Prepares a quantum state with amplitudes corresponding to a given array with two methods. Implementation of the paper Black-Box State Preparation without Arithmetic.
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 -
Grover's standard state preparation method, which requires calculation of arcsines.
A modified algorithm which does not require any arithmetic computation, but a comparision operation.
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Prepares a quantum state with amplitudes corresponding to a given array with two methods. Implementation of the paper Black-Box State Preparation without Arithmetic.