Quantum Computation and Quantum Information

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.

量子计算和量子信息在计算机科学，数学，物理科学和工程方面具有极大的兴趣。它们可能会导致通信，计算和加密技术方面的新技术创新浪潮。由于量子物理学的理论从根本上是随机性的，因此随机性和不确定性深深植根于量子计算，量子模拟和量子信息中。因此，量子算法本质上是随机的，量子模拟广泛利用了蒙特卡洛技术。因此，统计数据可以在量子计算和量子模拟中发挥重要作用，这反过来又为革命计算统计提供了巨大的潜力。虽然只能通过古典计算机生成伪随机数，但量子计算机能够产生真正的随机数。量子计算机可以指数级或四次加快中位数评估，蒙特卡洛集成和马尔可夫链仿真。本文简要审查了量子计算，量子模拟和量子信息。我们介绍了量子计算和量子模拟的基本概念，并介绍了量子算法，这些算法算法比可用的经典算法快得多。我们为分析量子算法和量子模拟提供了一个统计框架。