Quantum Phase Classification

🚀 FLIQ (Future Leaders in Quantum) 2025 Hackathon Submission

Track: Science | Challenge: Classiq x DuQIS | Hosted by: Classiq Technologies & Duke Quantum Information Society

---

🏆 Overview

This repository contains our winning 1st prize submission for the FLIQ 2025 Classiq x DuQIS Quantum Machine Learning Challenge, where we built a Quantum Machine Learning (QML) model to classify quantum phases of matter — specifically distinguishing between the Z2 and Z3 ordered phases in a Rydberg atom chain.

Note: Please consider Version 2 as a secondary solution. It explores an alternate model but is less refined and should not be considered the primary solution.

---

🧩 Problem Overview

Design a Quantum Machine Learning (QML) model to classify phases of quantum matter using classical shadows derived from randomized measurements of a Rydberg atom system.

• Input: Measurement outcomes encoded as Pauli-basis classical shadows.
• Output: Predict the phase label (Z2 or Z3) of the quantum state.
• Constraint: Avoid reconstructing the full quantum state (no full $\rho$).

---

🌀 Rydberg Atom Phase Diagram

This phase diagram shows the regions corresponding to the different ordered quantum phases studied in this challenge (Z2 and Z3).

🧠 Our Solution

We developed a QML pipeline using reduced density matrices and a parameterized quantum circuit trained to distinguish between the two phases.

✅ Key Features

• Encoding: Custom angle encoding of reduced observables.
• Architecture: Shallow quantum circuit optimized for width and depth.
• Inference: Hybrid quantum-classical optimization loop.
• Efficiency: Tuned to minimize parameters, depth, and qubits, as per the scoring function.

ℹ️ Note: Please refer to version_2/ for an alternate (experimental) architecture we explored.

---

🧪 Dataset Details

• Each sample: $T = 500$ randomized measurements of an $n = 51$ qubit state.
• Measurements: From ${ |g\rangle, |r\rangle, |+\rangle, |-\rangle, |+i\rangle, |-i\rangle }$
• Label: Phase category (Z2, Z3)

---

🛠 Repository Structure

.
├── FLIQ_Challenge_ClassiqDuQIS.ipynb  # Main solution notebook
├── version_2/                         # Secondary model (not primary)
│   └── alternate_model.ipynb
├── training_data.npz                 # Provided measurement data
├── phase_diagram.png                 # Reference for Rydberg phases
├── qprog.qprog                       # Saved quantum program
└── trained_model_params.npz         # Optimized model parameters

📊 Evaluation Metric

The scoring function used in the challenge is:

[ f(A, P, D, W) = A - 0.1P - 0.0002D - 0.1W ]

Where:

• A: Accuracy on the test set
• P: Number of trainable parameters
• D: Circuit depth
• W: Number of qubits (circuit width)

We optimized our model to maximize accuracy while keeping the number of parameters (P), depth (D), and width (W) as low as possible to achieve a high score.

---

📚 References

• Huang et al., Predicting Many Properties of a Quantum System from Very Few Measurements, arXiv:2002.08953
• Huang et al., Provably Efficient Machine Learning for Quantum Many-Body Problems, arXiv:2106.12627
• Sim et al., Expressibility and Entangling Capability of Parameterized Quantum Circuits, arXiv:1905.10876
• Bloqade.jl — Rydberg Atom Simulations

---

🧑‍💻 Team

Team Name: MerQury
Event: FLIQ 2025 Hackathon
Track: Science — Classiq x DuQIS Quantum Phase Classification
Submission: Primary model in root, alternate version in version_2/

Challenge Statement

https://github.com/dmitriikhitrin/Classiq-x-DuQIS-FLIQ-Challenge