# Preparing Many Copies of a Quantum State in the Black-Box Model

arXiv: https://arxiv.org/abs/2207.11014 · HTML: https://mlsanity.com/paper/2207.11014/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [Logarithmic-Regret Quantum Learning Algorithms for Zero-Sum Games](https://mlsanity.com/paper/2304.14197/) (2023)
- [Near-Optimal Quantum Coreset Construction Algorithms for Clustering](https://mlsanity.com/paper/2306.02826/) (2023)

## Abstract (arXiv)

We describe a simple quantum algorithm for preparing K copies of an N-dimensional quantum state whose amplitudes are given by a quantum oracle. Our result extends a previous work of Grover, who showed how to prepare one copy in time O(√N). In comparison with the naive O(K√N) solution obtained by repeating this procedure~K times, our algorithm achieves the optimal running time of θ(√KN). Our technique uses a refinement of the quantum rejection sampling method employed by Grover. As a direct application, we obtain a similar speed-up for obtaining K independent samples from a distribution whose probability vector is given by a quantum oracle.