# Nondeterministic quantum computation via ground state cooling and ultrafast Grover algorithm

## TL;DR

This paper introduces a nondeterministic quantum computation model that uses ground state cooling and selective measurements, enabling efficient Grover search with minimal runtime and overcoming challenges in ground state preparation.

## Contribution

It presents a novel nondeterministic quantum computation approach based on ground state cooling and selective measurements, improving efficiency over traditional adiabatic methods.

## Key findings

- Requires constant or logarithmic runtime for Grover search
- Eliminates difficulties in preparing initial ground states
- Demonstrates effectiveness of nondeterministic approach

## Abstract

Over the last decades, there have been many proposals for quantum computation. One of the promising candidates is adiabatic quantum computation (AQC). The central idea of AQC is about finding the ground state of a system with a problem Hamiltonian via particular adiabatic passages, starting from an initialized ground state of a simple Hamiltonian. One disadvantage of AQC is the significant growth of necessary runtime, in particular when there are quantum phase transitions during the AQC passages. Here we propose a nondeterministic ground state cooling quantum computation model based on selective projection measurements on an ancilla coupled to the system with the problem Hamiltonian previously cooled by conventional techniques. We illustrate the model by Grover search problem and show that our nondeterministic model requires a constant or at most logarithmic runtime and can also get rid of possible difficulties in preparing the ground state of the simple Hamiltonian.