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Questions tagged [quantum-phase-estimation]

For questions about the quantum phase estimation algorithm.

More information can be found in the following links:

QPE or QPEA are commonly used as abbreviations of the Quantum Phase Estimation (Algorithm).

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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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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 eigenvector of $U$, QPE allows us to find…
Adrien Suau
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Quantum algorithm for linear systems of equations (HHL09): Step 1 - Confusion regarding the usage of phase estimation algorithm

I have been trying to get my head around the famous(?) paper Quantum algorithm for linear systems of equations (Harrow, Hassidim & Lloyd, 2009) (more popularly known as the HHL09 algorithm paper) for some time, now. On the very first page, they say:…
Sanchayan Dutta
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Travelling salesman problem on quantum computer

Recently a pre-print of article Efficient quantum algorithm for solving travelling salesman problem: An IBM quantum experience appeared. The authors use a phase estimation as a core for their algorithm. This part of the algorithm is used for a…
Martin Vesely
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Can we use quantum phase estimation to learn anything about the dynamics of puzzles like the Rubik's cube?

Introduction Consider a state $\vert\psi\rangle$ such as below, which is in a superposition of a difference between a Rubik's cube in a solved state and a Rubik's cube in the "superflip" state. Here, with eight cells on each face (apart from the…
Mark Spinelli
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Quantum Amplitude Estimation vs Quantum Phase Estimation

Quick question concerning the probability of success after a phase estimation algorithm vs an amplitude estimation algorithm. Given the calculation on the wikipedia page, the probability of measuring the desired output in a phase estimation…
sheesymcdeezy
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What is the complexity of the quantum phase estimation in Grover's algorithm?

Suppose we are using GA (Grover's algorithm) such that we are given it has 2 or more solutions. The search space is of size $N$. We all know Grover's algorithm has, at worst, a time complexity proportional to $\sqrt{N}$. Now assume we are using…
Learner
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Chronology of discovery of quantum phase estimation algorithm

I'm a bit confused about exactly when the phase estimation algorithm was discovered. The Wiki article, as well as various textbooks and papers, says that it was introduced in 1995 by Alexei Kitaev, but Shor's algorithm, which uses phase estimation,…
tomdodd4598
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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 happening in the circuit is: Question: Cao et al.'s…
Sanchayan Dutta
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What is the difference between amplitude amplification, amplitude estimation, and phase estimation?

I'm confused about the difference among Amplitude amplification (AA) , phase estimation (PE), and Amplitude Estimation. I thought I understood AA and PE somewhat but when I heard the amplitude estimation and the circuit looked so similar to phase…
John Parker
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Can we get access to the second-lowest eigenstate?

I'd like to know if there's anything that can be said about whether and when we can efficiently prepare a state corresponding to the second-lowest eigenvalue $|\lambda_1\rangle$ of a given Hamiltonian, or in any other way learn what this energy…
Mark Spinelli
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Clarification on state prep for quantum phase estimation

I have a question about how to prepare a state $|\psi\rangle$ for quantum phase estimation (QPE). My question is about whether the state prepared in QPE has to be the exact eigenstate of the operator or whether it is sufficient for applications to…
Callum
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Why does quantum phase estimation complexity scale with maximum representable energy?

In Quantum simulation of chemistry with sublinear scaling in basis size Ryan Babbush and other authors from Google Quantum team argue, when talking about performing Quantum Phase Estimation in 1st quantization, that The reason for our greatly…
Pablo
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Derivation of Efficiency of Phase Estimation Algorithm

In the section Performance and requirements of the phase estimation algorithm of Page 224, Quantum Computation and Quantum Information by Nielsen and Chuang Let $b$ be the integer in the range $0$ to $2^t − 1$ such that $b/2^t = 0.b_1\cdots…
SOORAJ SOMAN
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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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