# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

1 Page

### Homework3

Course: ECE 227, Fall 2009
School: Duke
Rating:

Word Count: 180

#### Document Preview

Quantum ECE227/PHY272 Information Science Homework #3 Due in Class 2/25/2009 1. Unitarity of Quantum Fourier Transform Give a direct proof that the linear transformation that defines the quantum Fourier transform j 1 N e k =0 N 1 2 ijk N k is unitary. (Textbook Exercise 5.1) 2. Inverse Quantum Fourier Transform Give a quantum circuit to perform the inverse quantum Fourier transform. (Textbook Exercise 5.5)...

Register Now

#### Unformatted Document Excerpt

Coursehero >> North Carolina >> Duke >> ECE 227

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Quantum ECE227/PHY272 Information Science Homework #3 Due in Class 2/25/2009 1. Unitarity of Quantum Fourier Transform Give a direct proof that the linear transformation that defines the quantum Fourier transform j 1 N e k =0 N 1 2 ijk N k is unitary. (Textbook Exercise 5.1) 2. Inverse Quantum Fourier Transform Give a quantum circuit to perform the inverse quantum Fourier transform. (Textbook Exercise 5.5) 3. Alternative Unitary Transformation for Quantum Order Finding The quantum state produced in the order-finding algorithm, before the inverse Fourier is transform, = j U 1 = j x j mod N , j j =0 j =0 2t 1 2t 1 if we initialize the second register as 1 . (a) Show that the same state is obtained if we replace Uj with a different unitary transform V, which computes V j k = j k + x j mod N , and start the second register in the state 0 . (b) Show how to construct V using O(L3) gate...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Duke - ECE - 227
Quantum Error Correction1. 2. 3. 4. 5. Three Qubit Bit Flip and Phase Flip Codes The Shor Code Theory of Quantum Error Correction Calderbank-Shor-Steane (CSS) Codes Quantum Circuit for Encoding, Decoding and CorrectionJungsang Kim Spring 2009Qua
Duke - ECE - 227
Introduction to Computer Science1. 2. 3. 4. Turing Machine Model of Computation Circuit Model of Computation Resources in Computational Problems Energy and Reversibility in ComputationJungsang Kim Spring 2009Quantum Information Science ECE @ Duk
Duke - ECE - 227
Classical Error-Correcting Codes1. 2. 3. 4. 5. Redundancy and Error Correction Triple Modular Redundancy (TMR) Linear Codes Hamming Code The Dual CodeJungsang Kim Spring 2009Quantum Information Science ECE @ Duke UniversityRedundancy and Error
Duke - ECE - 227
Quantum Circuits1. 2. 3. 4. 5. Single Qubit Operations Controlled Operations Quantum Measurements Universal Quantum Gates Simulation of Quantum SystemsJungsang Kim Spring 2009Quantum Information Science ECE @ Duke UniversitySingle Qubit Operat
UCSB - ECE - 227
UCSB - ECE - 227
UCSB - ECE - 227
UCSB - ECE - 227
Boise State - CS - 354
Computer Science 354Programming Languages3 semester credits Spring 2007 TTh 9:15-10:30 in MEC 307PrerequisitesCS 225, Introduction to Computer Science II, or permission of instructor. Students entering this course are expected to possess a mode
Boise State - CS - 354
%!PS-Adobe-2.0 %Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %Title: handout.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 595 842 %DocumentFonts: CMBX10 CMBX12 CMR10 CMTI10 CMTT10 CMSY10 %DocumentPaperSizes: a4 %EndComments %DVIP
UCSB - ECE - 228
