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Questions tagged [phase-kickback]

For questions about phase kick-back. For a detailed description of the mechanism, go through https://quantumcomputing.stackexchange.com/questions/2565 and the answers therein.

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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 today, when I looked at it again, it doesn't…
Sanchayan Dutta
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Show that these two expressions for the oracle transformation are equivalent

Suppose $x \in \{0,1\}^n$. The standard way to make a query is with an oracle $O_x$ that given an input $|i,b \rangle $ returns $|i,b \oplus x_i \rangle$. Via the phase kick-back trick, this can be used to make another type of query $O_{x}^{''}$…
Karl
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Who discovered the phase kickback trick?

Was it David Deutsch? Can you say who was the first paper to mention the phase kickback trick?
R. Chopin
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Can we use Hadamard test to estimate phases?

There have been some questions discussing the Hadamard test and quantum phase estimation (QPE), but I did not find the answer to the following question. Suppose we are given $|\psi\rangle$, which is an eigenstate of $U$ such that $U|\psi\rangle =…
fagd
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controlled-Z rotation gates in symmetrical fashion

I was going through the qiskit textbook and in this chapter I came across a statement under the topic "Kickback with the T-gate" related to the Controlled-Z gate that the controlled-Z rotation gates are symmetrical in fashion (two controls instead…
neel.spartacus
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How to decompose a multi-target controlled gate?

I'm trying to replicate with qiskit the results of this paper in which basically they implement a quantum version of the Principal Component Analysis applying Quantum Phase Estimation algorithm in order to find eigenvalues and eigenvectors from a…
miki scande
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Resources and references about phase kickback trick

I am writing a piece of work on Grover's algorithm and I am looking for references on the phase-kickback trick to transform a state oracle in a phase oracle. Is there any paper or there a part on it in Nielsen and Chuang ?
BrockenDuck
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What is Quantum Phase Estimation in Shor's Algorithm?

While I'm studying Algorithm, I couldn't understand what Quantum Phase Estimation is. And I heard there is relation between Phase-Kickback and Quantum Phase Estimation. I wonder what it is. Also, I'm not sure what this is and how it works within the…
김동민
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Is the $|-\rangle$ state the only one that can do the trick for Grover's algorithm?

$\newcommand{\qr}[1]{|#1\rangle}$Grover algorithm's input is a superposition, representing the haystack, and the Bell state $\qr{-}$. The $\qr{-}$ seems utterly important: when I replaced $\qr{-}$ by, say, $\qr{+}$, the oracle became the identity…
R. Chopin
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How to understand intuitively the quantum gate phase kickback?

I do understand the math behind phase kickback. The math makes sense. For more context, I find this document very helpful. But I’m struggling a lot to intuitively understand, why the conditional phase change to the second qubit will end up change…
Kira Pina colada
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Obtaining phases of all basis states

I’m wondering that is there a way to separate phases of basis states from the magnitudes (namely putting phases on some new basis states with the same probability magnitude) if the exact values of phases and magnitudes are unknown? One way I can…
Sam
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Doubt on construction of phase oracle in Grover's Algorithm

In the above question from de Wolf's lecture notes, I'm facing difficulties in constructing the oracle. I'm unable to understand how to use the boolean oracle to construct a phase oracle. Any help would be appreciated!
spigen
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Is it possible to decompose a controlled gate with control qubit in the $|+\rangle$ state?

$\newcommand{\ket}[1]{\vert#1\rangle}\newcommand{\bra}[1]{\langle#1\vert}$ Given a quantum circuit with 2 qubits that executes a controlled gate $CU$ where the control qubit is in the $\ket{+}$ state, and the target qubit is in an arbitrary state…
upe
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Paradox on the evolution direction in controlled Hamiltonian simulation for Quantum Phase Estimation

Suppose we want to perform Quantum Phase Estimation over a Linear Combination of Unitaries Hamiltonian. One of the most efficient ways to do so is to use…
Pablo
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In the Bernstein-Vazirani circuit, if the secret is all 0s, would the oracle just be nothing?

I'm self-studying quantum computing and have gone through the Wikipedia article on the Berstein-Vazirani algorithm and believe that I understand it. I'm looking to verify my understanding and hope that someone could help me. If I have an 8 bit…
QuantumLearner
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