Skip to main content
Share Your Experience: Take the 2024 Developer Survey

# Questions tagged [quantum-phase-estimation]

For questions about the quantum phase estimation algorithm.

164 questions
Filter by
Sorted by
Tagged with
-3 votes
0 answers
29 views

### Difficulty in understanding Quantum Phase Estimation [closed]

I am trying to understand Quantum Phase Algorithm. I see circuit of Hadamard Test is very short. It contains 2 Hadamard gate, 1 controlled Unitary gate and finally measurement. Also notice that IBM ...
• 1
1 vote
1 answer
26 views

### quantum phase estimation overperiod value estimation

Basacally, QPE allows to find eigenvalue within a period $[0$ to $2\pi)$. Is there an extention that allows to calculate eigenvalue out of these limits, e.g. greater or equal to $2 \pi$?
3 votes
0 answers
38 views

• 911
2 votes
3 answers
94 views

### Shor: Modular exponentiation vs modular multiplication

In his original article Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer, Peter Shor constructed an algorithm for finding a period $r$ of the modular ...
• 14.5k
1 vote
1 answer
134 views

### Quantum Phase Estimation answers distribution

Suppose I have a random unitary matrix, known eigenvectors and eigenvalues. I know that exact eigenvalue for the given matrix is $0.5491617699847768+0.835716070437315j$. From here, if I'm not mistaken ...
3 votes
0 answers
32 views

### How to have seperate registers from scrach?

I am very new to quantum computing, so this might be a really simple question. I am coding a quantum computer simulator in python from scrach and I'm not sure how to make registers work. I would just ...
4 votes
1 answer
90 views

### How does the complexity of extracting eigenvalues via quantum phase estimation compare with the classical one?

Suppose, I have ideal quantum computer that allows me to find exact eigenvalues with QPE algorithm under perfect matrix, eigenvectors and eigenvalues conditions. How the complexity of this algorithm ...
1 vote
0 answers
79 views

### Deriving circuit templates for Hamiltonian simulation

Background I've been reading the paper entitled Some improvements to product formula circuits for Hamiltonian simulation. The authors propose three improvements motivated by phase estimation type ...
• 1,025
1 vote
0 answers
87 views

### How to determine the single-qubit phase?

In some works it is suggested to find the qubit phase by the following method: Apply $X/2$ (or $Y/2$) gate - preparing the qubit in superposition. Detune the qubit by flux pulse, for example here ...
• 259
1 vote
0 answers
49 views

### Can I get valid solution with HHL algorithm even if the QPE is not completely correct?

Can I get the valid solution of linear problem using HHL algorithm even if the QPE is not completely correct? My example is $A=diag(0.5, 0.2, 0.3, 0.6)$, so the solution is $[0.5, 0.2, 0.3, 0.6]$ ...
• 33
2 votes
2 answers
71 views

### How to estimate the negative amplitude of multiple qubits?

The probability of measurement is the square of amplitude. After measurement, how to guess the original amplitude of state?? For example, in linear problem, we would like to know the exact solution, ...
• 33
2 votes
0 answers
25 views

### Accuracy of QPE using histogram fit

In regular QPE, accuracy is $1/2^n$, where $n$ is estimation register size, and it is done with few shots and depth as $O(2^n)$ (total cost of $O(2^n*NumShots))=2^n=1/resolution$). I thought of the ...
• 1,432
1 vote
1 answer
97 views

### Problem with the mathematical definition of the eigenvalue algorithm on a specific exercise

I think I understand well how the eigenvalue algorithm works but when I try to define it mathematically I have problems. Specifically I have the matrix U:  U = \begin{pmatrix} 0 & i \\ i & 0 ...
2 votes
1 answer
160 views

### Problem with eigenvalue evaluation algorithm application on matrix $U$

Once I get to the end of the algorithm, I can't understand how to calculate the eigenvalue using formulas. Bear in mind that it is an exercise to be carried out with pen and paper. the matrix of $U$ ...
2 votes
0 answers
44 views

### 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 ...
3 votes
0 answers
100 views

### 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 ...
• 31
4 votes
2 answers
179 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 ...
• 41
2 votes
1 answer
406 views

### 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 ...
• 21
2 votes
0 answers
78 views

### 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 ...
• 25.4k
4 votes
0 answers
56 views

### 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 ...
• 12.6k
1 vote
1 answer
67 views

• 423
1 vote
0 answers
114 views

### 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? ...
0 votes
1 answer
230 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 ...
• 51
4 votes
1 answer
146 views

### 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-...
• 101
1 vote
0 answers
67 views

### 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 ...
• 1,432
4 votes
1 answer
346 views

0 votes
1 answer
563 views

### 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: ...
• 462
2 votes
1 answer
88 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 ...
• 219