Questions tagged [phase-estimation]
Refers to the quantum algorithm used to estimate the eigenvalue corresponding to an eigenvector of a unitary operator.
3
votes
2answers
78 views
Are the squared absolute values of the eigenvalues of a unitary matrix always 1?
I'm going through the phase estimation algorithm, and wanted to sanity-check my calculations by making sure the state I'd calculated was still normalized. It is, assuming the square of the absolute ...
6
votes
1answer
112 views
SWAP gate(s) in the $R(\lambda^{-1})$ step of the HHL circuit for $4\times 4$ systems
Context:
On the 5th page of the paper Quantum circuit design for solving linear systems of equations (Cao et al, 2012) there's this circuit:
Schematic:
A brief schematic of what's actually ...
9
votes
1answer
156 views
Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required?
The quantum phase estimation algorithm (QPE) computes an approximation of the eigenvalue associated to a given eigenvector of a quantum gate $U$.
Formally, let $\left|\psi\right>$ be an ...
7
votes
3answers
241 views
Why does the “Phase Kickback” mechanism work in the Quantum phase estimation algorithm?
I've probably read the chapter The quantum Fourier transform and its applications from Nielsen and Chuang (10 th anniversary edition) a couple of times before and this took this thing for granted, but ...
