Questions tagged [eigenvalues-and-eigenvectors]

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Geometrical difference between row and column vector [closed]

How to visualize/show geometrically the difference between a row (bra) and column (ket) vector within a coordinate system/plane; or to say a vector and its transpose in terms of quantum computing?
• 37
3 votes
2 answers
66 views

Solving Hamiltonian eigenvalue problem

I would like to solve an eigenvalue problem of a Hamiltonian. I was able to find the lowest eigenvalue by converting the Hamiltonian into a matrix and applying linear algebra eigenvalue techniques. ...
• 196
1 vote
1 answer
71 views

What are the eigenstates of an operator?

Sorry if this is a silly question, I am new to quantum computing I was just reading this article that talked about the eigenstates of an operator. And I wonder, how can we find those eigenstates for a ...
• 11
1 vote
2 answers
74 views

Surface Code Eigenstates as Circles

I learned that logical $|0\rangle$ of surface code, is an eigenstate, where all stabilizers are +1 value, and since the z-stabilizer is enforcing an even amount of edged in each node, and the x-stab ...
• 950
2 votes
1 answer
150 views

• 903
3 votes
1 answer
122 views

Why are all the eigenvalues of a "Hermitian block-encoding" equal to $\pm1$?

I was looking at the paper : https://arxiv.org/abs/2002.11649 and the eigenvalue discussion is not clear to me. Block-encoding is a general technique to encode a nonunitary matrix on a quantum ...
• 879
6 votes
3 answers
378 views

Interpretation of the unitaries involved in the eigenvalue decomposition of a density operator

If $\rho=\sum_{i}p_{i}|\psi_{i}\rangle\langle \psi_{i}|$, this ensemble doesn't require $\langle \psi_{i}|\psi_{j}\rangle$=0. Given that $\rho$ is positive semi-definite, by the spectral theorem it ...
• 1,123
1 vote
1 answer
78 views

• 495
3 votes
1 answer
343 views

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 ...
3 votes
1 answer
405 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 $3 \times 3$ (...
• 41
5 votes
2 answers
154 views

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 ...
• 1,695