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Phase estimation is the process by which you are given a controlled-$U$ unitary, and a state that you are promised is an eigenvector of $U$ with eigenvalue $e^{2\pi ix/2^t}$, then you can use a $t$-qubit register to affect the change $$|0\rangle^{\otimes t}|u\rangle\mapsto|y\rangle|u\rangle.$$ If $x$ is in integer, then the outcome is guaranteed to be $y=x$...

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If you have the circuit, you can get the registers the circuit acts on from eigs_circ.qregs. You can then create another circuit using the returned quantum register, add an instruction to it (initialize) and then add these two circuits together. Your final code should look something like qregs = eigs_circ.qregs # NB this is a list qc = ...

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Based on comment by DaftWullie and my experience with the algortihm, it seems that a title of the article is misleading. The authors claim that algorithm they proposed is efficient. However, this is true only partialy. The authors devised only part of an algorithm for solving TSP. In particular, they are able to calculate length of a Hamiltonian cycle ...

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As a general comment Aqua has function at different levels, algorithms such as VQE, QPE, HHL etc, pluggable components that were designed to be replaceable 'parts' of algorithms such as Variational Forms, Optimizers, Uncertainty models etc, and then there are circuits which can be used to build any of the above. When it comes to Phase Estimation it's a ...

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I believe this tutorial takes you through how to find eigenvectors. They use EigsQPE, through a helper function they define themselves, called create_eigs().

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