University of California, Santa Barbara Department of ECEWinter 2008ECE228B Fiber Optic Components and Systems Homework #1Problem 1: Consider a semiconductor material exposed to an impulse of light at t=0 that generates N electron-hole pairs bet
Middlebury - ENGL - 0215
Jessica Clayton May 16, 2006 Natures Meanings Professor Don Mitchell Final ExamHonor Code: I have neither given nor received any unauthorized aid on this exam:Part I1) The Wilderness World of John Muir Edited by Edwin Teale 2) Letters- Crevecoeur
Stanford - ENERGY - 281
Jim Lambers ENERGY 281 Spring Quarter 2007-08 Lecture 3 Notes These notes are based on Rosalind Archers PE281 lecture notes, with some revisions by Jim Lambers.1IntroductionThe Fourier transform is an integral transform. When viewed in the cont
University of Texas - ISCHOOL - 34389
License granted by Amy Armstrong (aearmst@ischool.utexas.edu) on 2008-04-11T19:05:17Z (GMT):The submitter grants to the repository all rights required to carry out preservation activities pursuant to prior agreement between donor and repository.
University of Texas - ISCHOOL - 3221
License granted by Amy Baker (amy.e.baker@gmail.com) on 2005-05-11T20:29:39Z (GMT):NOTE: PLACE YOUR OWN LICENSE HEREThis sample license is provided for informational purposes only.NON-EXCLUSIVE DISTRIBUTION LICENSEBy signing and submitting thi
Stanford - PUBS - 6500
SLACPUB6597 August 1994 (E) A Measurement of Quark and Gluon Jet Dierences at the Z 0 Resonance THE SLD COLLABORATION represented by Yoshihito Iwasaki Department of Physics, Tohoku University Sendai, 980-77, JapanPresented at the Meeting of the Ame
Stanford - PUBS - 13000
April 2008BABAR-PUB-08/011 SLAC-PUB-13197 arXiv:0804.2422 [hep-ex]Observation of B + + and search for B 0 Decays to , 0 , 0 , and 0B. Aubert,1 M. Bona,1 Y. Karyotakis,1 J. P. Lees,1 V. Poireau,1 E. Prencipe,1 X. Prudent,1 V. Tisserand,1 J
Stanford - PUBS - 7500
Properties of Z 0 ! b Events bgN. Oishi Nagoya University Chikusa-ku, Nagoya 464 Japan Representing The SLD Collaboration Stanford Linear Accelerator Center Stanford University, Stanford, CA94309SLAC PUB 7522 May 1997AbstractWe present studies
Stanford - PUBS - 8500
SLAC PUB 8687 August 2000Production of , K, p and p in Quark, Antiquark and Gluon JetsHyejoo Kang Rutgers University, Piscataway, NJ 08854 Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309AbstractWe present measuremen
Washington - PHYS - 2278
HW XIn[117]:= In[118]:= Out[118]= VectorAnalysis`SetCoordinates Cartesian x, y, z V x ^ 2, y ^ 2, z ^ 2 x 2 , y 2 , z 2 Cartesian x, y, z Ex 6.7:5In[119]:= Out[119]=Take the Div and the CurlIn[120]:= Out[120]=Div V 2x2y2zandIn[12
Washington - ENGLISH - 281
The Atmospheric Boundary Layer Alex K Chen English 281 0534813 The earth, where humans and other living organisms survive and thrive, is surrounded with a unique atmosphere that makes life possible and secure. It is composed of five layers, the lowes
Western Kentucky University - CS - 543
CS 543 Computer Information Systems Design Spring 2008Instructor: Office: Office Hours: Phone: Email: Text: Dr. Huanjing Wang TCCW 112 MWF 8:00-9:00, 10:10-11:30, other times by e_mail appointment 270-745-2672 huanjing.wang@wku.edu Database Manageme
Western Kentucky University - CS - 543
