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### Solving Hamiltonian eigenvalue problem

Have you ever seen a derivation of Grover's search? The approach that you want is very similar. Start by defining two states, perhaps  |a\rangle=|\psi_N\rangle, \qquad |b\rangle=|m\rangle-|a\rangle\...
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You can solve this by referring to this question. To estimate the eigenvalues of $H\left( s \right) =\left( 1-s \right) H_0+sH_m=I-\left( 1-s \right) |\psi _N\rangle \langle \psi _N|-s|m\rangle \... 2 votes ### Calculating entanglement with CRZ Gates on non-neighbor qubits Rather than constructing large matrices, you can continue using bra-ket notation with an outer-product representation for the operators. So your standard controlled-Z gate acting on target and control ... 2 votes Accepted ### Is it essential to apply Quantum Singular Value transformation twice for Hamiltonian simulation? You can find the answer to your question in page 22: How might this problem be solved with QSVT? Naively, one may try to employ QSVT with a polynomial approximation to$e^{ −ixt}\$ [...]. However, ...

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