

I am trying to use the quantum phase estimation(EigsQPE) of qiskit to find the eigen values of a matrix. As I am new to quantum computing so I am confused what to measure in the circuit to derive the ...
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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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In the quantum phase estimation algorithm, why can't we directly compute the eigenvalue from the known eigenvector?

The Quantum Phase Estimation algorithm wants to approximate the phase $\varphi$ of an eigenvalue $\lambda = e^{2\pi i \varphi}$ of a unitary operator $U$. Besides $U$ an eigenvector $x$ corresponding ...
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1answer
137 views

Using Qiskit VQE for solving an eigenvalue problem

I am a new user of Qiskit and I believe there is a simple answer to my question but I have had a very hard time finding a straightforward answer. I am trying to transform a given $3 \times 3$ (...
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2answers
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How are the eigenvalues of $\rho=\frac12(|a\rangle\!\langle a| +|b\rangle\!\langle b|)$ derived?

Let's say I have a density matrix of the following form: $$ \rho := \frac{1}{2} (|a \rangle \langle a| + |b \rangle \langle b|), $$ where $|a\rangle$ and $|b\rangle$ are quantum states. I saw that ...