Quantum Computation and Quantum Information

TL;DR

This paper reviews quantum computation and information, highlighting how quantum algorithms and simulations leverage randomness and offer exponential speedups over classical methods, with a focus on statistical analysis.

Contribution

It introduces quantum computation concepts, reviews faster quantum algorithms, and presents a statistical framework for analyzing quantum algorithms and simulations.

Findings

Quantum computers can generate genuine random numbers.

Quantum algorithms can exponentially speed up certain computations.

A statistical framework for quantum algorithm analysis is proposed.

Abstract

Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum simulation and quantum information. Consequently quantum algorithms are random in nature, and quantum simulation utilizes Monte Carlo techniques extensively. Thus statistics can play an important role in quantum computation and quantum simulation, which in turn offer great potential to revolutionize computational statistics. While only pseudo-random numbers can be generated by classical computers, quantum computers are able to produce genuine random numbers; quantum computers can exponentially or quadratically speed up median evaluation, Monte Carlo integration and Markov chain simulation. This paper gives a brief review on quantum computation, quantum simulation and quantum information. We introduce the basic concepts of quantum computation and quantum simulation and present quantum algorithms that are known to be much faster than the available classic algorithms. We provide a statistical framework for the analysis of quantum algorithms and quantum simulation.