Machine Learning for Quantum State Tomography

1 Overview

Quantum State Tomography reconstructs the density matrix ρ of an unknown quantum state from measurement data. The number of parameters grows as 4N for an N qubit system. This makes full state tomography impractical for systems larger than about twelve qubits on current noisy hardware.

Modern approaches such as Classical Shadows, compressed sensing and neural network based surrogate models make it possible to estimate important properties of structured quantum states with far fewer measurements. This project develops scalable and noise aware ML based tomography pipelines suitable for realistic quantum experiments with a focus on efficiency interpretability and robustness.

Suggested Background Reading
IBM Quantum Basics of Quantum Information
IBM Quantum General Formulation of Quantum Information
MIT 9.40 Introduction to Neural Computation

2 Applications

3 Technical Tracks

Track 1 Neural Shadow Tomography

Neural models operate on Classical Shadow measurement data to improve robustness under noise and to estimate nonlinear observables with reduced sample requirements.

Output A Python or Julia library for shadow assisted ML tomography for mid scale systems

Track 2 FPGA Accelerated Tomography

This track explores hardware acceleration using quantised models deployed through Vitis HLS Intel HLS or custom Verilog implementations.

Output A synthesizable and low latency hardware block for state property estimation

Track 3 Neuromorphic SNN Tomography

This track studies spiking encodings of measurement data and surrogate gradient training for energy efficient inference.

Output A prototype SNN showing reduced energy per inference compared to a classical network

4 Project Timeline

WeekDatesFocus
Week 0 10 December to 16 December Theory review and completion of prerequisites including Classical Shadows tomography methods neuromorphic basics and baseline quantum state tomography algorithms
Week 1 17 December to 23 December Environment setup and creation of measurement datasets using SIC POVM or Pauli projective measurements with either random quantum circuits or realistic algorithm based data generation using tools such as KetGPT
Week 2 24 December to 30 December Implementation of baseline methods including linear inversion maximum likelihood estimation and Classical Shadows
Week 3 31 December to 6 January Exploration and construction of model architectures for the selected track including design choice justification and initial validation
Week 4 7 January to 13 January Training hyperparameter tuning robustness testing and comparison under simulated noise
Week 5 14 January Core result analysis documentation model packaging and preliminary discussion
Week 6 15 January to 21 January Quantum machine learning enhanced quantum state tomography for quantum algorithm verification for example Grover and QAOA layer by layer including integration with existing tomography pipelines
Week 7 22 January to 28 January Qubit characterisation using quantum detector tomography on Qiskit noise models extraction of purity coherence and entanglement and final polishing of reports and code

5 Software Requirements

TrackRequired Tools
All Tracks Python 3.10 or later PyTorch NumPy Qiskit Cirq or PennyLane
Track 1 PyTorch Optional Julia and Yao
Track 2 Vitis HLS Intel HLS Verilog
Track 3 snnTorch preferred Norse Brian2 Optional Lava

6 Submission Format

Submissions must be made to a dedicated GitHub repository. The repository should be organized with a source code folder src a detailed documentation folder docs and a Python notebook for demonstration purposes. To begin you will need to fork the main project repository available at assignment and complete all tasks detailed within the assignments folder which are based on the project's prerequisites.

7 Discussions

For any questions clarifications or doubts please use the GitHub Discussions page or join the WhatsApp group.

8 Resources