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International Journal of Quantum Information

A UNIVERSAL QUANTUM ESTIMATOR

L. C. Kwek, Keng Wah Choo, Jiangfeng Du, ARTUR K. EKERT, CAROLINA MOURA ALVES, Michał Horodecki, Paweł Horodecki, Dagomir Kaszlikowski, NAVEEN NAZIMUDEEN, C. H. Oh, Daniel K. L. Oi

Published Nov 1, 2005• 0 citations
Publisher

Abstract

Almost all computational tasks in the modern computer can be designed from basic building blocks. These building blocks provide a powerful and efficient language for describing algorithms. In quantum computers, the basic building blocks are the quantum gates. In this tutorial, we will look at quantum gates that act on one and two qubits and briefly discuss how these gates can be used in quantum networks.

DOI
10.1142/s0219749905001304

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Almost all computational tasks in the modern computer can be designed from basic building blocks. These building blocks provide a powerful and efficient language for describing algorithms. In quantum computers, the basic building blocks are the quantum gates. In this tutorial, we will look at quantum gates that act on one and two qubits and briefly discuss how these gates can be used in quantum networks.
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Quantum computing addresses the construction and operation of quantum computers to solve more efficiently instances of specific problems that are difficult to tackle with classical computers. Even if we are currently in the so-called Noisy Intermediate Scale Quantum (NISQ), steady signs of progress are being made towards the realization of a fast and reliable quantum computer, materializing the basic building blocks of quantum circuits, i.e., quantum bits and gates. On the other hand, quantum communications cover the transmission of quantum states across distances. Recent advances in this context have led to the novel research area of quantum networking, which is set to define the programming interfaces and protocols for the practical operation of quantum communication and computing infrastructures. The tutorial has the objective of raising awareness about these emerging topics, i.e., quantum computing and quantum networking, in the research community by i) introducing briefly the latest technologies developed in each, then ii) providing hands-on examples of how to use them for simple use cases, and iii) finally sketching the more promising open research challenges.
This chapter introduces the basic building blocks of quantum computing and a variety of specific algorithms. It begins with a brief review of classical computing and discusses how its key elements – bits, gates, circuits – carry over to the quantum realm. It highlights crucial differences to the classical case, such as the impossibility of copying a qubit. The quantum circuit model is shown to be universal, and a peculiar variant of quantum computing, based on measurements only, is illustrated. That a quantum computer can perform some calculations more efficiently than a classical computer, at least in principle, is exemplified with the Deutsch-Jozsa algorithm. Other examples covered in this chapter are the variational quantum eigensolver, which can be applied to the study of molecules and classical optimization problems; quantum simulation; and entanglement-assisted metrology.
Computation is a process of performing a large number of simple operations. The main building blocks of classical computers are bits. Each of them can take either the value 0 or 1. A series of gates can change these values by acting on them selectively. This process is structured to fulfil a purpose. For example, if we are interested in adding two numbers, the numbers are encoded into bits and gates are performed such that the final state of the bits reveals the desired answer: a number which is the sum of the initial ones. While it is possible to build algorithms that can perform almost any computation, it is also desirable to find the answer within a reasonable length of time or with a reasonable amount of resources. There is an ever-growing demand in computational power for both scientific and commercial purposes. Indeed, it is surprisingly easy to find an application that can jam even the fastest computer. This fuels a vast effort in the research of information science to increase the speed and processing power of computers. Modern computational models are based on the universal Turing machine (Turing, 1937). This is a theoretical information processing model that employs the elementary gate processes described above. It can efficiently simulate any other device capable of performing an algorithmic process. Since the introduction of the Turing machine, physics has influenced computation in many ways.