Project Abstracts for CS 667, CO 681, PH 767, AM 871 (Fall 2009)

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Nov 21, 2013 (3 years and 11 months ago)

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Project
Abstracts for

CS 667, CO 681, PH

767, AM 871

(Fall 2009)


This file will be updated as more abstracts are received. If I didn’t receive a recent email about your abstract, I
may have extracted it from an earlier email and in some cases lightly
edited it. If you sent me an abstract but I
haven’t included it, please accept my apologies and resend it.

December 9 AM

10:00
-
10:30am Achar, Varun “Quantum proofs for non
-
membership in subgroups”


10:35
-
11:05am Avram, Catalin
-
Alexandru “The secrets of qua
ntum walks”

The main goal of this work is to provide readers with an understanding of what quantum walks are, how they are
performed and what are some possible uses. We will explore the similarities and differences between quantum
walks and their classical

counterparts: random walks and Markov chains. Finally, brief descriptions of algorithmic
applications of quantum walks as well as open problems are provided.


11:10
-
11:40am Markes, Sonia “Categorical quantum information”


11:45
-
12:15pm Ududec, Cozmin “One
-
way quantum computation on cluster states”

We review a model of quantum computation which consists of entirely of sequences of adaptive one
-
qubit
measurements on an initial entangled state called a cluster state.


This ‘one
-
way’ model provides a different

conceptual framework from the circuit or gate model in which the theoretical and experimental aspects of
quantum computing can be studied.


We discuss the equivalence of the one
-
way model to the circuit model, and
give some examples of how standard gates
are implemented.


Finally, we outline some interesting features and
results of this approach which give new insights into quantum computation and its relationship to classical
computation.


December 9 PM

2:00
-
2:30pm Tse, Stephen
"

Error detection and secre
t
-
key reconciliation by public discussion
"


Alice sends Bob a secret key via a privacy channel which is imperfect in the sense that Bob may not receive
exactly what Alice sends. By using another channel with perfect authenticity but no privacy, they may de
tect
errors and reconcile their keys, at the risk of giving out information about the key. We show how clever protocols
can be used to minimize the amount of information leaked out.


2:35
-
3:05pm Graydon, Matthew

“Equiangular positive operator valued measur
es in quantum cryptography”


This talk will review equiangular positive operator valued measures (POVMs) in the form of Grassmann frames,
focussing on the special case of symmetric informationally complete (SIC) POVMs. Equiangular spherical code
quantum ke
y distribution (ESC
-
QKD) has advantages over protocols based on mutually unbiased bases (e.g. BB84
and six
-
state). I will discuss the application of ESCs in the QKD protocols proposed by Renes.

3:10
-
3:40pm Yu, Ben “Quantum money”


3:45
-
4:15pm Dang, Hoan “O
rthogonality and the game of distinguishing quantum states

N quantum states in d
-
dimensional Hilbert space can only be perfectly distinguished if they are orthogonal. A
natural suggestion is to use the success probability as a measure of orthogonality. We
will derive a bound for this
quantity and investigate a few special cases, including symmetric informationally
-
complete states.


December 15 AM

10:00
-
10:30am Jung, Yong Soo Darren “Physical quantum computers in reality”

The development of quantum informati
on theory has shown us that the quantum computers could solve many
problems which the classical computers couldn’t. However all of the benefits of quantum information theory can
be achievable only if the quantum computer is physically possible. In this pap
er we are going to look at the
important aspects of the physical quantum computers in terms of where we are, and what need to be done.


10:35
-
11:05am Guo, Krystal “Graph states and codes”


11:10
-
11:40am Kallin, Ann

“Topological quantum computing”


11:45
-
12
:15pm Holden, Tyler “
Quantum tomography



Quantum tomography is the theory for determining quantum objects using informationally complete
measurement bases in appropriate Hilbert spaces. Through consistent and controlled experimental approaches,
one can in
fer to arbitrary precision the characteristics of quantum states, quantum processes and even
measurement procedures. We will begin by examining the foundations of quantum state tomography, which has
important applications to qubit determination in quantum
information theory. Afterwards, we shall consider
ancilla and standard quantum process tomography.

