Transformation of Quantum Expectation Value Problem to Classical ML/DL Problem

Quantum shadow tomography + VQE data generation + classical machine learning/deep learning for expectation value prediction.

Project overview

This repository contains undergraduate thesis work focused on converting a quantum expectation value estimation problem into a classical ML/DL prediction problem.

Main idea:

• Use quantum shadow tomography to build a compact classical representation of many-body quantum states.
• Generate measurement datasets from VQE-based setups.
• Train classical machine learning/deep learning models to predict expectation values from Pauli observables and coefficients.
• Evaluate whether strong prediction can be achieved with significantly fewer measurements (e.g., around 185) compared with larger baselines used in prior work.

Table of contents

• Project overview
• Repository structure
• Workflow
• How to run
• Key files
• Extended papers
• Reference implementations
• Learning resources

Repository structure

.
├── Classical Machine learning and Deep learning/
│   ├── V13/
│   ├── V14/
│   │   ├── WITH SMAGON/
│   │   └── WITHOUT APPLYING SMAGON/
│   └── V16/
│       ├── WITH SMAGON/
│       └── WITHOUT APPLYING SMAGON/
├── Derandomize Quantam Shadow Tomography/
│   ├── V4/
│   │   ├── CLASSICAL SHADOW/
│   │   └── DERANDOMIZE CLASSICAL SHADOW/
│   └── V6/
└── README.md

Workflow

1. Generate / design measurement procedures

• Randomized classical shadow and derandomized shadow variants.

2. Acquire shadow-based data

• Produce measurement operators/outcomes and expectation-related datasets.

3. Train classical ML/DL models

• Use generated classical datasets (CSV files) to train and evaluate predictive models.

4. Compare configurations

• Compare versions (V13, V14, V16) and experiment branches (with/without SMAGON).

How to run

The project is experiment-driven across multiple folders/versions. Run scripts from the corresponding experiment directory.

Typical steps:

# 1) Move into a target experiment folder (example)
cd "Classical Machine learning and Deep learning/V13"

# 2) Generate / process measurement procedures or datasets
python data_acquisition_shadow.py

# 3) Run prediction/evaluation flow
python prediction_shadow.py

If you are using notebook-based workflows, open and run:

• electronic_structure_problem_dcs_Hydrozen.ipynb

Key files

• data_acquisition_shadow.py: shadow measurement procedure generation.
• modified_derandomization.py: modified derandomized classical shadow routine.
• prediction_shadow.py: expectation value estimation/prediction utilities.
• Classical_data_H2.csv, file1.csv, file2.csv: generated datasets for model training/evaluation.

Extended papers

1. Predicting many properties of a quantum system from very few measurements
   https://www.nature.com/articles/s41567-020-0932-7

2. Efficient estimation of Pauli observables by derandomization
   https://arxiv.org/abs/2103.07510

3. Information-theoretic bounds on quantum advantage in machine learning
   https://arxiv.org/abs/2101.02464

Reference implementations

1. https://github.com/hsinyuan-huang/predicting-quantum-properties
2. https://github.com/renatawong/classical-shadow-vqe

Learning resources

1. https://www.youtube.com/watch?v=NXejv2wVwas
2. https://www.classiq.io/algorithms/variational-quantum-eigensolver-vqe
3. https://qiskit-community.github.io/qiskit-nature/tutorials/06_qubit_mappers.html
4. https://www.youtube.com/watch?v=YtepXvx5zdI