CS 543: Computer Information Systems DesignIntroduction Dr. Huanjing WangJanuary 23, 2008 CS 543 Lecture 1 1Outline Get to know each other Course information Syllabus DB foundationsJanuary 23, 2008CS 543 Lecture 12Myself Huanjing Wan
Western Kentucky University - CS - 543
CS 543: Computer Information Systems DesignOverview of Storage and IndexingDr. Huanjing WangSlides Courtesy of R. Ramakrishnan and J. Gehrke1Motivation DBMS stores vast quantities of data Data is stored on external storage devices and fetche
Western Kentucky University - CS - 543
CS 543: Computer Information Systems DesignStoring Data: Disks and Files Chapter 9Dr. Huanjing WangSlides Courtesy of R. Ramakrishnan and J. Gehrke1Disks and Files DBMS stores information on (hard) disks. This has major implications for DBMS
Western Kentucky University - CS - 543
CS 543: Computer Information Systems DesignTree-Structured Indexing Chapter 10Dr. Huanjing WangSlides Courtesy of R. Ramakrishnan and J. Gehrke1Introduction As for any index, 3 alternatives for data entries k*: Data record with key value k &lt;
Western Kentucky University - CS - 543
CS 543: Computer Information Systems DesignHash-based Indexing Chapter 11Dr. Huanjing WangSlides Courtesy of R. Ramakrishnan and J. Gehrke1Introduction As for any index, 3 alternatives for data entries k*: Data record with key value k &lt;k, ri
Western Kentucky University - CS - 543
CS 543: Computer Information Systems DesignOverview of Transaction Management Chapter 16Dr. Huanjing WangSlides Courtesy of R. Ramakrishnan and J. Gehrke1Transactions Concurrent execution of user programs is essential for good DBMS performance
Western Kentucky University - CS - 543
Direction: The following questions are based on the CAP database. Formulate the following queries in SQL. 1). Get customer identifiers and names for customers in Bowling Green.2). Get customer identifiers for customers who have ordered at least twi
Washington - ATMS - 212
ATM S 212: Air Pollution Autumn 2008 Homework 4 Assignment will be collected at the beginning of class on Thursday, October 30, 2008. Name_ 1. Briefly (one sentence each) describe 5 reasons we care about aerosol particles. [10 points]2. What is the
UConn - MATH - 1131
Name:Quiz 1 Math 1131Q It is not enough to have a good mind; the main thing is to use it well. Rene Descartes Let f (x) = 1 x2 1 and g (x) = x . Find1. Find (f g )(x) (3 points )2. Find (g f )(x) (3 points )3. Find the domain of (f g )(x
UConn - MATH - 1131
Name:Quiz 1 Math 1131Q It is not enough to have a good mind; the main thing is to use it well. Rene Descartes Let f (x) = 1 x2 1 and g (x) = x . Find1. Find (f g )(x) (3 points ) (f g )(x) = f (g (x) 1 =f x = = 2. Find (g f )(x) (3 points )
UConn - MATH - 1131
Name: Quiz 2 Math 1131Q Section 005Date:Pure mathematics is the worlds best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. Its free. It can be played anywhere - Archimedes did it in a bathtub.
UConn - MATH - 1131
Name: Quiz 2 Math 1131Q Section 005Date:Pure mathematics is the worlds best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. Its free. It can be played anywhere - Archimedes did it in a bathtub.
UConn - MATH - 1131
Name: Quiz 3 Math 1131Q Section 005Date:Physics is becoming too dicult for the physicists. David Hilbert 1. Let f (x) = 4x2 2x + 3. Using the limit denition of instantaneous rate of change nd f (1)2. Find the horizontal asymptotes of f (x) =
UConn - MATH - 1131
