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 $|\psi ⟩=\frac{1}{||A||}\sum _{i=0}^{m-1}{a}_i|i⟩$ 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 - $amp|i⟩|z⟩=|i⟩|z\oplus a_i^{(n)}⟩$

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.