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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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 ...
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What is the usefulness of the Suzuki-Trotter formula?

I can't seem to wrap my head around the suzuki-trotter formula. I have seen This answer but I am still confused of the applicability of the formula. Let me explain: As I understand it Trotterization ...
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Why must we take multiple measurements for different values of $M$?

The circuit for Kitaev phase estimation is given as: By varying $\theta$, we are able to determine $\sin(2 \pi M \phi_k)$ and $\cos (2 \pi M \phi_k)$ from sampling the circuit and calculating the ...
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Quantum Phase Estimation on a superposed state

Is it possible, using the QPE algorithm, to map the state $\sum_j\alpha_j\,\left|v_j\right\rangle\,|0\rangle^{\otimes n}$ to the state $\sum_j\alpha_j\,\left|v_j\right\rangle\,\left|\theta_j\right\...
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Quantum Phase Estimation Circuit and Modular Exponentiaton

In Nielsen and Chuang, it is stated that the effect of phase estimation circuit is mapping state $|j\rangle |u\rangle$ to $|j\rangle U^j |u\rangle$. Here is my solution: Consider the first $CU^{2^0}...
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Repeating Quantum Phase Estimation algorithm

In the Quantum Recommendation Systems paper, the authors use the Quantum Phase Estimation algorithm in a way that is slightly different from what I've seen so far. This is how it is described: The ...
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Is it possible to express u1(λ) through the gates rx, ry, rz while maintaining the phase? In Qiskit for example

Is it possible to express gate u1(λ) through the gates rx, ry, rz while maintaining the phase? Both in principle and in practice (in Qiskit for example)? The single gate rz(λ) is not suitable, because ...
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How to properly make phase estimation with qiskit's modules

I have been making several experiments with qiskits' Quantum Phase Estimation modules, such as with QPE and EigsQPE. For example,...