# Fast quantum search algorithm and Bounds on it

**Authors:** Arun Kumar Pati  
**arXiv:** [quant-ph/9807067](https://arxiv.org/abs/quant-ph/9807067)  
**Date:** 1998-07-24  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/quant-ph--9807067v1/

## Key points

- Arun Kumar Pati's paper explores Grover's generalised search algorithm within a geometric framework.
- The approach allows for the study of non-orthogonal states, potentially advancing the search process.
- Introducing an innovative approach based on an arbitrary unitary transformation suggests a faster search algorithm.
- Analysis of lower and upper bounds on transition matrix elements highlights the speed constraints of quantum search processes compared to classical methods.
- Addressing challenges such as perturbation in time-dependent search operations contributes valuable insights to quantum algorithms and computation.

## Summary

In his paper titled "Fast quantum search algorithm and Bounds on it," Arun Kumar Pati explores the intricacies of Grover's generalised search algorithm within a geometric framework. This approach allows for the study of non-orthogonal states, providing potential advancements in the search process. By introducing an innovative approach based on an arbitrary unitary transformation, Pati suggests a potential search algorithm that could further expedite the steps involved in the process. The study also delves into the lower and upper bounds concerning transition matrix elements when the unitary operator undergoes changes over time. This analysis leads to a significant implication - that the quantum search process cannot be too rapid or too sluggish, setting it apart from classical computation methods. Furthermore, Pati addresses various challenges such as perturbation and other issues that may arise in a time-dependent search operation. By shedding light on these complexities and limitations, this research contributes valuable insights to the field of quantum algorithms and computation.