# Questions tagged [phase-estimation]

Refers to the quantum algorithm used to estimate the eigenvalue corresponding to an eigenvector of a unitary operator. (Wikipedia)

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### Does this measurement for quantum phase estimation look correct?

I have implemented Shor's algorithm for $N=15$ from this tutorial. I understand the algorithm pretty well, but I'm a little confused at the output I'm getting from running the circuit. It appears to ...
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### Adiabatic state preparation for quantum phase estimation

I'm trying to understand the problem of state preparation for quantum phase estimation (QPE). Specifically how states are prepared adiabatically. I have a couple of questions: 1). Typically when one ...
118 views

### How to derive the expression for the probability in quantum phase estimation? ((5.27) Nielsen & Chuang)

I'm trying to understand the QPE algorithm that is presented in the Nielsen and Chuang textbook. More precisely, I do not understand Equation $(5.27)$. Context: In the following, let $b$ be a natural ...
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### Constructing a controlled phase gate from given gates

As part of a project in a quantum computing course we were asked to classically simulate the quantum phase estimation algorithm, which has inverse QFT as one of its components. On the Wikipedia page ...
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### Is the QFT optimal in the quantum phase estimation algorithm?

We can concisely summarise the quantum phase estimation (QPE) algorithm as follows: Generate the state $\sum_{k=0}^{2^n-1} \lambda^k |k\rangle$ efficiently using a series of controlled-unitary ...
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### We take the reciprocal $\lambda^{-1}$ of eigenvalues in HHL - but what's stopping us from raising them to a positive exponent $\lambda^m$?

The HHL algorithm generally can be thought of as diagonalizing our matrix $A$ with the quantum phase estimation algorithm, and applying a specific function $f(\lambda)=\lambda^{-1}$ to the eigenvalues ...
1 vote
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### HHL phase estimation step

I have got an HHL circuit that looks as follows: In the phase estimation part we are trying to find the eigenvalues of the matrix A. But what is the role of the piece of circuit hightlighted below? ...
129 views

### Quantum counting with ancillary qubits

I have been trying to implement quantum counting using my own oracle, however I've been unsuccessful getting results that make sense. The circuit I'm using looks like this (I'm only showing the ...
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### Is the phase-estimation a specific case of the Hidden Subgroup Problem?

I read Nielsen & Chuang and I have difficulties understanding the links between the Hidden Subgroup Problem and the Phase Estimation. In Exercise 5.14 (Section 5.3.1 "Application: order-...
1 vote
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### Reduced density matrix accuracy in amplitude estimation

I am implementing QAE (Quantum Amplitude Estimation), which is very similar to QPE (Quantum Phase Estimation) with a Grover Operator as the U matrix of QPE. I want to check my results, in the outputs ...
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### Accuracy of Quantum Phase estimation; Finding the max difference integer, e

Working through Lab 5 in the Qiskit text, I have been attempting to complete Part 1, Step B. I implemented the following code as it seemed, at the time, to be what the question was asking for: ...
78 views

### Confusion about Rodeo algorithm "spectral weight suppression" argument

In this first paper on the Rodeo algorithm, there is an argument on the second page about the suppression of "spectral weights" that I don't really understand. In short, the algorithm is ...
132 views

### Can we use quantum phase estimation to estimate the phase of an arbitrary single-qubit state?

Can we use quantum phase estimation (or any other) algorithm to estimate the phase of an arbitrary single-qubit state, without measuring it? That is: estimate the relative phase 𝜙 of the qubit 𝑎|0⟩ +...
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### Qiskit textbook: Shor's algorithm

The Qiskit textbook shows the following circuit for implementing the phase $(\frac{s}{r})$ estimation stage of Shor's algorithm for factorizing 15: My understanding is that the register of qubits 8-...
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### Why doesn't Z-gate change phase of |0⟩

Since the Pauli Z gate equate to a rotation around z axes of the Bloch sphere by $\pi$ radians, the phase of anything that lies on z axes is expected to change by $\pi$ by applying z-gate. As $|0⟩$ ...
1 vote
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### How can I understand the notation for the final state of QPE algorithm?

I've been reading about the standard phase estimation from the Qiskit tutorial and got stuck in interpreting the final state representation. What does the state $|2^t\theta\rangle$ mean? Is that the ...
406 views

### Does phase kickback require the system to be in the eigenstate?

I've been watching this video for the introduction to phase kickback. And here's a diagram: I got confused if we really need $|\psi_k\rangle$ to be an eigenstate to make the kickback work. It seems ...
1 vote
100 views

### Understand $U|\psi\rangle = e^{2\pi i\phi}|\psi\rangle$ in phase estimation algorithms

I'm trying to understand the motivations behind $U|\psi\rangle = e^{2\pi i\phi}|\psi\rangle$ in quantum phase estimation. In my interpretation, since $U$ is the unitary operator, this equation wraps ...
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### Why do we start from the least significant bit in phase estimation algorithms?

I've been watching some videos and tutorials for quantum phase estimation. Here's a video I found helpful, which explains the phase estimation in general. I also learned the iterative phase estimation ...
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### What phase should I expect from pauli X?

Here's an example I found that implements the phase estimation algorithm: Here the eigenvector is initialized to the $|+\rangle$ state, which is an eigenvector of Pauli X with eigenvalue 1. The ...
1 vote
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### Writing a Phase Estimation function in Cirq

I am trying to write a phase estimation algorithm using Cirq. The algorithm works for different inputs but I receive a few errors in the estimate_phi(mystery) function. ...
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### Expectation value of Pauli string for VQE

One approach to get the expectation value $\langle\psi|P\psi\rangle$ of a pauli string $P\in \{I, X, Y, X\}^{\otimes n}$ is the following. Let $(a_i, |\lambda_i\rangle)$ be eigenvalue-eigenvector ...
1 vote
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