April 6, 2006
Physics 681-481; CS 483: Discussion of #5
1. We know that r < 100 and that 11490/214 = 0.7012939453 . . . is within 1 2-14 < 2 1 1 2 of j/r for integers j and r. 2 100 My ancient HP-20S calculator tells me that 1 11490/214 = (1) 1 1+ 1
April 20, 2006
Physics 681-481; CS 483: Discussion of #6
1. The probability that you get the marked item on the first attempt is 1 . The 4 1 probability that you get the marked item on the second attempt is also 4 : the probability, 1 3 4 , that you
March 2, 2006
Physics 681-481; CS 483: Assignment #4
(please hand in after the lecture, Thursday, March 16th) I. Probabilities for solving Simon's problem. As described on pages 16-18 of Chapter 2, to estimate how many times a quantum computer has t
March 16, 2006
Physics 681-481; CS 483: Assignment #5
(please hand in after the lecture, Thursday, April 6th, in three weeks)
The two questions that follow illustrate the mathematics of the final (post-quantumcomputational) stage of Shor's period f
April 6, 2006
Physics 681-481; CS 483: Assignment #6 Searching for one of 4 items
(please hand in after the lecture, Thursday, April 20) We explore here Grover's algorithm when it is applied to identify one of only four items. This turns out to be a
Last revised 3/28/06 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2006 c 2006, N. David Mermin III. Breaking RSA Encryption with a Quantum Computer: Shor's Factoring Algorithm In Simon's problem we are pre
Last revised 3/30/06 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 c 2006, N. David Mermin IV. Searching with a Quantum Computer Suppose you know that exactly one n-bit integer satisfies a certain cond
February 2, 2006
Physics 681-481; CS 483: Discussion of #1
I. Tensor products and positional notation. We represent the digits 5, 3, and 2 by 10-component column vectors c, b, and a, given by 0 0 0 0 0 0 1 0 0 0 c = , b = , 0 1
March 16, 2006
Physics 681-481; CS 483: Discussion of #4
I. (a) According to Eq. (1) in Assignment #4, the probability of finding 2 linearly independent vectors (doing arithmetic modulo 2) among a random set of four 3-vectors of 0's and 1's orthogon
Last revised 1/31/06 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2006 c 2006, N. David Mermin I. Fundamental Properties of Cbits and Qbits It is tempting to say that a quantum computer is one whose operat
Last revised 5/4/06 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 c 2005, N. David Mermin VI. Quantum cryptography and some simple uses of entanglement Most of the examples that follow make use of a ve
March 2, 2006
Physics 681-481; CS 483: Discussion of #3
I. (a) For each of the four possibilities for the unknown function f , the corresponding forms for the state | = |0 |f (0) + |1 |f (1) (1) are | | | |
00
= = = =
1 2 1 2 1 2 1 2
|0 + |1
February 16, 2006
Physics 681-481; CS 483: Assignment #3
(please hand in after the lecture, Thursday, March 2nd) I. Other aspects of Deutsch's problem Suppose one tried to solve Deutsch's problem, not by the clever trick used in Chapter 2, Section B
February 2, 2006
Physics 681-481; CS 483: Assignment #2
(please hand in after the lecture, Thursday, February 16th) I. Non-spooky construction of a spooky 2-Qbit state Section A4 of the appendix to chapter 1 describes the strange properties of a pai
January 24, 2006
Physics 681-481; CS 483: Assignment #1
(please hand in after the lecture, Thursday, February 2) These assignments (which will appear every other week) have three purposes. They explore points not covered in the lectures or lecture n
April 20, 2006
Physics 681-481; CS 483: Assignment #7
(please hand in after the lecture, Thursday, May 4) This is the final assignment. 1. Suppose the only kinds of errors one had to worry about were bit-flip errors, but one wanted to take into acco
Last revised 4/5/06 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2006 c 2006, N. David Mermin II. Quantum Computation: General features and some simple examples A. The general computational process We woul
Last revised 5/3/06 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2006 V. Quantum Error Correction. c 2006, N. David Mermin Correcting errors might sound like a dreary practical problem, of little aesthetic