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Add Quantum Material Simulation Problem & Meta-Solver Strategy #136

@koalamitice

Description

@koalamitice

Material Simulation is a Use-Case that has large potential for quantum advantages. Similar to optimization problem solving, there are several decisions when performing a material simulation. These decisons can be modeled as a Meta-Solver Strategy, and we want to integrate such in ProvideQ.

Following are a few important notes that I made during a meeting with Vamshi, who explained the material simulation to me from a user perspective. I used his expert knowledge and tried to formulate the decisions a strategy with 3 steps:

Input -> Molecule Format

Step [1] Classical Preprocessing:
-> 1.1 Molecular orbital
-> 1.2 Active Space Selection
-> 1.3 Transform to qubit representation (Jordan-Wigner, Bravyi-Kataev, Parity mapping)
(All Transformation can have the same Output Standard)

Step [2] [Optional] State Preparation:
-> Warmstart / Initialize Reference State
-> Parametrizied Ansatz

Step [3] Quantum Algorithm Selection
-> 3.1 VQE (Ansatz, Optimizer, Measurement Type (Pauli, Shadow Tomography)?)
-> 3.2 Quantum Phase Estimation

Output ->
Energy Correction,
Property Extration (Diple Moments, Exited States, Spectra),
Error Analysis (Shot Noise, Gate Errors, Approximation Biases),
Some output might only be possible for specific algorithms

Lower Bounds: There a databases which you can use to compare your results. Check them out.
Benchmarking: Create example Python Script and link to it on the website, so that users have an easy start to batch processing.

OffTopic: Provide Example on how you can Benchmark via our API.

Libraries:
(Classical) PySCF, OpenFermion, QChem, ORCA,
(Quantum) Qiskit Nature, PennyLane, Cirq, Braket

See attached .pdf for more details.

QC_workflow_molecular_system.pdf

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