qiboteam / boostvqe

Using DBI to boost VQE optimization
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Energy expectation polynomial expansion #48

Closed wrightjandrew closed 4 months ago

wrightjandrew commented 4 months ago

Since for the boost VQE project we want to minimize the energy expectation, here's the polynomial expansion, as for the other cost functions, to estimate $s_{min}$:

$\langle \psi| Hk | \psi \rangle = \sum{n=0}^{\infty} \frac{s^n}{n!} \langle \psi| \Gamma_n | \psi \rangle$

We take the $n$ first terms of this sum (at least 3) and find the root of the derivative with respect to $s$