Quantum State Preparation

Implementation of the paper Black-Box Quantum State Preparation without Arithmetic.

Problem statement

Given an array of $m$ decimal values $$A = (a_0, ..., a_{m-1})$$ such that $a_i \in [0, 1)$, prepare the quantum state $$|\psi\rangle = \frac{1}{||A||}\sum_{i=0}^{m-1}a_i|i\rangle$$ where $||A||$ is the normalization constant, and is equal to the magnitude of the vector represented by $A$. $$||A|| = \sqrt{\sum_{i=0}^{m-1}{a_i}^2}$$

We have access to a black-box $amp$ which has the following action - $$amp|i\rangle|z\rangle = |i\rangle|z \oplus a_{i}^{(n)}\rangle $$

where $a_{i}^{n}$ is the data $a_{i}$ upto $n$ bits of precision.

Contents

The Jupyter notebook covers the following -

1. Grover's standard state preparation method, which requires calculation of arcsines.
2. A modified algorithm which does not require any arithmetic computation, but a comparision operation.