ASSIGNMENT 1: Solutions
CO 481/CS 467/PHYS 467 (Winter 2014)
1. Universality of reversible logic gates.
(a) [3 points] The cccnot (triple-controlled not) gate is a four-bit reversible gate that ips
its fourth bit if and only if the rst three bits are all
ASSIGNMENT 2: Solutions
CO 481/CS 467/PHYS 467 (Winter 2014)
1. Distinguishing states with local operations and classical communication.
Suppose Alice and Bob are each given one qubit of a two-qubit state that is promised to be
either | or | , for some xe
MIDTERM EXAM: Solutions
CO 481/CS 467/PHYS 467 (Winter 2014)
1. Partial measurement.
Suppose we measure the rst qubit of the state
1
(|00 |01 + i|10 )
3
in the basis cfw_|+ , | , where | =
1
(|0
2
|1 ).
(a) [2 points] What is the probability of getting
MIDTERM EXAM
CO 481/CS 467/PHYS 467 (Winter 2010)
1. Controlled-not gate.
(a) [1 point] Write the cnot gate using Dirac notation in the computational basis.
(b) [1 point] What are the eigenvalues of the cnot gate?
(c) [2 points] Give an orthonormal basis
ASSIGNMENT 2
CO 481/CS 467/PHYS 467 (Winter 2014)
Due in class on Tuesday, February 4.
1. Distinguishing states with local operations and classical communication.
Suppose Alice and Bob are each given one qubit of a two-qubit state that is promised to be
e
ASSIGNMENT 3: Solutions
CO 481/CS 467/PHYS 467 (Winter 2014)
1. Swap test.
(a) [3 points] Let | and | be arbitrary single-qubit states (not necessarily computational
basis states), and let swap denote the 2-qubit gate that swaps its input qubits (i.e.,
sw
Introduction to
Quantum
Information
Processing
CS467 C&O481 PHYS467
Lecture 6
Michele Mosca [email protected]
Lecture 5
1
Spectral decomposition
Often it is convenient to rewrite the density matrix as a mixture of its
eigenvectors.
Recall that eigenvect
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca
lecture 4
1
Overview
Global Phase
Some circuit notation for measurements
Holevos theorem
Bell Basis and Superdense Coding
Implementing Bell measurements
Postulates of Quantum
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca [email protected]
Lecture 10
1
Deutsch-Jozsa problem
Suppose
f : cfw_0,1n cfw_0,1 with the promise that
f is either constant or balanced.
Decide if f is constant or balance
CO481/CS467/PHYS467 Winter 2011 Midterm
(will constitute 15% of the nal grade)
01
10
The Pauli operators are X =
0 i
i0
,Y =
,Z=
10
0 1
.
1. 1 marks
What is the Bloch vector of the following state?
=
1
2
1
22
1
22
1
22
1
1
+ 22
2
2. 2 mark
Prove that the
ASSIGNMENT 3
CO 481/CS 467/PHYS 467 (Winter 2014)
Due in class on Tuesday, February 25.
(Please remember that your project proposal is due by February 27.)
1. Swap test.
(a) [3 points] Let | and | be arbitrary single-qubit states (not necessarily computat
ASSIGNMENT 1
CO 481/CS 467/PHYS 467 (Winter 2014)
Due in class on Tuesday, January 21.
1. Universality of reversible logic gates.
(a) [3 points] The cccnot (triple-controlled not) gate is a four-bit reversible gate that ips
its fourth bit if and only if t
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca [email protected]
Lecture 8
The art of quantum algorithmics is to
choreograph constructive interference
on desirable outcomes and destructive
interference on undesirable ou
Introduction to
Quantum
Information
Processing
CS467 C&O481 PHYS467
Lecture 7
Michele Mosca [email protected]
Lecture 5
1
Bit Commitment
https:/cs.uwaterloo.ca/~watrous/CPSC519/LectureNotes/19.pdf
Alice has a bit b she wishes to commit to Bob
But Alice
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca [email protected]
lecture 1
1
Course Web Page
Course Web page at http:/learn.uwaterloo.ca
Textbook: An Introduction to Quantum Computing, by Kaye et al.
Reference text:
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca [email protected]
Lecture 8
Bells Inequality
2
Motivation for Bells inequality
In lecture one we saw an experiment that gives evidence for
quantum mechanics
We can try to c
From quantum physics to a
new kind of computer
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca [email protected]
lecture 2
Classical bits (section 1.4 of text)
Probabilistic bits (section 1.4 of text)
Classical Circuit M
ASSIGNMENT 4
CO 481/CS 467/PHYS 467 (Winter 2014)
Due in class on Tuesday, March 11.
1. Finding a hidden slope. Let p be a prime number. Suppose you are given a black-box function
f : cfw_0, 1, . . . , p 1 cfw_0, 1, . . . , p 1 cfw_0, 1, . . . , p 1 such