Expected Value of Absolute Value Hamiltonians

[ComputationalBasis]

Hello again everyone,

Given a Hamiltonian (mine only depends on number operators), I was wondering if there is a qadence function or a simple way of calculating its absolute value, to later compute the expected value. Basically, given H, the thing I want to compute is <|H|>. I was trying using block_to_tensor but everything kept giving me errors.

Thank you in advance!

[awennersteen]

Hi, sorry we missed this.
Could you tell me a bit more about what you tried and how it failed?

I'd assume that block_to_tensor, diagonalize, then calculate should work, so I'm a bit confused.

Is the issue a dimension mismatch? we return our states batched in PyQTorch, so probably you have a N x 2^n x 2^n tensor coming out. where N is the batch size - also if the batch size is 1.

So you can probably do something like

Hmat = block_to_tensor(H).squeeze(0).to(torch.complex128)
evals, U = torch.linalg.eigh(Hmat)
absH = U @ torch.diag(torch.abs(evals)).to(Hmat.dtype) @ U.conj().T
  

or loop or slice through the batch when doing the eigen decomposition.

(do sanity check my maths there, I didn't run it)

[ComputationalBasis]

Do not worry for the delay,

The thing is, I want later to use the expectation function on that absH, and Qadence needs a block in expectation, this is my main problem

[awennersteen]

hmm, we can probably come up with a way to translate absH back to a pauli-string operator, if you need to.

But you could also just do the calculation manually.

# Compute <psi| |H| |psi>
psi = run(n_qubits, circuit)
exp_absH = torch.einsum("bi,ij,bj->b", psi.conj(), absH, psi).real

Would that suffice?