Quantum Computing

By Kimble, H.

Book Id: WPLBN0000177477
Format Type: PDF eBook
File Size: 4.3 MB
Reproduction Date: 2008

Title:	Quantum Computing
Author:	Kimble, H.
Volume:
Language:	English
Subject:	Government publications, Legislation., Government Printing Office (U.S.)
Collections:	Government Library Collection
Historic Publication Date:
Publisher:	Government Printing Office


Citation APA MLA Chicago Kimble, H. (n.d.). Quantum Computing. Retrieved from http://www.gutenberg.us/

Excerpt
Excerpt: As part of the 1995 Summer Study, the JASONS undertook an assessment of the field of quantum computing. The current flurry of activity in this field is fueled by the discovery in 1994 by P. Shor of an efficient quantum algorithm for finding the prime factors of large numbers. Because no classical algorithm of comparable efficiency is known, the supposed fundamental difficulty of the factoring problem has ensured the security of the RSA public key cryptosystem, which Shor's algorithm now brings into question. However, beyond the domain of cryptology, the marriage of quantum mechanics and information science represents a potentially profound development with possibly far reaching implications.

Table of Contents
Contents EXECUTIVE SUMMARY 1 1 INTRODUCTION 7 1.1 Study Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 What is a Quantum Computer? . . . . . . . . . . . . . . . . . 11 1.3 Quantum Factoring . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Quantifying the Essential Character of Quantum Computation 14 2 POSSIBILITIES BEYOND SHOR'S ALGORITHMS 17 2.1 Level Sets; Solutions of Homogeneous Linear Equations . . . . 17 2.2 Simulating Quantum Systems - The Hubbard Model . . . . . 22 2.3 Quantum Computers as Many-body Systems . . . . . . . . . . 26 2.4 Simulating quantum physics on a quantum computer . . . . . 37 2.5 Cold Baths and Optimization . . . . . . . . . . . . . . . . . . 45 3 QUANTUM NETWORKS 49 3.1 Circuits for Quantum Computation . . . . . . . . . . . . . . . 49 3.1.1 Qubit and State Representation . . . . . . . . . . . . . 50 3.2 Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . 53 3.2.2 Clear Operation . . . . . . . . . . . . . . . . . . . . . . 53 3.3 Gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.3.1 Controlled-Not . . . . . . . . . . . . . . . . . . . . . . 54 3.3.2 Controlled-Controlled-Not Operator . . . . . . . . . . . 55 3.3.3 Rotate Operation . . . . . . . . . . . . . . . . . . . . . 56 3.3.4 Condi tional-Complex Rotation . . . . . . . . . . . . . . 58 3.3.5 Measure . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3.6 Set of Operators . . . . . . . . . . . . . . . . . . . . . 60 3.4 Basic Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.1 Full Adder . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.2 Multi-bit Full Adder . . . . . . . . . . . . . . . . . . . 61 3.4.3 Multiplexor and Related Circuits . . . . . . . . . . . . 62 3.4.4 Multiplier . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.5 Subtractor . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.4.6 Adder for Recovering Scratch Space . . . . . . . . . . . 67