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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 Oct 1, 2005• 0 citations
Publisher

Abstract

Almost all computational tasks in the modem 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
10.1142/9789812701633_0011

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Almost all computational tasks in the modem 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.
The tutorial introduces quantum computing to a general audience. It begins with the concept of qubit and its representation, followed by 1-qubit quantum gates and qubit measurement. It will then move on to 2-qubit states, entanglement, and 2-qubit gates. Switching gears, the tutorial will discuss quantum Fourier transforms, unitary transforms, and quantum arithmetic. Finally, we will go through a simple quantum algorithm and discuss solid-state implementations of networks of qubits, highlighting the challenges for reading and controlling them. We conclude with future perspectives.
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.
In this tutorial we review basic ideas of quantum computing, from quantum bits and state entanglement to quantum gates and quantum networks [1]. In addition, we give an overview over possible physical implementations of quantum gates[2-6], with emphasis on quantum optical systems: this includes ion traps [2,3], and cavity QED in the optical and microwave domain [4-6], Fundamental problems of building quantum computers, in particular the decoherence problem, and error correction schemes for quantum memory elements [7] and quantum gates [8] will be discussed. We conclude with a critical evaluation what should be expected from quantum computing ideas in terms of applications in physics (quantum optics) and mathematics within the nest few years.