QPoland Global Quantum Hackathon

19-Oct-2024 to 27-Oct-2024 (For QML track submission deadline extended till 18-Nov-2024)

https://www.qaif.org/contests/qpoland-global-quantum-hackathon

Problem Statement:

Quantum Machine Learning: Solving Linear Systems of Equations

Re-Implementation of Variational Quantum Linear Solver from paper Bravo-Prieto et al. (2020)

Background

Linear systems of equations are fundamental in mathematics and have wide-ranging applications across several fields, including physics, engineering, economics, and computer science. This kind of equation can be found when solving numerically differential equations, analyzing electrical circuits, or performing 3D transformations in computer vision. Additionally, linear systems are critical in statistical analysis, particularly in regression models, which are used to find the best-fit line for data. Their importance lies in their simplicity, versatility, and ability to provide solutions in many practical scenarios.

Considering this, solving a linear system that grows in size becomes more difficult using classical computing techniques. In particular, Carlos Bravo-Prieto et al.'s paper "Variational Quantum Linear Solver" Ref[1] shows a solution to this problem using quantum machine learning methods.

Detailed Challenge Description

In this challenge, your goal is to reproduce the implementation of the quantum algorithm displayed in the Sec. 2.3 of the paper Ref [1], i.e. solve the following system of linear equations:

$$\textbf{A}\vec{x}= \vec{0}$$

$$A = \sum_{i=1}^{10} X_i + 0.1\sum_{i=1}^{9} Z_i Z_{i+1} +I,$$

Where $X_i$, adn $Z_i$ are the respective Pauli matrices, acting over the Qubit with index $i$. The submitted solution to this challenge consists of a quantum program written with Classiq that includes:

1) A correct cost function and quantum ansatz
2) A single execution of the quantum algorithm, using the state-vector simulator
3) The quantum program’s CX-gate count

Link to Video presentation

Click here

or use folllowing

https://drive.google.com/file/d/1LbDpcjjjcGa4rEkcdWiATgILXI1uOWyN/view?usp=sharing

References

[1]: Bravo-Prieto et al.,Variational Quantum Linear Solver. (2020)

[2]: The Hamiltonian Simulation Guides using Classiq

[3]: The Quantum Machine Learning Guide using Classiq

[4]: Variational Quantum Linear Solver (VQLS) with Linear Combination of Unitaries (LCU) Block Encoding.

[5]: Classiq resources:

1. Getting Started with Classiq - Classiq 101

2. Classiq’s documentation

3. Classiq Library of many implementation algorithms and applications

4. Classiq Community Slack is available for any questions you might have

Requirements: to run notebook required to install Classiq SDK.

1. Python 3.12 (NOTE - The Classiq SDK is currently supported for Python versions 3.8 to 3.12).
2. Jupyter (Optional for SDK, required to run this notebook)
3. User registration at platform. Note: To use Classiq platform for free for non-commercial purposes, you must register. Then you can optionally install the Python SDK package and authenticate your account. Click here for more derail...
4. Classiq 0.57 (Classiq's Python SDK for quantum computing) https://platform.classiq.io/
5. Once above four steps completed "Authenticate the device with your Classiq account" as mentioned in step 3 link.

Team members (Contributors) :

1. Abhishek Raj ( @Abhishek Raj-IND )
2. Ramesh Makwana ( @Ramesh Makwana )
3. Leszek Czajka ( @Spaghettificated )
4. Amar ( @Amar : India )
5. Priya ( @Priya )