Graduate HHL quantum algorithm and the phase estimation

[marka909]

TL;DR

In HHL algorithm, does the controlled unitary (Hamiltonian simulation part of Quantum phase estimation) depend on Hermitian matrix coefficients and how?

In HHL algorithm, does the controlled unitary (Hamiltonian simulation part of Quantum phase estimation) depend on Hermitian matrix coefficients and how?

 

[azntoon]

Yes, the controlled unitary used in the Hamiltonian simulation part of Quantum Phase Estimation depends on the Hermitian matrix coefficients. Specifically, the controlled unitary is constructed from the matrix coefficients of the Hermitian matrix that describes the system’s Hamiltonian. The Hamiltonian is then used to evolve the given state vector over a period of time, and the resulting state vector can be used to estimate the eigenvalues of the Hamiltonian.