Gaussian State Preparation

Introduction

State Preparation is a cornerstone of quantum algorithms and applications, enabling the initialization of quantum systems into specific states as a starting point for subsequent operations. Its efficiency directly impacts the accuracy and scalability of quantum computations.

A particular interest is the Gaussian state preparation, which is essential for simulating physical systems and tackling problems in quantum chemistry, machine learning, and optimization. Gaussian states, characterized by their Gaussian-shaped wavefunctions, are powerful tools for encoding probability distributions and modeling quantum systems.

This project leverages Classiq's quantum computing SDK to implement a Gaussian state preparation in the interval [-2, 2).

Target State: The Gaussian State Representation

The Gaussian state is defined as:

$$ |x_0\rangle_N = |0\rangle_N \longrightarrow \sum_{|x\rangle_N} \sqrt{G(x)} |x\rangle_N $$

Where $( G(x) )$ is represented as a vector:

$$ {G}(x_i) = \frac{\exp(-\lambda \cdot {x_i}^2)}{\sum_{x' \in \text{domain}} \exp(-\lambda \cdot (x')^2)} \text{, for } x_i \in \text{domain} $$

• $( G(x) )$ is the normalized Gaussian vector across the discrete domain.
• $( \vec{x} )$ represents the set of discrete points in the domain.
• $( \lambda )$ represents the decay rate, controlled by the variable EXP_RATE, which determines the spread of the Gaussian.
• The denominator ensures normalization across the entire domain.

Installation

To use this project, ensure you have the required dependencies installed:

pip install classiq

---

Authentication

If running for the first time, authenticate with Classiq:

import classiq
# classiq.authenticate()  # Uncomment to authenticate

---

Running the Code

Run the Jupyter Notebook to execute the Gaussian state preparation algorithm. The implementation initializes and prepares the quantum system in a Gaussian state within the specified interval.

---

Setting Up the Environment

This project includes a requirements.txt file that lists all the Python packages and their versions used in this project. You can use this file to recreate the exact environment required to run the code.

---

License

This project is intended for educational and research purposes. Please ensure compliance with any relevant licensing agreements for the Classiq SDK.