Incorporate SQD feedback #2460
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Incorporate SQD feedback #2460
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abbycross
reviewed
Dec 11, 2024
abbycross
reviewed
Dec 11, 2024
abbycross
reviewed
Dec 11, 2024
Co-authored-by: abbycross <[email protected]>
| @@ -1826,12 +1826,14 @@ | |||
| "\n", | |||
| "1. Use the `recover_configurations()` method to obtain a refined bitstring matrix and probability array based on the average orbital occupancy.\n", | |||
| "1. Use the `postselect_and_subsample()` to collect batches of subsamples to diagonalize over.\n", | |||
| "1. Then use the batches of subsamples as arguments to the `solve_fermion()` method to obtain an approximation of the ground state." | |||
| "1. Then use the batches of subsamples as arguments to the `solve_fermion()` method to obtain an approximation of the ground state.\n", | |||
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A little pedantic, but I guess we could say "function" instead of "method" to distinguish it from a class method.
| "1. Then use the batches of subsamples as arguments to the `solve_fermion()` method to obtain an approximation of the ground state." | ||
| "1. Then use the batches of subsamples as arguments to the `solve_fermion()` method to obtain an approximation of the ground state.\n", | ||
| "\n", | ||
| "It is important to note how to address the first iteration of the configuration recovery loop. Since the average orbital occupancy is not yet available, only the `postselect_and_subsample()` method is called. This removes any non-physical samples (samples with incorrect Hamming weight) before running the eigenstate solver, `solve_fermion()`. Afterward, the average orbital occupation is calculated across all batches and used as input to the `recover_configurations()` method, which flips individual bits probabilistically based on this average. The probability of flipping an individual bit is based on the distance between the value of the bit and the average orbital occupancy obtained. (See Section **II-A** of the supplementary information in the [SQD paper](https://arxiv.org/abs/2405.05068) for more information.)" |
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The probability to flip each bit is a bit more complicated than the description here suggests.
P(flip_0_to_1) and P(flip_1_to_0) are functions of both:
- avg orbital occupancy from the eigensolver solutions
- naive expectation of occupancy from electronic structure (# elec / # orbitals)
I think you could just remove the last sentence and point folks to the literature here and it'd be perfect
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Here is the source code for determing P(flip)
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Ah got it, that makes sense thanks. I ended up just following your suggestion and removed that last sentence and pointed the reader toward the literature.
abbycross
reviewed
Jan 23, 2025
docs/guides/qiskit-addons-sqd.mdx
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| @@ -60,7 +60,7 @@ $$ \hat{H}_{S^{(k)}} = \hat{P}_{\mathcal{S}^{(k)}}\hat{H}\hat{P}_{\mathcal{S}^{( | |||
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| where $\hat{H}_{\mathcal{S}^{(k)}}$ is the Hamiltonian of a given subspace. | |||
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| The bulk of the SQD workflow lies here wherein each of these subspace Hamiltonians is diagonalized. The ground states obtained from each of these subspaces, $|\psi^{(k)}\rangle$, are used to obtain an estimate of a reference vector of occupancies $\mathbf{n}^{(K)}$ averaged over each of the $K$ subspaces and sent back to the configuration recovery step. A new set of subspaces are then obtained and diagonalized, and this procedure iterates in a loop until a user specified criterion is met. | |||
| The bulk of the SQD workflow lies here wherein each of these subspace Hamiltonians is diagonalized. The ground states obtained from each of these subspaces, $|\psi^{(k)}\rangle$, are used to obtain an estimate of a reference vector of occupancies $\mathbf{n}^{(K)}$ averaged over each of the $K$ subspaces. A new set of configurations $\mathcal{X}_R$ is then generated by probabilistically flipping individual bits based on this average occupation and the known total number of particles (Hamming weight) in the system. This configuration recovery process is then repeated by preparing a new set of subspaces to diagonalize, obtaining new eigenstates and averaged orbital occupancy, and generating a new set of configurations. This loop is iterated until a user-specified criterion is met, and the overall process is analogous to filtering a noisy signal to improve its fidelity. | |||
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I just noticed the two "obtain"s in the second sentence 😆 but I don't know that it's worth wordsmithing since it makes sense, so I'll leave it for now.
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Good catch! Just changed the wording around a bit
abbycross
approved these changes
Jan 23, 2025
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Closes #2360
Tried to parse the feedback as best I could and would especially appreciate a review from either @garrison or @mrossinek to double check my work. Essentially all I did here was give a bit more detail on the configuration recovery step of SQD both in the intro and getting started pages.