Add Support for Adaptive Sample Selection in Sample-Based Quantum Diagonalization (SQD)

[AbdullahKazi500]

What should we add?

I would like to request the addition of adaptive sample selection capabilities to the Qiskit addon for sample-based quantum diagonalization (SQD). Adaptive sampling would enhance the efficiency and robustness of SQD by dynamically selecting the most informative samples during the iterative diagonalization process.

Motivation:
Improved Efficiency:

Current SQD implementations rely on user-provided samples obtained through predefined quantum circuits. While effective, this static approach might require a large number of samples for convergence, especially for challenging systems.
Adaptive sample selection can reduce the required sample size by focusing computational resources on sampling regions that contribute the most to the subspace expansion.
Enhanced Robustness:

Quantum noise can corrupt samples, impacting the accuracy of the diagonalization process. Adaptive sampling techniques could prioritize high-fidelity samples or refine the representation of subspaces impacted by noise.
Targeting Sparse Eigenstates:

The convergence rate of SQD improves with the sparseness of the target eigenstate. Adaptive sampling could dynamically identify and enhance contributions from relevant subspaces, further accelerating convergence.

Adaptive sampling is increasingly used in hybrid quantum-classical algorithms (e.g., Variational Quantum Eigensolvers). Adding it to SQD would align the tool with modern practices in quantum computing.
Proposed Implementation:
Dynamic Sample Evaluation:

Implement a mechanism to evaluate the quality or contribution of each sample to the subspace expansion. Metrics could include fidelity, overlap with existing subspace vectors, or contributions to the Hamiltonian's representation.
Feedback Loop:

Add a feedback loop between the classical solver and the quantum sampler to iteratively refine the sampling process.
Heuristics for Sample Prioritization:

Develop heuristics to identify underrepresented subspaces or improve sample diversity. For instance, sampling could focus on regions where the subspace projection has the highest residual errors.

References
https://arxiv.org/abs/2303.07417
https://link.springer.com/chapter/10.1007/978-3-031-63778-0_23

[caleb-johnson]

Hi @AbdullahKazi500 , thanks for submitting this issue.

We want to contain the SQD addon to the post-processing of noisy quantum samples, so including functionality for creating quantum circuits and updating their parameters in a VQE-type of workflow would be out of scope for this addon.

If you had good ideas for heuristics for updating the ansatz, it seems straightforward to embed the SQD addon within a larger VQE loop at the user level.

[AbdullahKazi500]

Hi @caleb-johnson So the feature request is out of scope for now ?

[caleb-johnson]

Hi @caleb-johnson So the feature request is out of scope for now ?

Yes, this is out of scope at this time