Name: Quiz 3 Math 1131Q Section 005Date:Physics is becoming too dicult for the physicists. David Hilbert 1. Let f (x) = 4x2 2x + 3. Using the limit denition of instantaneous rate of change nd f (1)f (1)= = = = = = =f (1 + h) f (1) 5 4(1 +
UConn - MATH - 1131
Name: Quiz 4 Math 1131Q Section 005Date:The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. Aristotle 1. Let y = x2 tan(x). Finddy dx .2. Let y =ex . Find csc(x)
UConn - MATH - 1131
Name: Quiz 4 Math 1131Q Section 005Date:The mathematical sciences particularly exhibit order, symmetry, and limitation; and these are the greatest forms of the beautiful. Aristotle 1. Let y = x2 tan(x). Finddy dx .dy dxd2 [x tan(x)] dx d2 d
UConn - MATH - 1131
Name: Quiz 5 Math 1131Q Section 005Date:Geometry is not true, it is advantageous. Henri Poincar e 1. Let y = 23 . Find y . (5 pts)x22. Let x2/3 + y 2/3 = 4. Finddy dx .(5 pts)
UConn - MATH - 1131
Name: Quiz 5 Math 1131Q Section 005Date:Geometry is not true, it is advantageous. Henri Poincar e 1. Let y = 23 . Find y . (5 pts) Letting f (x) = 2x , g (x) = 3x , and h(x) = x2 , then y = = = 2. Let x2/3 + y 2/3 = 4. Finddy dx .x2f (g (h(x)
UConn - MATH - 1131
Name: Quiz 6 Math 1131Q Section 005Date:Logic is the anatomy of thought. John Locke 1. Let y = log2 (x2x ). Find y .22. Let y = (tan(x) x . Find y .1
UConn - MATH - 1131
Name: Quiz 6 Math 1131Q Section 005Date:Logic is the anatomy of thought. John Locke 1. Let y = log2 (x2x ). Find y . log2 (x2x ) = log2 (x) + log2 (2x ) = log2 (x) + x2 log2 (2) = log2 (x) + x22 2 22 d [log2 (x2x )] dx= =d [log2 (x) + x2 ]
UConn - MATH - 1131
Practice Exam 2 Name:Math 1131 Section:Spring 2009IMPORTANT: All answers must include either supporting work or an explanation of your reasoning. These elements are considered part of the answer and will be graded. 1. (15 pts) For each part, i
UConn - MATH - 1131
This is NOT everything you need to know. It is just a consolidation of some of the denitions, formulas, and theorems that you will need. Chapter 2 Denition: We say the limit of f (x) as x approaches a is equal to L, orxalim f (x) = L,if and only
RIT - DAHLGREN - 20021
Jeremy Dahlgren jad0883@cs.rit.edu Fall 2002 Independent Study Summary ReportBackground and Motivation: The purpose of this independent study is to develop products for many-to-manyinvocation, or M2MI. M2MI is an object oriented paradigm used to dev
St. Francis IL - CHEM - 232
Chemistry 232 Kinetic Molecular Theory of GasesG. Marangoni 1. 2. Due: January 31, 2000.Calculate the most probable speed, the mean speed, and the root mean square speed of nitrogen molecules and helium atoms at 298 K. Assume that 0.300 mol of N2
St. Francis IL - CHEM - 232
Chemistry 232 Kinetic Molecular Theory of GasesG. Marangoni Due: January 25, 2001.1. By taking the first derivative of the Maxwell speed distribution equation (eq. 22, p. 26 Atkins), find the velocities that pertain to the maxima and minima of the
St. Francis IL - CHEM - 232
Chemistry 232 Practice pH and Electrochemistry Problems1. Calculate the pH of the following solutions a) 0.100 molal HCl b) 0.0100 molal NaOH c) 0.0050 M Ba(OH)2 d) 0.100 molal benzoic acid (Ka = 6.5 x 10-5) e) A solution composed of 0.100 mole of a
St. Francis IL - CHEM - 232
Transport Phenomena (Chapter 17 in Short Text Chapter 35 in Full Text)Question 2a)b) The ratio of collisional cross sections is given by:Question 6a) The energy flux is given byThe loss in energy is equal to the flux times the area (A) thro
