1D TFIM
The file names contain the ansatz depth $p$ as `_nlayer` and the parameters
of the target Hamiltonian as `v=` or `w=` (in the case of the 2D SSH model).
Files simply prefixed `per_ham` are the first runs done with random initial parameters,
files prefixed with `per_ham_extrapolated` are runs started with parameters
extrapolated from better, lower depth parameters, files prefixed with
`per_ham_iterative` are runs where better, lower depth parameters were simply
padded with zeros to get better initial parameters and finally files prefixed
with `per_ham_infosharing` are runs where better parameters found at different
Hamiltonian parameters $g$ where used to warm start the optimsation.
## File structures
Each file contains some (but not neccessarily all) of the following fields:
- `E0`: Groundstate energy of the exact groundstate
- `E_opt`: Lowest energy found by VQE after optimisation
- `fidelity`: Fidelity of the VQE state with the true groundstate
- `x0`: Initial parameters for the optimisation
- `x_opt`: Optimal VQE parameters.
- `ret`: Return value of the optimsation. Should be something like `SUCCESS`, `XTOL_REACHED`, ...
### For the TFIM
- `zz_correlations`: A matrix with entries $⟨ψ|Z_i Z_j|ψ⟩ - ⟨ψ|Z_j|ψ⟩⟨ψ|Z_i|ψ⟩$
where $|ψ⟩$ is the VQE state
- `zz_expvals`: A matrix with entries $⟨ψ|Z_i Z_j|ψ⟩$
- `z_magnetization`: $⟨ψ| ∑_i Z_i |ψ⟩$
- `x_magnetization`: $⟨ψ| ∑_i X_i |ψ⟩$
- `E_J`: $⟨ψ| ∑_i Z_i Z_{i+1} |ψ⟩$
- `E_hx`: $⟨ψ| ∑_i X_i |ψ⟩$
- `E_hz`: $⟨ψ| ∑_i Z_i |ψ⟩$
### For the BBC
- `E_bilinear`: $⟨ψ| ∑_i S_i ⋅ S_{i+1} |ψ⟩$
- `E_biquadratic`: $⟨ψ| ∑_i (S_i ⋅ S_{i+1})^2 |ψ⟩$
- `bilinear_dimerisation`: $⟨ψ|S_{i-1} ⋅ S_i - S_i ⋅ S_{i+1}|ψ⟩$
- `quadrupolar_fluctuations`: $⟨ψ|[(S_0^z)^2 - 2/3] [(S_i^z)^2 - 2/3]|ψ⟩$
- `string_order`: $⟨ψ|S^α_i [ ∏_{i