March 3, 2005
Physics 681-481; CS 483: Discussion of #3
(with postscripts on the Schmidt decomposition theorem) 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
April 7, 2005
Physics 681-481; CS 483: Assignment #6 Searching for one of 4 items
(please hand in after the lecture, Thursday, April 21) We explore here Grovers algorithm when it is applied to identify one of only four items. This turns out to be a
April 21, 2005
Physics 681-481; CS 483: Discussion of #6
1. The probability that you get the marked item on the rst 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 f
March 3, 2005
Physics 681-481; CS 483: Assignment #4
(please hand in after the lecture, Thursday, March 17th) I. Probabilities for solving Simons problem. As described on pages 16-18 of Chapter 2, to estimate how many times a quantum computer has to
Last revised 4/30/05 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 c 2005, N. David Mermin II. Quantum Computation A. The general computational process We would like a suitably programmed quantum compu
February 3, 2005
Physics 681-481; CS 483: Assignment #2
(please hand in after the lecture, Thursday, February 17th) I. Constructing a spooky 2-qubit state Section A3 of the appendix to chapter 1 describes the strange properties of a pair of qubits i
Last revised 5/5/05 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 c 2005, N. David Mermin VI. Quantum Cryptography and Some Uses of Entanglement A. Quantum cryptography A decade before Shors discovery
Last revised 4/7/05 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 c 2005, N. David Mermin III. Breaking RSA Encryption with a Quantum Computer In Simons problem we are presented with a subroutine which
January 25, 2005
Physics 681-481; CS 483: Assignment #1
(please hand in after the lecture, Thursday, February 3) These assignments (which will appear every other week) have three purposes. They explore points not covered in the lectures or lecture n
Last revised 4/7/05 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 c 2005, N. David Mermin IV. Searching with a Quantum Computer Suppose you know that exactly one integer between 1 and N satises a certa
Last revised 2/14/05 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 c 2005, 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 4/7/05 LECTURE NOTES ON QUANTUM COMPUTATION Cornell University, Physics 481-681, CS 483; Spring, 2005 V. Quantum Error Correction. c 2004, N. David Mermin The discovery in 1995 of quantum error correction by Peter Shor and, independently
February 3, 2005
Physics 681-481; CS 483: Discussion of #1
I. Manipulating simple operators. (a) An algebraic way (ridiculously complicated, of course, since the result is obvious from the non-algebraic denition) to check that the square of the SWAP
February 17, 2005
Physics 681-481; CS 483: Assignment #3
(please hand in after the lecture, Thursday, March 3rd) I. Other aspects of Deutschs problem To solve Deutschs problem (Chapter 2, Section B) one must apply transformations to the output regis
March 17, 2004
Physics 681-481; CS 483: Discussion of #4
I. (a) According to Eq. (1) in Assignment #4, the probability of nding 2 linearly independent vectors (doing arithmetic modulo 2) among a random set of three 3-vectors of 0s and 1s orthogonal
March 17, 2005
Physics 681-481; CS 483: Assignment #5
(please hand in after the lecture, Thursday, April 7th, in three weeks)
The two questions that follow illustrate the mathematics of the nal (post-quantumcomputational) stage of Shors period ndin
April 21, 2005
Physics 681-481; CS 483: Assignment #7
(please hand in after the lecture, Thursday, May 5) This is the nal assignment. 1. Suppose the only kinds of errors that one had to worry about were one-qubit bit-ip (i.e. Xi ) errors. (a) Make a
April 8, 2004
Physics 681-481; CS 483: Discussion of #5
1. We know that r < 100 and that 11883/214 = 0.725280 . . . is within 1 214 < 2 of 1/r. My HP-20S calculator tells me that 11883/214 = 1+ 2+ 1+ 1+ 1+ 3+ 1+ 1+ 1 1 1 1 1 1 1 1 1 19 +
112 2 10
May 5, 2005
Physics 681-481; CS 483: Discussion of #7
1. (a) If only one-qubit bit-ip errors are allowed, then the general corruption of an n-qubit code word | is of the form
n
|d 1 +
i=1
|a i Xi | .
(1)
We need 2(n+1) dimensions to accomodate e