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I am trying to use the quantum phase estimation(EigsQPE) of qiskit to find the eigen values of a matrix. As I am new to quantum computing so I am confused what to measure in the circuit to derive the eigen values of the input matrix.

I know how to identify phase and derive eigen value using phase derived from the most probable bit string for a single eigen value. But deriving multiple eigen values from QPE circuit is confusing. Any help will be much appreciated.

Code : https://github.com/Anand-GitH/HLL-QauntumComputing/blob/main/Qiskit-QPEStandalone.ipynb

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  • $\begingroup$ Hi and welcome to the community! I didn't work with QPE a lot but I am still quite confused about some of the stuff you did on your code: first, you don't use a unitary matrix, I thought the matrix had to be unitary to get the QPE to work, and second you never use the eigenstates on your circuit, but the controlled-evolution are controlled by it, could you elaborate a little bit more on what you did about that? $\endgroup$
    – Lena
    Mar 24, 2021 at 16:52
  • $\begingroup$ Hi Lena, Thank you. Its not a unitary matrix I am using a matrix which was mentioned in the qiskit HHL example qiskit.org/textbook/ch-applications/hhl_tutorial.html I have not build any circuit I was just calling QPE of qiskit and I had query on how to measure eigen values from this circuit. $\endgroup$
    – Anand Prabhu
    Mar 25, 2021 at 16:50

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Two things to note:

  1. EigsQPE needs the eigenvalues to be scaled onto the range (0,1]. You can use evo_time to set the scaling. If you don't pass this value, a scaling value will be set automatically. You can get this value using eigs.get_scaling().

  2. If the eigenvalue is $e^{2\pi i\theta}$, then the register contents will be $2^n\theta$

That means if the register contains the value $x$, and evo_time equals $s$, then your eigenvalue will be $2\pi x/(2^ns)$

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