As of May 31, 2023, we have updated our Code of Conduct.

# Tag Info

### Why does the "Phase Kickback" mechanism work in the Quantum phase estimation algorithm?

A first remark This same phenomenon of 'control' qubits changing states in some circumstances also occurs with controlled-NOT gates; in fact, this is the entire basis of eigenvalue estimation. So not ...
Accepted

### Why does the "Phase Kickback" mechanism work in the Quantum phase estimation algorithm?

Imagine you have an eigenvector $|u\rangle$ of $U$. If you have a state such as $|1\rangle|u\rangle$ and you apply controlled-$U$ to it, you get out $e^{i\phi}|1\rangle|u\rangle$. The phase isn't ...
Accepted

### Quantum phase estimation and HHL algorithm - knowledge of eigenvalues required?

You should know a bound on the eigenvalues (both upper and lower). As you say, you can then normalise $A$ by rescaling $t$. Indeed, you should do this to get the most accurate estimate possible, ...
Accepted

Accepted

### What is the difference between amplitude amplification, amplitude estimation, and phase estimation?

To find the differences between them, you only need to know the aim of the problems. The aim of AA is to find the answers from unstructured data(or more directly, amplify the probability of the right ...
Accepted

### Can we use Hadamard test to estimate phases?

So QPE using $\mathcal{O}(1/\epsilon)$ queries to $U$ outputs an estimate of the eigenphase $\theta$ given a corresponding eigenvector with additive error and $\Omega(1)$ probability. The method using ...
Accepted

Accepted

### Simulating QPE + Grover using Low-Rank Stabilizer Decomposition

I agree that the Bravyi et al. paper is not easy to understand and they should have made some reference implementation available. Without going into details, I don't think it is likely to get an ...

### Question about the phase kickback in the phase estimation algorithm

The phase is applied to the overall wave function $|\phi\rangle$, therefore you can factor the phase to any individual qubit. For example if we have a wave function as a result of a controlled ...
Accepted

### Interpreting the phase in QPE

Given your definition $U|\psi\rangle=e^{2\pi i\theta}|\psi\rangle$, then the $U$ that you use can be any value of $\theta$. However, the answer you get out will (with high probability) be the best $t$-...

### Is Shor demonstration wrong?

In Equation 5.4, the expression of the state is given, which is: \newcommand\ket{\left|#1\right\rangle}\ket{\psi}=\frac1q\sum_{a=0}^{q-1}\sum_{c=0}^{q-1}\exp\left(\frac{2\mathrm{i}\pi ac}{q}\...