St. Francis IL - CHEM - 232
Elementary Chemical Kinetics (Chapter 18 in Short Text Chapter 36 in Full Text)Question 2a) The rate is given asR1 d PC4 H8 RT dtP t01 d PC2 H4 2RT dtPC2H4 . Where P 0 is the initial tThe pressure at time t is given as Pt4 8 2 4PC4H8
St. Francis IL - CHEM - 232
Chemistry 232 pH Calculations and Kinetic Molecular Theory of GasesG. Marangoni 1. Due: Wednesday, June 17, 2009.Calculate the pH of the following solutions a) 0.100 molal HCl b) 0.100 molal NaOH c) 0.100 molal benzoic acid (Ka = 6.5 x 10-5) d) A
St. Francis IL - CHEM - 232
TABLE 1 Prices for Detailed Testing Requirements for Biodiesel (B100) According to ASTM D67511Property Metals (Calcium Magnesium, Phosphorus, Sodium Potassium) Flash point (closed cup) Alcohol control - Flash point Water and sediment Kinematic visc
Oakland University - L - 552
Heaven Audiobook(unabridged);Fiction Cassettetape:2soundcassettes(2.75hrs.) CompactDisc:3sounddiscs(2.75hrs.) 2000,PrinceFrederick,MD:RecordedBooks Audience:MiddleSchoolYoungAdult Narrator:AndreaJohnson ISBN:0788745638(audiocassette) ISBN:1402519699
University of Florida - CAP - 4410
Programming in Java Advanced ImagingRelease 1.0.1 November 1999JavaSoft A Sun Microsystems, Inc. Business 901 San Antonio Road Palo Alto, CA 94303 USA 415 960-1300 fax 415 969-9131 1999 Sun Microsystems, Inc. 901 San Antonio Road, Palo Alto, Ca
University of Florida - CAP - 4410
The Discrete Fourier TransformThe discrete-time Fourier transform (DTFT) of a sequence is a continuous function of , and repeats with period 2 . In practice we usually want to obtain the Fourier components using digital computation, and can only eva
University of Florida - CAP - 4410
38 @u7 1 t 2rEW 2D t 1S )A D 7S b 3A7 I W x XU yS 7 4 8 Ex6Da97 1 t XU W3F4D8 xPHGau7 XU 8) W 3F4D8 QxPcHxa97 XU W g73 W Epwv XU 38 @u7 1 t sH 1S ) p97 r@GUq ph)Rfe Rdcba`YECXVTSRQPH GECB@97 6153 20( i g3 D3 4 8 3S 7 A W U 43 I F D 7 A3 8 4 1
UCSB - ECE - 235
Department of Electrical &amp; Computer Engineering University of California, Santa BarbaraECE 235 Fall 2007 Shynk H.O. #1ECE 235 COURSE INFORMATIONTitle: Stochastic Processes in Engineering Lectures: Tuesday, Thursday 6:30 8:30 p.m., Webb Hall 11
UCSB - ECE - 235
Department of Electrical &amp; Computer Engineering University of California, Santa BarbaraECE 235 Fall 2007 Shynk H.O. #4HOMEWORK #2 Due Friday, October 19, 2007 (5:00 p.m.) (new due date)(revised)Reading: Read Chapters 3 and 4 Problems: 1. Proble
UCSB - ECE - 235
Department of Electrical &amp; Computer Engineering University of California, Santa BarbaraECE 235 Fall 2007 Shynk H.O. #16HOMEWORK #6 Due Friday, November 30, 2007 (5:00 p.m.)Reading: Read Chapter 8 Problems: 1. Problem 6.46 2. Problem 7.3 3. Prob
UCSB - ECE - 235
Department of Electrical &amp; Computer Engineering University of California, Santa BarbaraECE 235 Fall 2007 Shynk H.O. #8HOMEWORK #4 Due Friday, November 2, 2007 (5:00 p.m.)Midterm Exam: Thursday, November 8, 6:30 8:00 p.m. (open book, open notes
UCSB - ECE - 235
Department of Electrical &amp; Computer Engineering University of California, Santa BarbaraECE 235 Fall 2007 Shynk H.O. #2ECE 235: STOCHASTIC PROCESSES IN ENGINEERING TENTATIVE COURSE OUTLINE1. Events and algebras. Review of probability theory, dis