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Quantum Computing

Questions tagged [quantum-phase-estimation]

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For questions about the quantum phase estimation algorithm.

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2votes
1answer
136views

By high-precision here I mean that the algorithm returns the first $n$ bits of the true answer with high probability. By tractable I mean that the algorithm can be implemented with $O(\mathrm{poly}(n))...
0votes
1answer
132views

I'm trying to find whether there are any eigenvalue of an arbitrary matrix that is (close to) zero without measurement using quantum phase estimation (QPE). I am experimenting with the code below. I'm ...
1vote
1answer
196views

Assume to have a quantum circuit that generates the ground state of a Hamiltonian $H$:$$H|\phi\rangle = E_0|\phi\rangle.$$Even if my quantum computer has the ground state, I don't know how to ...
1vote
1answer
127views

To my understanding—from this paper for example (arXiv)—given a state $\frac{1}{\| w\| } \sum_x w(x) |x\rangle$ and given an algorithm that produces $k$ copies of the state $|u\rangle$, we can ...
2votes
1answer
271views

In QPE, we first accumulate the phase in control bits and then apply inverse QFT to them to get the actual phase.So it means that QPE must be converting the phase into its Fourier basis states in the ...
0votes
1answer
147views

Given a Hamiltonian $H$ and a state $|\psi\rangle = c_1|E_0\rangle + c_2|E_1\rangle + \cdots$, with $|E_i\rangle$ being an eigenstate of $H$.Can I use the QPE algorithm for $U|\psi\rangle= e^{-iHt}|\...
3votes
1answer
411views

Let $U$ be a unitary transform with eigenvalues $±1$, which acts on astate $|ψ〉$. Using the phase estimation procedure, construct a quantumcircuit to collapse $|ψ〉$ into one or the other of the two ...
1vote
1answer
109views

In HHL the forward phase estimation allows to set the phases of eigenvalues. It does not change the input ket $|b\rangle$ as far as this is a combination of the eigenvalues of the operator (and ...
2votes
1answer
311views

Reading the paper (arXiv) about HHL I misunderstood the following points:$$|{x}\rangle = A^{-1} \cdot |b\rangle = \sum^{2^nb-1}_{i=0}\lambda_i^{-1}b_i|u_i\rangle$$How do we inverse the eigenvalues? ...
2votes
1answer
175views

I'm trying to understand mathematical intuition of HHL algorithm using original paper (arXiv)For now I stuck at the part of Phase estimation. If I understand correctly, if vector b is the eigenvector ...
4votes
3answers
199views

Let us have a Hamiltonian $H$ and a state $|\psi\rangle = \sum_i a_i |E_i\rangle$, a linear combination of eigenstates $|E_i\rangle$ of $H$ with eigenvalues $E_i$. What is the best way to achieve a ...
1vote
1answer
164views

In the paper 'Complexity of the Guided Local Hamiltonian Problem:Improved Parameters and Extension to Excited States' by Cade et. al (2022), they define the following problem[From page 2; last ...
5votes
0answers
172views

I am working on implementing QPE for calculating the ground state energy of a small molecule like H2 or HeH+. I've written some code that is getting results within about 10% accuracy, but I'm not ...
2votes
1answer
263views

I've implemented a quantum counting algorithm for a sudoku example by followingthe amplitude estimation algorithm introduced in Mosca's textbook (An Introduction to Quantum Computing, page#172):...
1vote
1answer
55views

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 $2 \pi$?

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