December 15 PM

2:00
-
2:30pm Mullin, Natalie


Mutual
ly

u
nbiased
b
ases


In this talk I will give an overview of mutually unbiased bases and highlight several
applications of MUBs in
quantum information processing. In particular, I will describe the use of MUBs in secure quantum key exchange. I
will also discuss some algebraic methods for constructing mutually unbiased bases and briefly mention some
related open

problems.


2:35
-
3:05pm LeCompte, Nicholas “
Unitary
d
esigns


We discuss the concept of a un
itary design, finite subsets of
the unitary group that in a sense approx
imate the
entire group. Part of
the discussion is a brief description of
requisite mathematic
al tools to
understand them. We
also highlight a few application
s of these objects,
such as efficiently simulating random unitary matrices and
state

tomography.


3:10
-
3:40pm Pitkanen, David


Decoherence in quantum computing




I will talk about the error r
ates inherent in different approaches to quantum computing, how and when error
correction can be used to help this, and about decoherence free subspaces.


3:45
-
4:15pm Hoo, Jason Soo “Measurement
-
based quantum computation”


December 17 PM

2:00
-
2:30pm McConk
ey, Thomas


Optical
q
uantum
c
omputing


I will present an overview of optical quantum computing, such as the methodology and current models (such as
cluster state and KLM). I will further focus on a particular model and an algorithm .


2:35
-
3:05pm Paetznic
k, Adam


Simulation of
q
uantum
s
ystems


Simulation is an important tool in understanding the characteristics of quantum systems.


Unfortunately, the
number of (classical) computational resources required for exact simulation grows exponentially with the
size of
the quantum system.


Quantum computers, in principle, could simulate a variety quantum system with only a
polynomial number of resources.


I will discuss the methods simulation on a quantum computer, the types of
quantum systems that may be simulat
ed efficiently, and some known limitations.


3:10
-
3:40pm Deng, Chunqing


Quantum
algorithm for l
inear
s
ystems of
equations”

This algorithm computes an approximation of the expectation value of some operator associated with the
solutions of the linear equat
ions, which is exponentially faster than the best classical algorithm.


3:45
-
4:15pm Zhang, Yingjie “Accuracy Threshold for Quantum Computation”

With classical initial states, if a minimum gate accuracy can be achieved, a concatenation technique can be used

to reach any desired accuracy in quantum computing. The assumptions used here are more general than
stochastic error heuristic that many other work have used.

December 21 PM

2:00
-
2:30pm Gharibi, Mirojtaba


Quantum
f
ault
tolerant c
omputing
:

the
r
eason
q
uan
tum
c
omputers
a
re
r
ealizable in the
p
resence of
e
rrors



After the introduction of unbelievable power of quantum computers to the scientific community, many people
have been engaged in realizing that dream. One of the early barriers was the belief that due

to the high level of
error occurring in the quantum blocks, it is impossible to have large quantum computers. These errors are due to
uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical
operations. The si
mple idea behind that belief was if error is being occurred in every step of running a quantum
algorithm, then the error sums up in the output and makes it completely unreliable after a few steps. That is true;
in the case it is impossible to correct the e
rror in every step to prevent it from growing. Fortunately a number of
error correction techniques were discovered in late 90s which were categorized under the name of "Theory of
Quantum Fault Tolerant Computing". My presentation is dedicated to elaborate
on one of these early techniques
presented to the scientific community.


2:35
-
3:05pm Soukarev, Vladimir “Hidden subgroups for arbitrary groups”

The Hidden Subgroup Problem (or simply HSP) is stated as follows: Given a group G and a function f on G that is
promised to be strictly H
-
periodic for some subgroup H of G, find a generating set for H. Known classical
algorithms make polynomial number of calls in size of G (hence exponential in log of size of G) to the oracle. I will
present a quantum algorithm that

makes polynomial number of calls to the oracle in log of size of G. Abelian and
non
-
abelian cases will be considered separately.


3:10
-
3:40pm Pathak, Vinayak


Quantum
a
lgorithms for
m
iscellaneous
t
raditional
p
roblems



3:45
-
4:15pm Anzala
-
Yamajako, Alexand
re “
Quantum
o
ne
-
t
ime
p
ad


The
topic is the
quantum analog of the one
-
time pad for encrypting quantum data
, where 2n

key secret key bits
are necessary and sufficient to perfectly e
ncrypt n qubits.